Assignments and Exercises for Students for Kiess and Green Statistical Concepts for the Behavioral Sciences Fourth Edition prepared by Bonnie A. Green East Stroudsburg State University Joshua D. Sandry New Mexico State University Allyn & Bacon Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo
Transcript
Assignments and Exercises for Students
for
Kiess and Green
Statistical Concepts for the Behavioral Sciences
Fourth Edition
prepared by
Bonnie A. Green
East Stroudsburg State University
Joshua D. Sandry New Mexico State University
Allyn & Bacon
Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto
Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo
Making Sense of Variability: An Introduction to Statistics Note to the instructor. In our general discussion of approaches to teaching statistics, we suggested that students often approach introductory statistics with both concern and apprehension. They may doubt their own mathematical skills and may also be skeptical of the potential value of the course to them. How should an instructor deal with these apprehensions and concerns? As we discussed, one approach is to acknowledge these issues in the first class meeting. The following exercises offer several options to aid students in discussing their concerns about the course.
Assignments 1.1 to 1.4 deal directly with helping students to focus on their behaviors or attitudes that may help or hinder their progress in behavioral statistics. It is not our intention that students complete all of these assignments, and depending on the population from which your students come, there may be no need for such assignments. However, if you have ever experienced students behaving in a destructive fashion (e.g., not coming to class, not being intellectually engaged during class, not completing all assignments), then you may find that by helping students to focus on their attitudes and behaviors, and helping them to plan how they will approach this class, their comfort level and performance may improve. Assignment 1.1 Coupled with the research discussed in the textbook about the benefits of adopting an incremental view of intelligence, helping students to think about their attitudes with regard to this class may assist them in adopting more adaptive behaviors. Assignment 1.1 helps students to face their hopes and fears related to this class, with the expectation that this assignment will help students think more candidly about their attitudes, particularly the ones that may be interfering with their success in this class. Assignment 1.2 This activity is to help students focus on successful and unsuccessful behavior. This assignment can also be used to begin introducing the concept of individual differences without entering into terms like sampling error or error due to individual differences. Moreover, by helping students to find general trends in behaviors, you can help them to see that they are finding consistency in the seeming randomness. Sure, many of us know the person who spent a great deal of time in college in an “altered” state and still found a way to graduate with honors. However, such behavior could be considered an “outlier” and atypical of academic success. As such, this assignment can be used to both get students to look at productive behaviors as well as to begin to understand concepts like outliers and sampling error. For this assignment to be successful, it is best coupled with an in-class discussion so that the professor may begin to introduce statistical concepts and help students to focus on ideas of typical and atypical behaviors. Assignment 1.3 This assignment is similar to Assignment 1.2 in that it helps students to focus upon behavior that will aid or hinder their performance in behavioral statistics. Of the two activities, this activity is better as a homework assignment when little or no in-class discussion will be taking place. Assignment 1.4 The purpose of this assignment is to have students think about how they plan on behaving to assure maximum success in the class. All too often, students wait until a couple of days before an exam to begin to think about how to be successful in a particularly class. One way to assist students in achieving better course goals is through proper planning. The assignment requires students to set a log-term goal of a grade for the course and then to identify behaviors that will help to achieve that goal. This assignment works best when followed up with professor feedback, either in the form of written comments or during class discussion.
Chapter 1. Making Sense of Variability: An Introduction to Statistics
Assignment 1.5 This assignment requires students to identify and define the four uses of statistics discussed in the textbook. In addition, students are asked to formulate an example of each use of statistics. This assignment can be used as a basis to help students better focus on material covered in the textbook. It is an excellent assignment prior to covering the material in class to help encourage students to read and think about material before coming to class. It can be used in class as a partner or small group assignment. It could also be used as an in or out-of- class assignment, helping students to focus on the four uses of statistics discussed in the book. Finally, this assignment can also be used as a test question. Assignment 1.6 This assignment is a set of 15 multiple choice questions that can be used as a homework assignment, in-class assignment, or quiz. The questions are a varied sample of the information covered in this chapter. Answers are provided on the page following the assignment.
Chapter 1. Making Sense of Variability: An Introduction to Statistics
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 1.1 As you begin learning about behavioral statistics, it is important that you think about your own attitudes regarding this class. Please think about what grade you hope to obtain in this class and write it in the table below. Now think about what grade you fear you might obtain and write it in the table below. Finally, think about the grade you expect to obtain and write it in the table below. For each situation, write a statement explaining why you feel this way.
Situation Grade Explanation
Hope
Fear
Expectation
Chapter 1. Making Sense of Variability: An Introduction to Statistics
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 1.2 We have all seen students adopt behaviors that are conducive to being academically successful versus. students who adopt behaviors that are incompatible with academic success. Please think of a few people who are academically successful. What kind of behaviors do they exhibit, particularly with regard to attending class, completing assignments, and being intellectually engaged? Now think of a few people who are not academically successful. How do their behaviors compare with students who are academically successful? Please complete the table below.
Behaviors of Academically Successful Students
Behaviors of Academically Unsuccessful Students
Chapter 1. Making Sense of Variability: An Introduction to Statistics
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 1.3 Here is a list of behaviors that instructors often notice among students studying statistics. Please check the behaviors that you believe lead to success in a course.
• Never bring a calculator to class
• Complete homework assignments until a sense of understanding is achieved
• Fully complete all homework assignments
• Avoid the professor, even though she has put notes on your test to see her
• Cram for the exam the night before
• Complete the homework assignment when it is due
• Do not get enough sleep the night before an exam
• Following each class, look over your notes and test your understanding and
knowledge of symbols
• Never go more than one or days without at least completing a quick self test
• Come to class with questions, and ask them when appropriate
• Do not buy or use the textbook
• Sell back the textbook two weeks before finals begin
• Do not take notes
• Come to class late
Now go back and identify any behaviors that may be characteristic of you. Do you think you will need to change any of your behaviors to be successful in this class?
Chapter 1. Making Sense of Variability: An Introduction to Statistics
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 1.4 Becoming aware of your own attitudes and the behaviors that accompany them can help you to adopt attitudes and behaviors that will better assure your success in a class. Focus on the grade you hope to obtain in this class while you answer the next two questions. 1. What are some behaviors that you can exhibit that will increase the likelihood of
obtaining the grade you hope for? 2. Set a goal for your first exam grade and develop a plan to achieve that goal.
Chapter 1. Making Sense of Variability: An Introduction to Statistics
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 1.5 Thinking back regarding the four examples of the uses of statistics discussed in your textbook, please list each of the four uses, give a description of the use, and provide an example of each use. Try to use an example that was neither presented in the textbook nor discussed in your class.
Use of Statistics
Description of the Use
Example
Chapter 1. Making Sense of Variability: An Introduction to Statistics
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 1.6 Read each of the questions carefully and then select the best answer.
1. Which of the following is a variable? A. The number of days in the month of September. B. The number of players allowed to be on the field during a football game. C. The test grades of the students in a statistics course. D. The number of words in the first verse of the Star Spangled Banner.
2. The scores or measurements obtained in research are referred to as
A. samples. B. data. C. parameters. D. statistics.
3. Procedures used to summarize, analyze, and draw conclusions from
measurements obtained in research are called A. hypotheses. B. summarizations. C. samples. D. statistics.
4. A complete set of objects, events, people, or animals that share a common
characteristic is called a A. population. B. sample. C. total. D. statistic.
5. Which of the following could be a descriptive statistic?
A. Your total income for last year. B. The final score in the last game of the 2008 World Series. C. The number of CD’s that you own. D. The average score of a class on a history examination.
Chapter 1. Making Sense of Variability: An Introduction to Statistics
6. A number that describes a characteristic of a complete set of objects, events,
people, or animals that share a common characteristic is called a/an A. statistic. B. variable. C. parameter. D. estimate.
7. Statistical inference refers to
A. estimating population parameters from statistics. B. calculating statistics from sample data. C. manipulating a variable. D. selecting a sample from a population.
8. Random sampling
A. is used to create populations from samples. B. selects individuals from a sample so that each person has an equal chance
of being selected. C. selects individuals from a population so that each person has an equal
chance of being selected. D. selects individuals from a population so that the selection of one person
affects the probability of selecting someone else.
9. The ____ is manipulated in an experiment to determine its effect on behavior. A. extraneous variable B. dependent variable C. sample D. independent variable
10. An experimenter created two different groups of subjects and had each group read
material on a computer monitor. For each group, the material was presented in a different text style. The experimenter measured how long it took each person to read the material. The measurement of how long it took to read the material was the ____ variable in this experiment.
A. dependent B. extraneous C. independent D. subject
11. Two different groups of subjects created so that the groups do not differ in any
systematic way are called ____ groups. A. parallel subjects B. equivalent C. equal D. identical
Chapter 1. Making Sense of Variability: An Introduction to Statistics
A. any difference between the groups is due to the dependent variable. B. the subjects in the two groups are identical in every way. C. the groups will always differ by a large amount. D. any differences between the groups are due to random variation.
13. To conclude that two means differ significantly implies that the difference
between the means is A. probably due to random effects of chance. B. not due to chance effects. C. very important and meaningful. D. due to the effect of the dependent variable.
14. If two variables ____, then they change consistently in relation to each other.
A. are independent B. covary C. do not vary D. are unrelated
15. A ____ indicates the extent of the relationship between two sets of scores.
A. parameter B. research hypothesis C. statistical hypothesis test D. correlation coefficient
Chapter 1. Making Sense of Variability: An Introduction to Statistics
Note to the instructor. There are not as many assignments in this chapter as you will find in other chapters, due in part, to this chapter being very vocabulary rich. Please encourage students to focus on learning the vocabulary words introduced in this chapter; doing so will ease their learning as they enter into the more quantitatively challenging chapters in the future. Assignment 2.1 This assignment helps students to organize information with regard to the different types of research methods, their uses, limitations, and examples. This table can be used in several different ways. One use is to provide students a copy to help with taking notes during class or when reading the textbook. The table can also be given to the students as a homework assignment after the material has been covered in class. We encourage students to use this assignment in a “self-testing” format by not looking at notes or the textbook when completing the table until they can no longer remember additional information. Of course, the table can also be given as a quiz or a test item. Assignment 2.2 This assignment is a table that students can use to help structure information regarding the different types of measurement. As with Assignment 2.1, this table can be used in several different ways. One use is to provide students a copy to help with taking notes during class or when reading the textbook. The table can also be given to the students as a homework assignment after the material has been covered in class. We encourage students to use this assignment in a “self-testing” format by not looking at notes or the textbook when completing the table until they can no longer remember additional information. The table can also be given as a quiz or a test item. Assignment 2.3 This assignment is a set of 15 multiple choice questions that can be used as a homework assignment, in-class assignment, or quiz. The questions are a varied sample of the information covered in this chapter. Answers are provided on the page following the assignment.
Chapter 2. Statistics in the Context of Scientific Research
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 2.1 Using the information discussed in class and covered in your textbook, complete this table with regard to the six types of research methods. Try to use an example that was not in the textbook or discussed in your class.
Research Method Description Appropriate Use Limitation Example
Naturalistic observation
Case study
Archival records
Survey
Experiment
Quasi-experiment
Chapter 2. Statistics in the Context of Scientific Research
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 2.2 Complete the table below with regard to the four types of measurement. Try to use an example that was not in the textbook or discussed in your class.
Type of Measurement
Definition
Example
Chapter 2. Statistics in the Context of Scientific Research
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 2.3 Read each of the questions carefully and then select the best answer.
1. Empirical data refers to A. knowledge obtained by reasoning or thinking. B. knowledge obtained through intuition. C. scores or measurements obtained from existing records. D. scores or measurements obtained by observation and sensory experience.
2. An environmental psychologist unobtrusively observes how people use a small
city park. The research method used by this psychologist is called A. survey research. B. naturalistic observation. C. archival records research. D. experimentation.
3. A sociologist uses death certificates to study the occurrence of suicide in different
geographic regions. This research method is called A. survey research. B. naturalistic observation. C. archival records research. D. experimentation.
4. Which of the following is an example of survey research?
A. You are interviewed to find out information about your shopping habits. B. People are unobtrusively observed as they shop at a mall. C. A psychologist asks people to learn a list of words and records how many
trials it takes each person to learn the list. D. A psychologist correlates college grade point averages with student scores
on a personality inventory.
5. An educational psychologist manipulates the loudness of a background noise that people are exposed to while solving complex problems. One group of people solves the problems while listening to a loud noise. A second group solves the problems while listening to a soft noise, and a third group solves the problems in a quiet condition. The research method used by this psychologist is called
A. survey research. B. naturalistic observation. C. quasi-experimentation. D. experimentation.
Chapter 2. Statistics in the Context of Scientific Research
6. A psychologist compares 20 to 25 year-old females to 50 to 55 year-old females
on the length of time taken to solve a simple cross-word puzzle. The research method used by this psychologist is called
A. survey research. B. naturalistic observation. C. quasi-experimentation. D. experimentation.
7. ____ are used to specify the procedures used to manipulate an independent
variable or measure a dependent variable in research. A. Archival records B. Operational definitions C. Statistics D. Naturalistic observations
8. Which of the following is a nominal measurement?
A. Your college ID number. B. Your college grade point average. C. Your income last year. D. Your height in inches.
9. Suppose you are an office manager and you recently ranked your employees in
order of work performance as follows: 1. Tammy 2. Ricardo 3. Maria 4. Herb 5. Patricia
Which of the following conclusions is appropriate from this ranking?
A. Tammy is an excellent worker. B. Patricia is a very poor worker. C. Both Herb and Patricia are likely to be very poor workers. D. Tammy is ranked highest of the five workers, but we cannot tell how
much her performance differs from the others.
10. ____ measurement scales have an arbitrary zero point. A. Nominal B. Ordinal C. Interval D. Ratio
Chapter 2. Statistics in the Context of Scientific Research
11. Rating scales, such as those that are used to measure a person’s attitude toward an
issue, are generally treated as representing ____ measurement. A. nominal B. ordinal C. interval D. ratio
12. A subject in an experiment is given a task of solving a complex maze and the
amount of time needed to complete the maze is recorded. The measurement of the amount of time used here used here is
A. nominal. B. ordinal. C. interval. D. ratio.
13. Which of the following is a discrete variable?
A. The number of names listed in your local telephone directory. B. The amount of time you devote to studying each day. C. The temperature which you keep your house or room. D. The speed at which you normally drive on an interstate highway.
14. Which of the following is a continuous variable?
A. The number of students enrolled in your statistics course. B. The time it takes you to commute to work each day. C. Your income from last year. D. The number of runs scored by the Philadelphia Phillies in the third game
of the 2008 World Series.
15. Suppose you are timing how long it takes people to learn a grocery list of 10 items and one person takes 46 seconds. The lower and upper real limits for this score are ____ and ____ seconds, respectively.
A. 45; 47 B. 45.6; 45.4 C. 45.5; 46.5 D. 44.5; 47.5
Chapter 2. Statistics in the Context of Scientific Research
Looking at Data: Frequency Distribution and Graphs
Assignment 3.1 This assignment assists students in learning the symbols, definitions, and formulas discussed in this chapter. The assignment helps students become comfortable with statistical notation and formulas. For some students, completing this assignment more than once is necessary to assure they remember the meaning of each symbol and formula. Assignment 3.2 The questions of this assignment ask students to compare and contrasts the uses, benefits, and limitations of ungrouped and grouped frequency distributions. Students are then asked to complete an ungrouped frequency distribution. Answers are provided on the page following the assignment. Assignment 3.3 This assignment is to provide students with practice in preparing a grouped frequency distribution. Answers are provided on the page following the assignment. Assignment 3.4 Assignment 3.3 must first be assigned to students in order for them to complete this assignment. This assignment has students calculate and interpret percentile ranks and percentiles. Answers are provided on the page following the assignment. Assignment 3.5 This assignment is a set of 15 multiple choice questions that can be used as a homework assignment, in-class assignment, or quiz. The questions are a varied sample of the information covered in this chapter. Answers are provided on the page following the assignment.
Chapter 3. Looking at Data: Frequency Distributions and Graphs
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 3.1 The purpose of this assignment is to help you to become more comfortable in recognizing what each statistical symbol and formula in Chapter 3 represents. For each item in the table below, either the term, symbol, or definition is given. Complete the following table with the missing information. For example, for the term frequency, provide the symbol and definition in the appropriate columns. It is best to complete this page without looking at your notes or textbook. Once you have completed it, refer back to your notes and textbook to verify you are correct.
Term
Symbol
Definition (also include formula as appropriate)
Frequency
i
This calculation provides the percentage of times a particular score has been observed in relation to the total number of observations multiplied by 100
X
Total number of scores
Cumulative frequency
XP
Indicates the percentage of scores in the distribution that are equal to or less than that score
Percent frequency
Accumulated relative frequency of a score
c%f
Chapter 3. Looking at Data: Frequency Distributions and Graphs
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 3.2 1. What is the first step in analysis of data? Why? 2. Organizing data into a frequency distribution is one method that can be used to make
it easier to identify the trends in data. There are two types of frequency distributions: ungrouped and grouped. How are they similar? How are they different? Why do we need two different types of frequency distributions? When would you use a grouped frequency distribution instead of an ungrouped frequency distribution? What is lost in using a grouped frequency distribution?
3. A statistics professor noticed that there was a group of students in her behavioral
statistics class who tended to miss class, didn’t complete their homework, and failed to bring their calculators to class. She decided to see if this group of students had a belief that intelligence is fixed or changeable, as discussed in your textbook in Chapters 1 and 3. Using a measure of Implicit View of Intelligence where the lowest total score is 3 and the highest total score is 18, she obtained the following scores: 9, 5, 3, 15, 8, 8, 5, 4, 10, 7, 10, 4, 4, 6, 5, 4, 7, 6, 5, 5. Construct an ungrouped frequency distribution that shows the simple frequency, relative frequency, and percent frequency for these scores. After you have organized the data, identify what the most common score was. If lower scores indicate that a person is more likely to have a fixed view of intelligence and higher scores indicate a person is more likely to have a changeable view of intelligence, how would you characterize the students in this sample in general?
Chapter 3. Looking at Data: Frequency Distributions and Graphs
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 3.3 Hsee, Hastie, and Chen (Hsee, C. K., Hastie, R., & Chen, J. 2008. Hedonomics: Building decision research with happiness research. Perspectives on Psychological Science, 3, 224 – 243) tested different theories of happiness by having children play with toy blocks. In one condition, children were instructed to use toy blocks to come up with as many different types of objects as they could. The data below represent child happiness measures taken after they played with the toy blocks. The happiness measure ranges from 0 to 50 with the higher the value, the higher the level of happiness. Complete the following grouped frequency distribution.
Looking at the data, what was the most typical response? Assume that the higher the number, the greater the happiness. Thus, when children were encouraged to use the same set of blocks to design more creative projects, did they tend to be happy or unhappy?
Chapter 3. Looking at Data: Frequency Distributions and Graphs
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 3.4 Using the grouped frequency distribution from Assignment 3.3, answer the following questions. A. Find the percentile for each of the following values of X.
X 49 43 40 34 30 22 20 14 5 3
B. Find the percentile rank, that is, the value of X for each of the following percentiles.
Percentile 98 94 85 65 50 46 34 19 12 5
Chapter 3. Looking at Data: Frequency Distributions and Graphs
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 3.5 Read each of the questions carefully and then select the best answer.
1. When listing the values for X in a simple frequency distribution it is important that you
A. only list the values you feel are the most important. B. only list the values that have been observed. C. only list the ten most frequently observed values. D. list all possible values.
2. The simple frequency of scores in an ungrouped frequency distribution is
indicated by ____. A. sf B. f C. F D. simfreq
3. Which score has the highest simple frequency in the distribution below?
X f 35 3 34 1 33 8 32 5 31 0 30 2
A. 36 B. 34 C. 33 D. 32
4. The relative frequency of a distribution is obtained by
A. dividing the frequency of a score by the total number of scores in the distribution.
B. dividing the total number of scores in a distribution by the frequency of a score.
C. multiplying the frequency of a score by 100 D. multiplying the frequency of a score by the total number of scores in the
distribution.
Chapter 3. Looking at Data: Frequency Distributions and Graphs
10. The percentile rank of Jessica’s score on a language exam was 73. This value
indicates A. Jessica obtained a score of 73 out of 100 on the exam. B. 27 percent of the scores were less than Jessica’s. C. 73 percent of the scores on the exam were equal to or greater than
Jessica’s. D. 73 percent of the scores were equal to or less than Jessica’s.
11. If the 57th percentile on an examination is 74, then
A. 57 percent of the scores on the exam were 74 or less. B. 57 percent of the scores on the exam were 74 or higher. C. 43 percent of the scores on the exam were 74 or less. D. 43 percent of the scores on the exam were 74 or higher.
12. A frequency polygon always indicates the frequencies
A. on the Y axis. B. on the X axis. C. at the lower stated limit of a class interval. D. at the upper stated limit of a class interval.
13. A ____ distribution would have a large number of high scores and only a few
very low scores. A. normal B. bimodal C. positively skewed D. negatively skewed
14. When a distribution is bimodal,
A. the majority of the scores are at the high end of the score range. B. the majority of the scores are at the low end of the score range. C. there are two scores that occur equally often with the highest frequency in
the distribution. D. all scores occur approximately equally often.
15. If you see ____ on a graph, you should be concerned about the graph being
misleading. A. a missing or awkward scale B. everything properly labeled C. bars D. categories
Chapter 3. Looking at Data: Frequency Distributions and Graphs
Assignment 4.1 This assignment assists students in learning the symbols, definitions, and formulas discussed in this chapter. The assignment helps students become comfortable with statistical notation and formulas. For some students, completing this assignment several times is necessary to assure they remember the meaning of each symbol and formula. Assignment 4.2 This assignment contains nine small data sets for students to calculate the mean, median, and mode. Answers are provided on the page following the assignment. Assignment 4.3 This assignment is to be completed along with Assignment 4.2. It asks students a series of questions regarding the nine data sets with respect to which measure of central tendency best captures the typicality of the data. Answers are provided on the page following the assignment. Assignment 4.4 This assignment contains nine small data sets. Students are to calculate the SS for each data set. The answers accompanying this assignment show each of the intermediate steps to help students find their errors as they learn this most critical of calculations. Answers are provided on the page following the assignment. Assignment 4.5 This assignment is to be completed with Assignment 4.4. Students are to look at the data sets and the SS they calculated when answering a series of questions designed to help them to understand that the SS is sensitive to outliers and tends to get larger as the data set gets larger. This assignment prepares students to think about dividing the SS by N to obtain a more useful statistic, the variance. Answers are provided on the page following the assignment. Assignment 4.6 This assignment is a set of 15 multiple choice questions that can be used as a homework assignment, in-class assignment, or quiz. The questions are a varied sample of the information covered in this chapter. Answers are provided on the page following the assignment.
Chapter 4. Looking at Data: Measures of Central Tendency
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 4.1 The purpose of this assignment is to help you to become more comfortable in recognizing what each statistical symbol and formula in Chapter 4 represents. For each item in the table below, either the term, symbol, or definition is given. Complete the following table with the missing information. For example, for the term sample mean, provide the symbol and definition in the appropriate columns. It is best to complete this page without looking at your notes or textbook. Once you have completed it, refer back to your notes and textbook to verify you are correct.
Term Symbol Definition (also include formula as appropriate)
Sample mean
Mdn
None One of the three measures of central tendency covered in the textbook. It represents the most frequently occurring score.
Σ
SS
Population mean
This intermediate step is needed for finding the sum of the squared deviations. If you sum this and your work is correct, it will sum to zero.
Chapter 4. Looking at Data: Measures of Central Tendency
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 4.2 Find the mean, median, and mode for each of the nine data sets given below.
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 4.3 Using the data sets from Assignment 4.2, identify the measure of central tendency that you think is the best indication of a typical score for each data set. Explain your answer for each data set.
Set Measure of Central Tendency Explanation
A
B
C
D
E
F
G
H
I
Chapter 4. Looking at Data: Measures of Central Tendency
Set A. Mean: the data are symmetrical Set B. Median: the data are negatively skewed Set C. Mean: the data are symmetrical Set D. Mean: the data are symmetrical Set E. Mode: Nominal data Set F. Median: the data are positively skewed Set G. Median: the data are negatively skewed Set H. Mean: the data are symmetrical Set I. Mean: there is no variability in the data
Chapter 4. Looking at Data: Measures of Central Tendency
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 4.4 Of all of the calculations you will have to do for this class, none is more important than learning how to find the sum of the squared deviations, called the sum of squares (SS). For each data set below, find X , then find X X− and ( )2X X− for each score. Use these values to find the SS for each data set.
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 4.5 This assignment is to be completed with Assignment 4.4. After you have found the SS for each data set, answer the following questions.
1. Which pairs of data sets have the same variability but different SS? What is causing the differences in the SS if the data sets have equal amounts of variability?
2. There is an important internal check to make sure you have correctly calculated the SS, what is it?
3. Compare Data Sets G and H. How are their values similar? How are the values different? How do their SS compare? What seemingly small change is causing this large difference in the SS?
Chapter 4. Looking at Data: Measures of Central Tendency
Answers for Assignment 4.5 1. Data Sets A and D have the same variability. Data Sets B and E have the same variability. The only
difference is that the second data set for both pairs has twice the number of observations, which increases the size of the SS.
2. The sum of the deviations should always add to zero unless there is rounding error, then it should be very close to zero.
3. In Data Set H there is one additional score, 13. This additional score is not typical of the other scores, which are all 5, 6, or 7. Thus, it is an outlier. The addition of a single outlier causes a large increase in the SS.
Chapter 4. Looking at Data: Measures of Central Tendency
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 4.6 Read each of the questions carefully and then select the best answer.
1. The symbol used to represent the sample mean is ____. A. X B. X C. Mdn D. Mn
2. A teacher observed the number of aggressive acts by five children over a one-
hour period in a child care center. She obtained the following set of scores: 7, 4, 4, 6, 4. What is the mean for this sample of scores?
A. 4 B. 6 C. 3 D. 5
3. Suppose you obtained the following scores on three 10-item quizzes in one of
your classes: 8, 9, 10. What is the sum of squares for these scores? A. 0 B. 2 C. 9 D. 1
4. In journal articles following the Publication Manual of the American
Psychological Association style, the mean is usually indicated by the symbol ____.
A. M B. X C. X D. Mn
5. The mean of a population is represented by the symbol ____.
A. X B. M C. μ D. X population
Chapter 4. Looking at Data: Measures of Central Tendency
6. An instructor calculated a statistic on the scores of a biology exam so that as
many students had a score above the value as students had a score below the value. This instructor calculated the
A. mode. B. median. C. mean. D. unimode.
7. A psychologist asked a group of people to remember a list of 20 names and then
asked them to recall the names a week later. He found the following distribution of items recalled for 11 people: 5, 6, 7, 7, 7, 8, 9, 9, 13, 14, 15. The median for this set of scores is ____.
A. 7 B. 8 C. 8.5 D. 9.1
8. A characteristic of the median is that it
A. cannot be calculated for a bimodal distribution. B. is the most frequently occurring score in a distribution of scores. C. is not affected by very extreme scores in the tails of a distribution. D. cannot be calculated if the number of scores in a distribution is an even
number.
9. The ____ is the most frequently occurring score in a distribution of scores. A. mode B. median C. mean D. percentile
10. An instructor gives students a 10-item multiple choice test. The distribution of
scores was 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 9, 9, 9, 10, 10 for 18 students. The mode for this distribution is _____.
A. 6 B. 6.5 C. 7 D. 7.5
11. A high school baseball coach created a distribution of hits by her players over five
games. The distribution was 0, 1, 2, 2, 2, 3, 4, 5, 5, 5, 6, 7, 8, 8, 8 for 15 players. This distribution is
A. nonmodal. B. unimodal. C. bimodal. D. multimodal.
Chapter 4. Looking at Data: Measures of Central Tendency
12. Suppose you obtained the following distribution of scores of errors made by
participants solving a difficult maze: 9, 9, 10, 12, 14, 17, 19, 20, 94. What would be the most appropriate descriptive measure of central tendency for this distribution?
A. Median B. Mean C. Mode D. All the measures of central tendency would be equally appropriate.
13. Suppose an experimenter obtained the scores 2, 4, 3, 6,10, 6. If a score of 98 were
to be added to this distribution, it would most affect the value of A. the mode. B. the median. C. both the mode and median. D. the mean.
14. Suppose the mean salary for the employees of an organization is $95,000,
whereas the median salary for these employees is $41,200. The distribution of salaries in this organization is
A. positively skewed. B. negatively skewed. C. bimodal. D. unimodal.
15. The sample mean is often preferred as a measure of central tendency because it is
A. easier to calculate than either the mode or median. B. more resistant to the effects of extreme scores than either the mode or
median. C. more useful for inferential statistics than either the mode or median. D. not affected by a skewed distribution.
Chapter 4. Looking at Data: Measures of Central Tendency
Assignment 5.1 This assignment assists students in learning the symbols, definitions, and formulas discussed in this chapter. The assignment helps students become comfortable with statistical notation and formulas. Some students benefit from completing this assignment more than once. Assignment 5.2 This assignment is similar to assignment 4.4. It contains nine small data sets. Students are to calculate the SS for each data set. Answers are provided on the page following the assignment. Assignment 5.3 Seldom does a student have access to an entire population, but for this exercise we are pretending that we do. Students are given ten small population data sets. Students are to calculate the population mean, variance, and standard deviation. Answers are provided on the page following the assignment. Assignment 5.4 This exercise provides students with ten small data sets for which to calculate the variance and standard deviation that can be used to estimate the population variance or standard deviation. Answers are provided on the page following the assignment. Assignment 5.5 This assignment assists students in reviewing terminology and symbols. It helps students to focus on the differences between population parameters and sample statistics, as well as variances and standard deviations. Assignment 5.6 This assignment is a set of 15 multiple choice questions that can be used as a homework assignment, in-class assignment, or quiz. The questions are a varied sample of the information covered in this chapter. Answers are provided on the page following the assignment.
Chapter 5. Looking at Data: Measures of Variability
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 5.1 The purpose of this assignment is to help you to become more comfortable in recognizing what each statistical symbol and formula in Chapter 5 represents. For each item in the table below either the term, symbol, or definition is given. Complete the following table with the missing information. For example, for the term range, provide the definition in the appropriate column. It is best to complete this page without looking at your notes or textbook. Once you have completed it, refer back to your notes and textbook to verify you are correct.
Term Symbol Definition (also include formula as appropriate)
Range None
2σ
An unbiased statistic used to estimate the population variance. Include the formula.
s
SS
Population standard deviation
Measures of variability None
Chapter 5. Looking at Data: Measures of Variability
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 5.2 For each data set below, find X . Then find X X− and ( )2X X− for each score. Use these values to find the SS for each data set.
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 5.3 Assume that each data set given below represents a complete population of scores. First calculate μ for each set of scores. Use this value of μ to calculate 2σ using the formula on page 89 of the textbook. Then find the value of σ for each data set.
Set A Set B Set C Set D Set E Set F Set G Set H Set I Set J X X X X X X X X X X 49 0.10 3 86 15 2.5 0 9 46 –5 51 0.30 9 86 24 1.5 1 10 30 –8 32 0.20 10 86 13 0.5 2 11 18 –10 40 0.10 11 87 18 1.0 3 12 22 –6 48 0.05 12 100 20 2.0 4 13 29 –11 μ
2σ σ
Chapter 5: Looking at Data: Measures of Variability
Answers for Assignment 5.3 (Note. Answers for σ are given to 3 decimal places to facilitate checking the accuracy of computations. Your answers may differ slightly from those given here due to rounding differences.) Set A Set B Set C Set D Set E Set F Set G Set H Set I Set J
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 5.4 Assume that each data set given below represents a sample of scores. First calculate X for each set of scores. Use this value of X to calculate s2 using the formula on page 91 of the textbook. Then find the value of s for each set.
Set A Set B Set C Set D Set E Set F Set G Set H Set I Set J X X X X X X X X X X 114 20 33 750 68 445 23 9 56 5 98 18 34 450 65 514 24 10 40 8 76 24 37 625 72 498 27 11 28 10 132 17 36 500 78 616 26 7 42 6 95 21 35 550 72 507 25 8 39 11
X s2 s
Chapter 5: Looking at Data: Measures of Variability
Answers for Assignment 5.4 (Note. Answers for s are given to 3 decimal places to facilitate checking the accuracy of computations. Your answers may differ slightly from those given here due to rounding differences.)
Set A Set B Set C Set D Set E Set F Set G Set H Set I Set J
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 5.5 Eight symbols are listed in the first column of the table below. At the top of the second column are four terms. For each symbol, write the term that corresponds to the symbol. In the third column indicate how the symbol is calculated, and in the fourth column indicate whether the symbol represents a mean, a variance, a standard deviation or other value. We have completed the row for σ as an example.
Symbol
Parameter Statistic Either a parameter
or a statistic Neither
Calculated from a: sample Population Either a sample or
a population Other
Mean Variance Standard deviation Other
σ Parameter Population Standard deviation μ
N
s2
X
2σ
∑
s
Complete the following table giving the appropriate symbol and formula for each term either as a population parameter or as a statistic used to estimate a population parameter.
Population parameter Statistic used to estimate the population parameter
Mean
Variance
Standard Deviation
Chapter 5: Looking at Data: Measures of Variability
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 5.6 Read each of the questions carefully and then select the best answer.
1. An instructor gave students a 20-item quiz on a course topic. The distribution of scores on the quiz was: 8, 8, 10, 10, 11, 12, 12, 13, 13, 13, 15, 15, 16, 17, 19, 19, 20, 20, 20. What is the range for these scores?
A. 20 B. 12 C. 13 D. A range cannot be calculated for this set of scores.
2. The sample variance when divided by ____ is an unbiased estimate of the
population variance. A. range B. N C. N – 1 D. median
3. Although s is a(n) ____ estimate of the population standard deviation, it is more
regularly reported than s2 because ____. A. biased; it is easier to calculate because the standard deviation is reported in
units instead of squared units B. biased; it is easier to understand as the standard deviation is reported in
units instead of squared units C. unbiased; the sample variance is always a biased estimator of the
population variance D. unbiased; the standard deviation is easier to understand
4. The symbol for the sample standard deviation used to estimate the population
standard deviation is ____. A. s B. s2 C. σ D. 2σ
Chapter 5: Looking at Data: Measures of Variability
10. The SS for a set of scores is 80 based on a sample of size 21. Thus, s2 for the
scores is ____. A. 4 B. 2.0 C. 2 D. 16
11. If s2 for a set of scores is 81, then s for those scores is ____.
A. 3 B. 9 C. (81)2 D. cannot be determined from the information given.
12. Which of the following sets of scores would you expect to have the largest value
of s? A. 5, 5, 6, 7, 7 B. 7, 7, 7, 7, 7 C. 5, 6, 7, 8, 9 D. 5, 5, 7, 9, 9
13. If s = 0 for a distribution of scores, then which of the following is true?
A. An error was made in the calculation because s cannot equal 0 B. All the scores in the distribution are equal to each other. C. The sample variance of the scores was equal to 10. D. The distribution was either positively or negatively skewed.
14. In journal articles following the Publication Manual of the American
Psychological Association style, the standard deviation is usually represented by ____.
A. SD B. S C. s D. σ
15. You have collected a set of scores from subjects performing a reaction time task.
You decide that the most appropriate measure of central tendency for the scores is the mean. The most appropriate measures of variability would thus be
A. the standard deviation. B. the sample variance. C. biased. D. the range.
Chapter 5: Looking at Data: Measures of Variability
The Normal Distribution, Probability, and Standard Scores
Assignment 6.1 This assignment requires that students list and define the properties of the normal distribution. Assignment 6.2 This assignment has students working with the normal distribution, z scores, and the observations that correspond with μ and σ . It also requires students to include the relative frequency for the major regions from three standard deviations below to three standard deviations above the mean. Assignment 6.3 This assignment has students calculate z scores for different values of X, μ , and σ . Answers are provided on the page following the assignment. Assignment 6.4 This assignment has students find the probability of a score falling above, below, or between the negative and positive value of a specified z score. Answers are provided on the page following the assignment. Assignment 6.5 This assignment is a set of 15 multiple choice questions that can be used as a homework assignment, in-class assignment, or quiz. The questions are a varied sample of the information covered in this chapter. Answers are provided on the page following the assignment.
Chapter 6. The Normal Distribution, Probability, and Standard Scores
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 6.1 There are four properties of a normal distribution. Without looking at your textbook or notes, identify each property and describe what it means. Finally, draw an illustration of a normal distribution and indicate the property on the drawing.
Property Description Illustration
Chapter 6. The Normal Distribution, Probability, and Standard Scores
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 6.2 Shown below is an illustration of a normal distribution. Assume μ of the distribution is 50 and σ is 5. 1. On the line labeled with a σ , place the values of σ the correspond to the distribution
(i.e., +1σ , +2σ , –1σ , and so forth). 2. On the line labeled z, place the values of z that correspond to the values of σ on the
line above. 3. On the line labeled X, place the numerical values of X that correspond to each value
of z on the line above assuming μ = 50 and σ= 5 for the distribution. 4. On the line labeled rf, identify the relative frequency of scores occurring between
each value of z. For example, .1359 of the scores occur between –1z to –2z.
σ
z
X
rf
Chapter 6. The Normal Distribution, Probability, and Standard Scores
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 6.3 For each data set below, calculate the value of z for each value of X for the μ and σ given.
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 6.4 For each value of z given below, identify the probability of a value of X coming from the same population equal to or greater than the z score shown [i.e., ( )p X z≥ ]. Then identify the probability of a value of X coming from the same population equal to or less than the z score shown [i.e., ( )p X z≤ ]. Finally, identify the probability of a value of X coming from the same population falling between positive and negative values of the listed z score [i.e., ( )p z X z≤ ≤ ].
z ( )p X z≥ ( )p X z≤ ( )p z X z≤ ≤
0.00
–2.10
+0.35
+1.77
–0.59
+0.28
–1.28
–0.99
+0.05
+2.45
–2.87
–0.25
+1.03
–1.56
+2.00
+2.99
Chapter 6. The Normal Distribution, Probability, and Standard Scores
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 6.5 Read each of the questions carefully and then select the best answer.
1. If a distribution of scores is normally distributed, then the distribution can be completely described by
A. its mean and range. B. its mean and standard deviation. C. finding the mode and median for the scores. D. its median and range.
2. The relative frequency under the normal distribution
A. depends upon the shape of the distribution. B. depends upon the mean and variance of the distribution. C. is equal to 100. D. is equal to 1.0.
3. Assume you have a distribution of scores that is approximately normally distributed. What proportion of scores can you expect to be between one standard deviation below the mean and one standard deviation above the mean?
A. .68 B. .50 C. .95 D. .99
4. Assume you have a distribution of scores that is approximately normally distributed. What proportion of scores fall between the mean and the highest value in the distribution?
A. 1.00 B. .68 C. .50 D. .25
5. A scientist obtained a normally distributed population of scores with a mean of 70
and a standard deviation of 10. What proportion of scores do you expect to find in the interval between 60 to 80?
A. 1.00 B. .50 C. .34 D. .68
Chapter 6. The Normal Distribution, Probability, and Standard Scores
6. The mean of a standard normal distribution is equal to ____ and its standard
deviation is equal to ____. A. 1; 0 B. 0; 1 C. 1; 1 D. 100; 10
7. Which of the following formulas would you use to convert a score from a normal
distribution to a score on the standard normal distribution?
A. μσ
Xz −=
B. σμ
Xz −=
C. ( )μ σz X= −
D. ( )μ σz X= −
8. Suppose you have a set of scores that are normally distributed with a mean equal
to 90. The standard deviation for the scores is 15. If a score in the distribution is equal to 75, then the z for this score is ____.
A. +1.0 B. +2.0 C. –1.0 D. –2.0
9. If a population of scores is normally distributed and has a mean of 300 and a
standard deviation of 50, then what proportion of scores would you expect to find between 200 to 400?
A. .34 B. .68 C. .95 D. .99
10. Suppose a student takes a standardized test measuring college level skills. Scores
on the test are normally distributed with a mean of 500 and a standard deviation of 100. The student obtains a z score of 0.0 on the test. Which of the following statements is true of this person’s score?
A. The student received a score of zero on the test. B. The student’s score is above the mean of 500. C. The student’s score is below the mean of 500. D. The student scored 500 on the test.
Chapter 6. The Normal Distribution, Probability, and Standard Scores
11. A maker of breakfast cereal sponsors a contest. For each 100 cartons of cereal, 90
boxes contain a baseball rookie card, 5 boxes contain a package of chewing gum, 4 boxes contain a coupon worth half the price of another box of the cereal, and one box contains a coupon for a free box of the cereal. The boxes are randomly distributed to stores. If you buy a box of the cereal, what is the probability you will buy a box containing a half-price coupon?
A. 4 B. .4 C. .04 D. .5
12. The statement “The probability that X is equal to or greater than 25 and equal to
or less than 56 is .34” is expressed in probability notation as_____.
A. p(25 ≤ X ≤ 56) = .34
B. p(25 ≥ X ≤ 56) = .34
C. p(25 ≥ X ≥ 56) = .34
D. p(25 ≤ X ≥ 56) = .34
13. If A and B are mutually exclusive outcomes in a probability distribution, and the
p(A) = .30 and the p(B) = .20, then the p(A or B) equals ____. A. .10 B. .06 C. .60 D. .50
14. If a set of scores is normally distributed with μ = 150 and σ= 15, what is the
probability of a score being between 120 and 180? A. .50 B. .68 C. .95 D. .34
15. Suppose an instructor returned an exam with standard scores in place of raw
scores. For five students, the standard scores were: Jenn, +.54; Whitney, .00; Ramon, +1.21; Michelle, –.67; Clay, –.34. Based on these scores, ____ had the highest score on the exam, and ____ score was at the mean of the exam.
A. Michelle; Clay’s B. Ramon; Whitney’s C. Whitney, Michelle’s D. Ramon; Jenn’s
Chapter 6. The Normal Distribution, Probability, and Standard Scores
Understanding Data: Using Statistics for Inference and Estimation
Assignment 7.1 This assignment assists students in learning the symbols, definitions, and formulas discussed in this chapter. The assignment helps students become comfortable with statistical notation and formulas. For some students, completing this assignment several times is necessary to assure they remember the meaning of each symbol and formula. Assignment 7.2 Students are to read a list of characteristics and place them on a Venn diagram to compare and contrast a normal distribution to a sampling distribution of the means. Answers are provided on the page following the assignment. Assignment 7.3 Students are provided with μ and σ , and a sample mean and are asked to calculate a z statistic to identify the location of the sample mean on a sampling distribution of the mean. Students are then asked to find the probability of a sample mean being drawn from the same population falling above a z value, below a z value, or between positive and negative z values. Answers are provided on the page following the assignment. Assignment 7.4 Given eight sample data sets, students are asked to calculate Xs . Answers are provided on the page following the assignment. Assignment 7.5 Using the values from assignment 7.3, students are to calculate a 95% confidence interval for μ using each sample mean. Note that students do not have to be assigned Assignment 7.3 to complete this assignment. Answers are provided on the page following the assignment. Assignment 7.6 This assignment is a set of 15 multiple choice questions that can be used as a homework assignment, in-class assignment, or quiz. The questions are a varied sample of the information covered in this chapter. Answers are provided on the page following the assignment.
Chapter 7. Understanding Data: Using Statistics for Inference and Estimation
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 7.1 The purpose of this assignment is to help you to become more comfortable in recognizing what each statistical symbol and formula in Chapter 7 represents. For each item in the table below, either the term, symbol, or definition is given. Complete the following table with the missing information. For example, for the term unbiased estimator, provide the definition in the appropriate column. It is best to complete this page without looking at your notes or textbook. Once you have completed it, refer back to your notes and textbook to verify you are correct.
Term Symbol Definition (also include formula as appropriate)
Unbiased estimator None
σ
This is the standard error of a sampling distribution of the mean
None This class of statistics is considered to consistently over- or under-estimate the population parameter
Consistent estimator None
Population mean
From a sampling distribution of the mean, equals the population mean
Sampling distribution of the
mean None
Estimated standard error
Provides a range of score values that is expected to contain the value of the population mean with a certain level of confidence
Central limit theorem None
Chapter 7. Understanding Data: Using Statistics for Inference and Estimation
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 7.2 This exercise asks you to compare and contrast the normal distribution with the sampling distribution of the mean. For each statement listed below, write the letter of the statement in the appropriate circle. If a statement applies only to a normal distribution, then write the letter of that statement in the section to the left labeled Normal Distribution. If a statement applies only to a sampling distribution of the mean, then write the letter of that statement in the section to the right labeled Sampling Distribution of the Mean. If a statement applies to both a normal distribution and a sampling distribution of the mean, then write the letter of that statement in the section labeled Both.
A. Has the properties: unimodal, symmetrical, asymptotic, and continuous B. Distribution of all scores in a population C. Distribution of all sample means of size N taken from a population D. Theoretical distribution that provides us with information on sampling error E. Though typically does not occur naturally, it is an important distribution for our
understanding of statistics F. Can use the standard normal deviate to find location on the distribution
G. μσ
Xz −=
H. μσ
Xz −=
I. μX and σX
J. μ and σ
K. Can use Table C.1, the proportion of area under the standard normal distribution, to better understand the z score
Normal Sampling Distribution Distribution Both of the Mean
Chapter 7. Understanding Data: Using Statistics for Inference and Estimation
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 7.3 The following sample means were obtained from random samples selected from a population with μ = 100 and σ = 12. For each set, find σX and the z value for the X given. Then find the probability that a mean for a sample randomly selected from the same population would be equal to or larger than the sample mean given [i.e.,
( )p X z≥ ].
Set 1 X N σX z ( )p X z≥
A 104 144 B 104 9 C 94 144 D 94 9
The following sample means were obtained from random samples selected from a population with μ = 500 and σ = 50. For each set, find σX and the z value for the X given. Then find the probability that a mean for a sample randomly selected from the same population would be equal to or less than the sample mean listed [i.e., ( )p X z≤ ].
Set 2 X N σX z ( )p X z≤
A 525.00 25 B 512.50 100 C 498.00 100 D 489.00 25
The following sample means were obtained from random samples selected from a population with μ = 25 and σ = 5. For each set, find σX and the z value for the X given. Then find the probability that a mean for a sample randomly selected from the same population would be between –z and +z for the z value you found [i.e., ( )p z X z− ≤ ≤ + ].
Set 3 X N σX z ( )p z X z− ≤ ≤ +
A 24 16 B 26 25 C 24 100 D 26 400
Chapter 7. Understanding Data: Using Statistics for Inference and Estimation
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 7.4 For each of the following sample data sets, find X , s, and Xs Set A Set B Set C Set D Set E Set F Set G Set H
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 7.5 The following sample means were obtained from random samples selected from a population with μ = 100 and σ = 12. Find the 95% confidence interval for μ for each sample mean.
Set 1 X N Confidence Interval A 104 144 B 104 9 C 94 144 D 94 9
The following sample means were obtained from random samples selected from a population with μ = 500 and σ = 50. Find the 95% confidence interval for μ for each sample mean.
Set 2 X N Confidence Interval A 525.00 25 B 512.50 100 C 507.50 100 D 503.75 25
The following sample means were obtained from random samples selected from a population with μ = 25 and σ = 5. Find the 95% confidence interval for μ for each sample mean.
Set 3 X N Confidence Interval A 24 16 B 26 25 C 24 100 D 26 400
Chapter 7. Understanding Data: Using Statistics for Inference and Estimation
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 7.6 Read each of the questions carefully and then select the best answer.
1. Suppose you were able to select an infinite number of random samples of a certain size from a population and calculate a statistic on the samples. You found that the mean value of the statistics was equal to the population parameter. The statistic you calculated on these samples was
A. an interval estimator. B. an inconsistent estimator. C. a biased estimator. D. an unbiased estimator.
2. For consistent estimators, samples that are ____ will provide more accurate
estimates of population parameters. A. smaller B. larger C. not randomly selected D. bimodal
3. Suppose an experimenter selects a sample using simple random sampling. Using
this method requires that the A. members of the population from which the sample is selected must be
identical on most characteristics. B. members of the population randomly volunteer for the sample. C. selection of one member of the population for the sample does not affect
the probability of the selection of any other member of the population. D. probability of the selection of a member of the population depends upon
who was previously selected.
4. A researcher is interested in understanding what effect putting a person into a sad mood by listening to sad music has on the subject’s likelihood to recall sad events. The researcher finds the mean for her sample. In this example, the mean can be thought of as a
A. dependent variable. B. parameter. C. variance. D. point estimate of μ .
Chapter 7. Understanding Data: Using Statistics for Inference and Estimation
5. The most accurate estimates of population parameters will occur with samples
that are ____ from populations with ____ variability in scores. A. large; little B. large; large C. small; little D. small; large
6. The ____ is the distribution of X values when all possible samples of size N are
selected from a population and the mean calculated for each sample. A. mean distribution B. simple mean C. sampling distribution of the mean D. normal distribution
7. The ____ states that as the sample size increases, a sampling distribution of the
mean will approximate a normal distribution regardless of the shape of the distribution of the scores in the population.
A. normalcy theorem B. central limit theorem C. empirical limit theorem D. mean distribution principle
8. The term sampling error refers to
A. using a nonrandom sampling method. B. the difference X X− . C. mistakes made when selecting a sample from a population. D. the difference between the value of a sample mean and its corresponding
population mean.
9. The standard error of the mean is A. the standard deviation of the sampling distribution of the mean. B. obtained by dividing the standard deviation by the sample size. C. obtained by dividing the mean by its standard deviation. D. the value of μX − .
10. A population of scores has a mean of 75 and a standard deviation of 15. If
samples of size N = 25 are randomly drawn from this population, then the standard error will be equal to ____.
A. 15 B. 5 C. 3 D. 0.6
Chapter 7. Understanding Data: Using Statistics for Inference and Estimation
Is There Really a Difference? Introduction to Statistical Hypothesis Testing
Assignment 8.1 This assignment is to assist students in learning the symbols, definitions, and formulas discussed in this chapter. The assignment helps students become comfortable with statistical notation and formulas. For some students, completing this assignment several times is necessary to assure they remember the meaning of each symbol and formula. Assignment 8.2 Students are given the population mean and standard deviation along with the sample size and sample mean for 10 problem sets. They have to calculate a z test using a two-tailed test with α = .05. Students must decide whether to reject or fail to reject the null hypothesis. Answers are provided on the page following the assignment. Assignment 8.3 Given the sample size, students have to find df for a one-sample t test and identify the critical value, based on the df, for a two-tailed, α = .05 significance level. Answers are provided on the page following the assignment. Assignment 8.4 Students are given six sample data sets and asked make a judgment if they think the scores were selected from a population with a mean of 5. After making the judgment, they calculate the one-sample t test on the scores. Answers are provided on the page following the assignment. Assignment 8.5 For the first five problems, students are given sample data sets and are to calculate X and the 95 percent confidence interval for μ . For the last four problems, students are provided X , N, and s and are to calculate a 95 percent interval for μ . Answers are provided on the page following the assignment. Assignment 8.6 This assignment is a set of 15 multiple choice questions that can be used as a homework assignment, in-class assignment, or quiz. The questions are a varied sample of the information covered in this chapter. Answers are provided on the page following the assignment.
Chapter 8. Is There Really a Difference? Introduction to Statistical Hypothesis Testing
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 8.1 The purpose of this assignment is to help you to become more comfortable in recognizing what each statistical symbol and formula in Chapter 8 represents. For each item in the table below either the term, symbol, or definition is given. Complete the following table with the missing information. For example, for the two-tailed test, provide the definition in the appropriate column. It is best to complete this page without looking at your notes or textbook. Once you have completed it, refer back to your notes and textbook to verify you are correct.
Term Symbol Definition (also include formula as appropriate)
Two-tailed test None
α
The probability of failing to find a statistically significant difference when H1 is true
None The area on a normal distribution or t distribution that marks when you reject H0 and accept H1
Confidence interval
Null hypothesis
df
Power
Alternative hypothesis
zobs
tcrit
Chapter 8. Is There Really a Difference? Introduction to Statistical Hypothesis Testing
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 8.2 For each of the following data sets, calculate a z test comparing X to μ . Then, for each value of zobs, indicate if you reject or fail to reject H0. Use a two-tailed test with α = .05. Set N μ σ X z Reject H0
A 100 555 45 560
B 64 400 40 385
C 729 985.5 48.6 990
D 25 100 15 103
E 2500 40 5 40.2
F 121 27.3 33 20.4
G 256 100 15 103
H 2500 560 139 560
I 36 2.5 3 3
J 400 1.75 2 1.8
Chapter 8. Is There Really a Difference? Introduction to Statistical Hypothesis Testing
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 8.3 The purpose of this assignment is to help you practice finding critical value and rejection regions for the one-sample t test. For each value of N given, find the df. Then, with α = .05, indicate the value of tcrit for a two-tailed test. On what page in your textbook will you find the table for identifying the critical value for a one-sample t test?
N df tcrit
61
30
14
2
121
25
As the degrees of freedom decrease, what happens to the value of tcrit? Why?
Chapter 8. Is There Really a Difference? Introduction to Statistical Hypothesis Testing
As the degrees of freedom decrease, what happens to the value of tcrit? Why? The critical value increases. Because the sample is smaller, there is greater sampling error, that is, error due to individual differences. As such, there is a greater risk of making a Type I error because of the larger sampling error. Thus, the critical value of t increases to maintain α = .05.
Chapter 8. Is There Really a Difference? Introduction to Statistical Hypothesis Testing
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 8.4 Below are six data sets with 6 randomly selected scores in each data set. Your task is to determine if the scores were drawn from a population with μ = 5. Before you calculate the one-sample t test for each sample, make a guess as to whether or not you think the sample came from the population with μ = 5. After you make your guess, calculate a one-sample t test with α = .05 and a two-tailed test of significance. Then, based on tobs, indicate the decisions you would make for the statistical hypotheses.
Set A Set B Set C Set D Set E Set F 5 6 8 5 4.75 5 6 3 9 5 3.25 6 7 3 1 5 3.00 7 5 4 8 4 3.25 8 6 3 9 6 4.75 7 7 5 7 5 5 6
X
SS
s2
Xs
tobs
H0
H1
Chapter 8. Is There Really a Difference? Introduction to Statistical Hypothesis Testing
Answers for Assignment 8.4. (Note. Some answers are given to 2 decimal places to facilitate checking computations. Your answers may differ slightly from those given here due to rounding differences. )
Set A Set B Set C Set D Set E Set F
X 6 4 7 5 4 6.50
SS 4 8 46 2 4.25 5.50
s2 0.80 1.60 9.20 0.40 0.85 1.10
Xs 0.36 0.52 1.24 0.26 0.38 0.43
tobs +2.78 –1.92 +1.61 0.00 –2.63 +3.48
H0 Reject Fail to reject
Fail to reject
Fail to reject Reject Reject
H1 Accept Do not accept
Do not accept
Do not accept Accept Accept
Chapter 8. Is There Really a Difference? Introduction to Statistical Hypothesis Testing
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 8.5 For each of the five sample data sets below, calculate X and Xs , and then find a 95% confidence interval for μ .
Set A Set B Set C Set D Set E 6 15 235 85 8 7 20 240 97 7 8 16 212 115 9 9 17 246 108 5 2 13 232 95 2 4 15 130 7 16 4
For the next four problems, calculate a 95% confidence interval for μ .
Problem 1 Problem 2 X 65.8 X 1010N 121 N 27s 2.5 s 50
Problem 3 Problem 4 X 21 X 50N 61 N 10s 2 s 2.5
Chapter 8. Is There Really a Difference? Introduction to Statistical Hypothesis Testing
Answers for Assignment 8.5 (Note. Some answers are given to 2 decimal places to facilitate checking computations. Your answers may differ slightly from those given here due to rounding differences.)
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 8.6 Read each of the questions carefully and then select the best answer.
1. If you are using a parametric statistical test, then the hypotheses of the test will be about
A. statistics calculated from samples. B. measures of central tendency or variability of a sample. C. the characteristics of a population such as the population mean. D. either the mode or median of a sample.
2. You are testing a hypothesis about how much time preschool children watch
television per day. You hypothesize that the population mean is 212 minutes. Which of the following would be an appropriate null hypothesis for such a study?
A. H0: μ = 212 minutes. B. H0: μ ≠ 212 minutes. C. H0: X = 212 minutes. D. H0: X ≠ 212 minutes.
3. If an experimenter sets α equal to .01, then she is defining a “statistically rare”
event as A. an event occurring more than one time in 100 if the alternative hypothesis
is true. B. an event occurring more than one time in 100 if the null hypothesis is true. C. an event occurring five or fewer times in 100 times if the null hypothesis
is true. D. an event occurring one or fewer times in 100 times if the null hypothesis is
true.
4. In statistical hypothesis testing, a rejection region represents the values of a test statistic that have a probability
A. equal to or less than α if H1 is true. B. equal to or less than α if H0 is true. C. greater than α if H1 is true. D. greater than α if H0 is true.
Chapter 8. Is There Really a Difference? Introduction to Statistical Hypothesis Testing
5. An experimenter tested a sample mean against a hypothesized population mean.
He obtained zobs = +2.41. zcrit for a two-tailed test at the .05 level = 1.96. Based on this information, the experimenter should have
A. accepted H0 and rejected H1. B. rejected both H0 and H1. C. not accepted H0 and accepted H1. D. rejected H0 and accepted H1.
6. If a difference between a sample mean and a hypothesized population mean is
statistically significant, then A. the population mean must be larger than the sample mean. B. H0 was not rejected and H1 was not accepted. C. H0 was rejected and H1 was accepted. D. the value of α was incorrectly set.
7. The one-sample t test is calculated from the formula,
A. μ
X
Xts−
=
B. μ
X
Xts+
=
C. μXts+
=
D. μσX
Xt −=
8. An experimenter uses a one-sample t test to test a sample mean against a
hypothesized population mean. The sample mean was based on 81 scores. The df for this t test are ____.
A. 82 B. 81 C. 80 D. 79
Chapter 8. Is There Really a Difference? Introduction to Statistical Hypothesis Testing
9. You are testing a hypothesis about how much time preschool children watch
television per day. You hypothesize that the population mean is 212 minutes. Which of the following would be an appropriate alternative hypothesis for a one-sample t test on this study?
A. H1: μ = 212 minutes B. H1: μ ≠ 212 minutes C. H1: X = 212 minutes D. H1: X ≠ 212 minutes
10. Suppose the tobs for a one-sample t test falls into a rejection region for a study.
Which of the following is true? A. H1 is not accepted. B. H0 is not rejected. C. The probability of obtaining tobs if H0 is true is greater than the value of
alpha. D. H0 is rejected.
11. Suppose an experimenter found a nonsignificant difference between a sample
mean and a hypothesized population mean. In this instance, any difference observed between the sample mean and the population mean is attributed to
A. the sample being drawn from a population different from that hypothesized.
B. the value of alpha chosen. C. sampling error. D. the standard error of the mean.
12. An experimenter reported that the results of a study using the one-sample t test
were t(40) = 2.363, p < .05. Based on this report, you would know that the experimenter used ____ subjects in the study and the null hypothesis was ____.
A. 41; rejected B. 41; not rejected C. 40; rejected D. 40; not rejected
13. Which of the following situations represents a Type II error in statistical
hypothesis testing? A. H1 is true and H0 is not rejected. B. H0 is true and it is not rejected. C. H1 is accepted when it is true and H0 is false. D. H1 is true and H0 is rejected.
Chapter 8. Is There Really a Difference? Introduction to Statistical Hypothesis Testing
The Basics of Experimentation and Testing for a Difference Between Means
Assignment 9.1 This assignment assists students in learning the symbols, definitions, and formulas discussed in this chapter. The assignment helps students become comfortable with statistical notation and formulas. For some students, completing this assignment several times is necessary to assure they remember the meaning of each symbol and formula. Assignment 9.2 Students are provided with six sets of data from a between-subjects design experiment with two levels of the independent variable. Calculating and interpreting an independent t test, students are to determine if the two groups statistically differ. When appropriate, students will calculate and interpret 2η . Answers are provided on the page following the assignment. Assignment 9.3 Students are provided with six sets of data from a within-subjects design experiment with two levels of the independent variable. Calculating and interpreting a related t test, students are to determine if the two groups statistically differ. When appropriate, students will calculate and interpret 2η . Answers are provided on the page following the assignment. Assignment 9.4 In this assignment, students read four descriptions of research studies and have to determine whether an independent or related t test is appropriate for the design. Students must identify the critical value for the t test and decide if they are going to reject or fail to reject the null hypothesis. Students are also expected to interpret the findings and write a paragraph describing the results following the style of the Publication Manual of the American Psychological Association. Answers are provided on the page following the assignment. Assignment 9.5 This assignment is a set of 15 multiple choice questions that can be used as a homework assignment, in-class assignment, or quiz. The questions are a varied sample of the information covered in this chapter. Answers are provided on the page following the assignment.
Chapter 9. The Basics of Experimentation and Testing for a Difference Between Means
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences , 4/e Assignment 9.1 The purpose of this assignment is to help you to become more comfortable in recognizing what each statistical symbol and formula in Chapter 9 represents. For each item in the table below, either the term or the definition is given. Complete the table with the missing information. For example, for the between-subjects design, write the definition in the appropriate column. It is best to complete this page without looking at your notes or textbook. Once you have completed it, refer back to your notes and textbook to verify you are correct.
Term Definition
Between-subjects design
Within-subjects design
The probability of failing to find a statistically significant difference when one is actually there
Obtaining subjects from among people who are accessible or convenient to the researcher
Extraneous variables
The amount a sample mean differs from its population mean
Confound
Groups in which the subjects are not expected to differ in any systematic or consistent way
Alternative hypothesis
Standard deviation of a theoretical sampling distribution of
1 2X X−
Random assignment
Developed for measuring the effect of the independent variable on the dependent variable
Statistically significant difference
Chapter 9. The Basics of Experimentation and Testing for a Difference Between Means
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 9.2 The data sets below provide scores obtained from two independent groups of subjects, each group was given a different treatment condition, X1 and X2, respectively. For each data set, calculate a t test for independent groups. Then indicate the decisions you would make for the statistical hypotheses. If you do find a statistically significant difference, calculate the size of that effect.
Set A Set B Set C X1 X2 X1 X2 X1 X2 43 39 15 13 540 400 50 37 14 14 460 415 61 35 11 15 600 440 60 38 13 13 520 430 58 40 12 15 430 420 49 36 13 460
t –0.51 Fail to reject H0 Do not accept H1 No need to calculate 2η
If you are having trouble figuring out why you obtained an incorrect answer, it helps to know where to look for errors. If your answer doesn’t match with the answer listed here, check the following:
• Did you include all of the correct values? • Did you take the square root of the entire denominator? • Did you subtract the means in the numerator? • Did you use the variance or sum of squares instead of the standard deviation in the formula?
Set F X1 X2 3 5 5 4 4 3 3 5 5 3
Sum 20 20 n 5 5
X 4 4 SS 4 4 s2 1 1 df 8
t 0.00 Fail to reject H0 Do not accept H1 No need to calculate 2η
Chapter 9. The Basics of Experimentation and Testing for a Difference Between Means
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 9.3 The data sets below provide scores for a set of subjects where each subject was measured twice, Time 1 and Time 2, respectively. For each data set, calculate a t test for related scores. Then indicate the decisions you would make for the statistical hypotheses. If you do find a statistically significant difference, calculate the size of that effect.
Set A Set B Set C Time 1 Time 2 Time 1 Time 2 Time 1 Time 2
Answers for Assignment 9.3 (Note. Some answers are given to 2 decimal places to facilitate checking computations. Your answers may differ slightly from those given here due to rounding differences.)
Set A Time 1 Time 2 D 9 10 –1 9 9 0 9 10 –1 10 12 –2 10 11 –1 10 11 –1
Set C Time 1 Time 2 D 5 5 0 6 3 3 6 6 0 2 5 –3 3 2 1 3 2 1
X 4.17 3.83 SSD 19.33 Npairs 6 Ds 1.97 Ds 0.80 df 5 t +0.42 Fail to reject H0 Do not accept H1 No need to calculate 2η Set D Time 1 Time 2 D 9 11 –2 9 12 –3 9 12 –3 9 7 2 10 10 0 X 9.2 10.4 SSD 18.8 Npairs 5 Ds 2.17 Ds 0.97 df 4 t –1.24 Fail to reject H0 Do not accept H1 No need to calculate 2η
Chapter 9. The Basics of Experimentation and Testing for a Difference Between Means
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 9.4 Read the brief description of the research studies given below. Then, from the information presented in the study, answer the questions that follow. A. A behavioral scientist wanted to see if the mood a person was in increased the
likelihood of the person experiencing a false memory. Positive and negative mood was manipulated by having subjects in a positive mood-group listen to the happy, upbeat song “Beautiful Day” by U2 while different subjects, in a negative mood-group, listened to the sad song “Gloomy Sunday” by Billie Holiday. The subjects were then exposed to a standard false memory-inducing task. In a false memory-inducing task, a subject is briefly shown a list of words with a common theme, such as: rain, ice, weather, hot, drizzle, snow, cool, sunny, foggy, and winter. The subject is then shown the list a second time with a lure word, for example cold, that was not included in the original list, and asked to identify the words in the original list. If the subject identifies the lure, (i.e., cold) as having been in the original list, then a false memory has been created. The dependent variable was the number of lure words identified out of 10 different lists of words. The following results were obtained.
1. Which t test should be used to analyze the scores of this study? 2. What is the value of tcrit for α = 0.05 with a two-tailed test? 3. What decisions do you make with respect to the statistical hypotheses for this study? 4. Write a report of the results of this study following the style of the Publication
Manual of the American Psychological Association. 5. What conclusion do you reach regarding the regarding the effect of the independent
variable in this study?
Chapter 9. The Basics of Experimentation and Testing for a Difference Between Means
B. A psychologist wanted to test if static (still) or dynamic (moving) faces are viewed as more attractive. Subjects judged the attractiveness of faces shown on a screen using a 5-point scale (1 = very unattractive, 5 = very attractive). Half of the faces each subject saw were still photos (i.e., the static condition). The other half of the faces subjects saw were video clips (i.e., the dynamic condition). The psychologist obtained the following results.
1. Which t test should be used to analyze the scores of this study? 2. What is the value of tcrit for α = 0.05 with a two-tailed test? 3. What decisions do you make with respect to the statistical hypotheses for this study? 4. Write a report of the results of this study following the style of the Publication
Manual of the American Psychological Association. 5. What conclusion do you reach regarding the regarding the effect of the independent
variable in this study?
Chapter 9. The Basics of Experimentation and Testing for a Difference Between Means
C. Two psychologists wanted to test if having aging rats live in an environmentally stimulating environment helped to keep their memory from declining. Elderly rats were assigned to one of two conditions: an environmentally simulating environment or a standard laboratory rat environment. The rats spent 12 weeks in their assigned environments, after which they learned a complex maze to receive a food reward. The longer the time taken to learn the maze, the weaker their memory. The following results were obtained. Stimulating Environment: 1X = 750 seconds; 1 105s = Control Environment : 2X = 1250 seconds; 2 127s = tobs(10) = –3.15; 2η .50=
1. Which t test should be used to analyze the scores of this study? 2. What is the value of tcrit for α = 0.05 with a two-tailed test? 3. What decisions do you make with respect to the statistical hypotheses for this study? 4. Write a report of the results of this study following the style of the Publication
Manual of the American Psychological Association. 5. What conclusion do you reach regarding the regarding the effect of the independent
variable in this study?
Chapter 9. The Basics of Experimentation and Testing for a Difference Between Means
D. Students in a social psychology class learned that people who are exposed to images of “perfect bodies” as we often see in models or movie stars, experience a decline in positive attitudes about their own body. When the students were asked to design a study for their research class, they decided to test if the same effect is true for attitudes about intelligence. They obtained a group of subjects and randomly assigned them to one of two conditions. In one condition, the subjects saw a short video of people behaving in a very foolish fashion. In the other condition, subjects saw a short video of people behaving in an extremely intelligent fashion. Following the completion of a distracting activity, the subjects were given a measure of attitude about intelligence. Higher scores on the measure indicate that subjects believe themselves to be more intelligent in relation to others, whereas lowers scores indicate that subjects believe themselves to be less intelligent in relation to others. The following results were obtained. Intelligent Exposure: 1X = 21.0; 1 4.3s = Foolish Exposure: 2X = 24.5; 2 4.6s = tobs(200) = –1.89
1. Which t test should be used to analyze the scores of this study? 2. What is the value of tcrit for α = 0.05 with a two-tailed test? 3. What decisions do you make with respect to the statistical hypotheses for this study? 4. Write a report of the results of this study following the style of the Publication
Manual of the American Psychological Association. 5. What conclusion do you reach regarding the regarding the effect of the independent
variable in this study?
Chapter 9. The Basics of Experimentation and Testing for a Difference Between Means
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 9.5 Read each of the questions carefully and then select the best answer.
1. An experimenter obtains subjects for her experiment by asking people she knows to participate in her experiment. This form of obtaining subjects is called ____ sampling.
A. simple random B. convenience C. stratified random D. selective
2. A psychologist was interested in determining the difference in ease between
reading materials on a computer screen and on paper. One group of subjects was given a set of materials to read on a computer screen while a second group of subjects was given the same material to read in a printed booklet. The psychologist measured the time each group took to read the materials. The levels of the independent variable in this experiment are:
A. reading the material on a screen and reading the material in a booklet. B. the amount of time each group takes to read the material. C. the type of presentation given to the subjects. D. the actual material given to the subjects to read.
3. A psychologist was interested in determining the difference in ease between
reading materials on a computer screen and on paper. One group of subjects was given a set of materials to read on a computer screen while a second group of subjects was given the same material to read in a printed booklet. The group reading the material on the computer screen was strongly encouraged to read the material as quickly as possible. The psychologist did not give the same encouragement to the group reading the material in booklet form. In this experiment, the encouragement given one group but not the other is
A. the independent variable. B. the dependent variable. C. the experimental treatment. D. an extraneous variable.
Chapter 9. The Basics of Experimentation and Testing for a Difference Between Means
4. A psychologist was interested in determining the difference in ease between
reading materials on a computer screen and on paper. One group of subjects was given a set of materials to read on a computer screen while a second group of subjects was given the same material to read in a printed booklet. Suppose the psychologist found that the mean amount of time to read the material was less for the booklet than for the material presented on the computer screen. In order to decide that the difference in the means was due to the way in which the material was read, the experimenter will need to determine
A. how much of a difference in the means might be expected from the effect of the dependent variable.
B. the mode for each group. C. how much of a difference in the means might be expected from the effect
of the independent variable. D. how much of a difference in the means might be expected from sampling
error alone.
5. The formula for the t-test for independent groups is ____.
A. μσX
X −
B. ( )2
1
X X
N
−∑
−
C. 1 2
1 2X X
X Xs
−
−
D. 2 2
1 1 2 2
1 2 1 2
( 1) ( 1) 1 12
n s n sn n n n
⎡ ⎤ ⎡ ⎤− + −+⎢ ⎥ ⎢ ⎥+ −⎣ ⎦ ⎣ ⎦
6. If all possible pairs of samples of a certain size are selected from a population, the
distribution of the difference between the two samples means for each pair is called the
A. t distribution. B. sampling distribution of the difference between means. C. standard error. D. sampling distribution of the mean.
Chapter 9. The Basics of Experimentation and Testing for a Difference Between Means
7. An experimenter compares two groups of subjects on a task involving the
perception of illusions. The null hypothesis for the tind on the data of this experiment is H0: ____.
A. 1 2μ μ= B. 1 2μ μ≠ C. 1 2X X= D. 1 2X X≠
8. If an experimenter comparing two groups of people on a task involving the
perception of illusions had 20 subjects in one group and 18 in the other, then the tind on the data of this experiment would have ____ degrees of freedom.
A. 2 B. 34 C. 36 D. 38
9. If tobs for the t test for two independent groups does not fall into a rejection region,
then A. a Type I error may have occurred. B. the null hypothesis is rejected and the alternative hypothesis is accepted. C. the null hypothesis is not rejected. D. the sample means represent two different population means.
10. One of the assumptions of the t test for two independent groups is that the
A. variances of the populations sampled are equal. B. sample means differ significantly. C. variances of the samples are equal. D. sample means do not differ significantly.
11. The power of a statistical test is defined as the probability of rejecting H0 when it
is ____and H1 is ____. A. true; true B. true; false C. false; true D. false; false
12. Suppose a researcher conducts an experiment in which there is great deal of
variability in the dependent variable measured. This large variability will A. increase the probability of a Type I error. B. increase the power of the statistical test used. C. allow the experimenter to use a smaller sample of subjects. D. decrease the power of the statistical test used.
Chapter 9. The Basics of Experimentation and Testing for a Difference Between Means
13. The value of 2η in an experiment provides a measure of the
A. amount of error variation in the scores. B. effect size of the independent variable. C. effect size of the dependent variable. D. how large a sample of subjects is needed in the experiment.
14. An experimenter summarized the results of a t test for two independent groups as
t(64) = +1.723, p >.05. From this summary you would know that the total number of subjects in the study was (N) ____ and the null hypothesis was ____.
A. 64; rejected B. 64; not rejected C. 66; rejected D. 66; not rejected
15. An experimenter uses a within-subjects design to test a research hypothesis. In
this design A. one group of subjects is given both levels of the independent variable. B. two equivalent groups of subjects are created. C. more subjects are needed than would be needed for a between-subjects
design. D. each level of the independent variable is given to a different group of
subjects.
Chapter 9. The Basics of Experimentation and Testing for a Difference Between Means
One-Factor Between-Subjects Analysis of Variance Assignment 10.1 This assignment is a set of four data sets from one-way between subjects designs. Students are to calculate a between-subjects analysis of variance, determine if there is a statistically significant difference, and calculate a Tukey HSD CD and 2η when appropriate. Answers are provided on the page following the assignment. Assignment 10.2 This assignment is a set of two data sets from one-way between subjects designs that include a theoretical research scenario relating to the data. Students are to calculate a between-subjects analysis of variance, determine if there is a statistically significant difference, and calculate a Tukey HSD CD and 2η when appropriate. Students are also expected to interpret the findings and write a paragraph describing the results following the style of the Publication Manual of the American Psychological Association. Answers are provided on the page following the assignment. Assignment 10.3 This assignment is a set of 15 multiple choice questions that can be used as a homework assignment, in-class assignment, or quiz. The questions are a varied sample of the information covered in this chapter. Answers are provided on the page following the assignment.
Chapter 10. One-Factor Between-Subjects Analysis of Variance
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 10.1 For each of the following data sets, complete a between-subjects analysis of variance. Determine if the differences between the means are statistically significant with α = .05. If needed, find the Tukey HSD CD for post hoc comparisons and calculate 2η .
Data Set A
1AX 2AX
6 11 7 7 4 9 5 10 3 9
Data Set B
1AX 2AX 3AX
17 18 16 15 19 17 16 20 15 18 18 18 19 15 15
Data Set C
1AX 2AX 3AX
5 9 8 5 7 6 7 8 3 7 12 5 3 10 4
Chapter 10. One-Factor Between-Subjects Analysis of Variance
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 10.2 Complete a one-factor between-subjects analysis of variance for each of the following data sets. Determine if the differences between the means are statistically significant with α = .05. If needed, find the Tukey HSD CD for post hoc comparisons and calculate 2η . Describe the results in a paragraph following the style of the Publication Manual of the American Psychological Association. A. Many students switch majors after coming to college, but students who come to
college with an “undeclared” major are likely to struggle more academically than those students who have an academic major. Some colleges help undeclared students by having them take a first-year experience class, which deals with many of the problems that first-year students encounter. One professor, however, hypothesized that an activity that trains students to think about themselves in the future would be more effective than a typical first-year experience class. In this activity, students practice thinking about their professional future-self and the personal future-self. Then, as students consider possible majors, they are encouraged to think about themselves in the future in the context of that particular career. To test this hypothesis, the professor obtained a group of 15 undeclared students and randomly assigned them to one of three conditions: (1) students in the control group simply had a standard semester with no special intervention or courses, (2) students in the standard class condition were assigned to a first-year experience class designed to assist them in becoming acclimated to college and selecting a major, and (3) students in the modified class attended a class similar to the typical first-year experience class, except the students were trained to think about their professional and personal future selves when evaluating a possible career choice. A measure of “academic struggling,” which included questions on comfort level in college, sense of self worth, sense of control of what happens academically, and ability to achieve academic success, was used as the dependent variable. The scores obtained on this measure are given below for each class condition. Use these data to test the professor’s hypothesis.
Type of Class
Control Standard Modified
95 86 75 85 87 70 92 84 80 84 93 81 91 88 74
Chapter 10. One-Factor Between-Subjects Analysis of Variance
B. A school counselor hypothesized that exposing students to an online program allowing access to sample questions and strategies about how to answer those questions would improved their performance on a standardized achievement test. To evaluate this hypothesis, the counselor randomly assigned 10 students planning to take the achievement test to one of two conditions. The control group took the test without any prior preparation. The training group received 3 hours of practice with the online program. The results of the students’ performance on the academic achievement test are given in the table below. Test to see if the training improved students’ performance.
Group
Control Training 860 970 850 925 940 950 840 930 920 1010
Chapter 10. One-Factor Between-Subjects Analysis of Variance
5. In the equation partitioning the score of a subject in a one-factor between-
subjects analysis of variance, the term A GX X− reflects A. the effect of factor A plus sampling error. B. only sampling error. C. the total variation in the score. D. only the effect of factor A.
6. An experimenter used a one-factor between-subjects analysis of variance with a
total of 40 subjects who were randomly assigned to one of four equal-sized groups. The df for SSA in this analysis are ____.
35 in a one-factor between-subjects analysis of variance. MSA for this analysis is then ____.
A. 3.00 B. 0.33 C. 20.00 D. 46.25
8. A psychologist used a one-factor between-subjects analysis of variance on the
scores of an experiment. If the independent variable in this experiment has an effect on the scores, then MSA should be ____ MSError and the value of F should be ____.
A. about equal to; about 1.00 B. less than; less than 1.00 C. less than; greater than 1.00 D. greater than; greater than 1.00
9. An experimenter used a one-factor between subjects design with five levels of the
independent variable. The null hypothesis for the one-factor between-subjects analysis of variance for this experiment is ____.
A. 1 2 3 4 5
μ μ μ μ μA A A A A= = = =
B. 1 2 3 4 5 6
μ μ μ μ μ μA A A A A A= = = = =
C. 1 2 3 4
μ μ μ μA A A A= = =
D. the μ A ’s are not all equal
Chapter 10. One-Factor Between-Subjects Analysis of Variance
10. Suppose an experimenter failed to reject H0 in a one-factor between-subjects
analysis of variance. He or she would then conclude that the A. sample means differ because of the effect of the independent variable. B. sample means differ more than would be expected from sampling error
alone. C. variances of each group are equal. D. sample means differ because of sampling error.
11. Multiple comparison tests are used to find which ____ differ significantly from
each other in a one-factor multilevel design. A. population variances B. grand means C. group means D. mean squares
12. The ____ in an experiment is the probability of making at least one Type I error
when performing statistical tests on an experiment. A. error rate B. relative error frequency C. error probability D. mistake rate
13. Which of the following situations would require the use of a multiple comparison
test? A. Four levels of an independent variable are manipulated in an experiment
and Fobs is nonsignificant. B. Two levels of an independent variable are manipulated in an experiment
and Fobs is nonsignificant. C. Two levels of an independent variable are manipulated in an experiment
and Fobs is statistically significant. D. Four levels of an independent variable are manipulated in an experiment
and Fobs is statistically significant.
14. A researcher reported the results of a one-factor between-subjects analysis of variance as F(2, 60) = 4.63, p < .05. From this report you would know that a total of ____ subjects were used in the experiment and the null hypothesis was
A. 62; rejected. B. 63; rejected. C. 63; not rejected. D. 62; not rejected.
Chapter 10. One-Factor Between-Subjects Analysis of Variance
Two-Factor Between-Subjects Analysis of Variance Assignment 11.1 This assignment is a set of six data sets from two-factor between subjects designs. Students are to calculate the cell means and the main effect means for each data set. The data sets for this assignment are also used in Assignment 11.2. Answers are provided on the page following the assignment. Assignment 11.2 This assignment is a set of six data sets from two-factor between subjects designs. The data sets are the same as those of Assignment 11.1. Students are to calculate a between-subjects analysis of variance, determine if there are any statistically significant differences, and calculate the Tukey HSD CD for simple effects and 2η when appropriate. Students are then to interpret the outcome represented in the data set using the cell and main effect means they found for Assignment 11.1. Answers are provided on the page following the assignment. Assignment 11.3 This assignment includes a research scenario and results from a two-factor between subjects design. Students are to calculate the cell and main effect means. Students will also calculate a between-subjects analysis of variance and determine if there are statistically significant main effects or an interaction of the independent variables. Students are also expected to interpret the findings and write a paragraph describing the results following the style of the Publication Manual of the American Psychological Association. Answers are provided on the page following the assignment. Assignment 11.4 This assignment is a set of 15 multiple choice questions that can be used as a homework assignment, in-class assignment, or quiz. The questions are a varied sample of the information covered in this chapter. Answers are provided on the page following the assignment.
Chapter 11. Two-Factor Between-Subjects Analysis of Variance
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 11.1 Find the cell and main effect means for each of the following data sets.
Answers for Assignment 11.1 (Note. Some answers are given to 3 decimal places to facilitate checking computations. Your answers may differ slightly from those given here due to rounding differences.)
Data Set A 1A 2A
1B 5.71 5.86 5.79
2B 6.43 8.29 7.36
6.07 7.07
Data Set B 1A 2A
1B 93.4 88.6 91.0
2B 96.6 88.4 92.5
95.0 88.5
Data Set C 1A 2A
1B 48.4 52.2 50.3
2B 51.2 57.4 54.3
49.8 54.8
Data Set D 1A 2A
1B 35.13 48.13 41.63
2B 35.00 39.00 37.00
35.06 43.56
Data Set E 1A 2A
1B 37.250 42.500 39.875
2B 40.500 37.750 39.125
38.875 40.125
Data Set F 1A 2A
1B 83.2 88.8 86.0
2B 88.8 90.8 89.8
86.0 89.8
Chapter 11. Two-Factor Between-Subjects Analysis of Variance
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 11.2 The following data sets are the same as those presented in Assignment 11.1. For each data set, calculate a two-factor between subjects analysis of variance. Using a two-tailed test with .05α = , decide whether there is a statistically significant: (1) main effect for Factor A, (2) main effect for Factor B, and (3) an interaction between Factors A and B. If necessary, calculate a Tukey HSD CD for simple effects. Present 2η where appropriate. After completing the statistical analysis, interpret the outcome shown in each data using the cell and main effect means you found for Exercise 11.1.
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 11.3 For the following research scenario, find the cell and main effect means. Then analyze the scores to determine (1) if there is a main effect for either independent variable and (2) if there is an interaction of the independent variables. If needed, use the Tukey HSD test to determine the statistically significant simple effects. Use .05α = . Where appropriate, calculate 2η . Describe the results in a paragraph following the style of the Publication Manual of the American Psychological Association. Suppose you were asked to learn a list of words. One way would be to simply memorize the words. Another approach would be to try to use a mnemonic (i.e., memory) aid. One such mnemonic aid is called the “word-pegging” technique. This technique is based on the children’s rhyme “one is a bun, two is a shoe, three is a tree,” and so on. Using this technique, a person uses the rhyme to form a mental image of the word to be learned. For example, suppose the first three words in the list to be learned were luggage, pancake, and garage. Using the rhyme, a person would form an image of a piece of luggage in a bun, an image of a pancake wrapped around a shoe, and an image of a tree growing in a garage. It appears this strategy might work well with concrete words, words such as those given above that refer to concrete objects all of us have seen in our lives. But would the strategy work with abstract words, such as heat, debt, or justice, words that don’t refer to concrete objects? A psychologist hypothesized that the word-pegging strategy would improve learning with concrete words, but not abstract words. The psychologist also hypothesized that learning using simple memorization without a word-pegging strategy would not differ between concrete and abstract words. To test this hypothesis, the psychologist randomly assigned 20 students to one of four treatment conditions: (1) using a pegging strategy with concrete words, (2) not using a pegging strategy with concrete words, (3) using a pegging strategy with abstract words, and (4) not using a pegging strategy with abstract words. Five subjects were assigned to each treatment condition. Each subject was given one trial to learn a list of 20 words. After the learning trial, the subjects were asked to recall as many words from the list as possible. The following results were obtained. The scores represent the number of words correctly recalled by a subject.
Chapter 11. Two-Factor Between-Subjects Analysis of Variance
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 11.4 Read each of the questions carefully and then select the best answer.
1. A 3 4× factorial design has A. 12 independent variables. B. four independent variables, each with three levels. C. two independent variables, one with 3 levels and one with 4 levels. D. three independent variables, each with 4 levels.
2. A 3 2× factorial design creates ____ cells.
A. six B. two C. four D. three
3. The difference ____ represents the main effect of factor A in a 2 2× factorial
design. A.
1 2B BX X−
B. 1 2B BX X+
C. 1 2A AX X−
D. 1 2A AX X+
4. ____ is the definition of an interaction in a factorial design.
A. A situation in which the effect of one independent variable depends upon the level of the other independent variable
B. The effect of one independent variable averaged across all levels of the other independent variable
C. A situation in which the main effect of one independent variable is the same as the main effect of the other independent variable
D. A situation in which the main effects of each independent variable are different from each other
5. When computing SS in a two-factor between-subjects analysis of variance, the
difference B GX X− is involved in the calculation of ____. A. SSA B. A BSS × C. SSError D. SSB
Chapter 11. Two-Factor Between-Subjects Analysis of Variance
6. The term ____represents the effect of the interaction of factors A and B in the partitioned score of a subject in a two-factor between-subjects analysis of variance.
A. B GX X− B. AB A B GX X X X− − + C. AB A B GX X X X+ + − D. AB A B GX X X X− − −
7. An experimenter used a 2 3× between-subjects design with 11 subjects randomly
assigned to each treatment condition. For this design, the df for A BSS × are equal to ____ and the df for SSError are equal to ____.
A. 1; 60 B. 2; 60 C. 2; 66 D. 6; 66
8. Suppose you performed a two-factor between-subjects analysis of variance and
obtained the following values: SSTotal = 290; SSA = 14; SSB = 20; A BSS × = 40; SSError = 216; dfTotal = 77; dfA = 1; dfB = 2; A Bdf × = 2; and dfError = 72. Given these values, MSB equals ____ and A BMS × equals ____.
A. 14; 3 B. 20; 10 C. 10; 20 D. 20; 20
9. Suppose you performed a two-factor between subjects analysis of variance and
obtained the following values: MSA = 12.00; MSB = 8.00; A BMS × = 16; MSError = 4. Then Fobs for factor A equals ____, Fobs for factor B equals ____, and Fobs for the interaction of factors A and B equals ____.
A. 3.00; 2.00; 4.00. B. 2.00; 3.00; 4.00. C. 4.00; 3.00; 2.00. D. 2.00; 4.00; 3.00.
10. Suppose an experimenter used a 4 3× between subjects design. The null
hypothesis for factor B in the analysis of variance of this design is ____. A.
1 2 3 4 5μ μ μ μ μB B B B B= = = =
B. 1 2 3 4
μ μ μ μB B B B= = =
C. 1 2 3
μ μ μB B B= =
D. the μB ’s are not all equal
Chapter 11. Two-Factor Between-Subjects Analysis of Variance
11. Suppose an experimenter used a 2 4× between subjects design. The alternative hypothesis for factor B in the analysis of variance of this design is ____.
A. 1 2 3 4 5
μ μ μ μ μB B B B B= = = =
B. 1 2 3 4
μ μ μ μB B B B= = =
C. 1 2 3
μ μ μB B B= =
D. the μB ’s are not all equal
12. A psychologist reported the following values of Fobs for a two-factor between-subjects analysis of variance: F(1, 60) for factor A = 2.46; F(1, 60) for factor B = 3.24; and F(1, 60) for the interaction of factors A and B = 3.87. The value of Fcrit for 1 and 60 df = 3.15. Given these values, you would ____ H0 for factor A, ____ H0 for factor B, and ____ H0 for the interaction of actors A and B.
A. reject; reject; reject B. reject; fail to reject; fail to reject C. fail to reject; fail to reject; fail to reject D. fail to reject; reject; reject
13. The comparison, ____, represents a simple effect of factor B in a 2 2× between-
subjects design. A.
1 2 2 1A B A BX X−
B. 1 1 2 2A B A BX X−
C. 2 1 2 2A B A BX X−
D. 1 2 2 2A B A BX X−
14. A(n) ____ main effect in a factorial design is one that cannot be meaningfully
interpreted because of the interaction of the independent variables. A. artifactual B. spurious C. redundant D. unusual
15. Suppose an educational researcher manipulated the font size of written text
material and background noise in an experiment on reading comprehension. She reported the results of her analysis of variance on the interaction of the factors in the experiment as F(2, 48) = 4.21, p < .05. Given this report, you would know that a ____ design was used and the F for the interaction was ____.
A. 2 2× ; statistically significant B. either a 2 3× or a 3 2× ; statistically significant C. either a 2 3× or a 3 2× ; nonsignificant D. either a 3 4× or a 4 3× ; statistically significant
Chapter 11. Two-Factor Between-Subjects Analysis of Variance
One-Factor Within-Subjects Analysis of Variance Assignment 12.1 This assignment provides six data sets from one-way within-subjects designs. Students are to calculate a within-subjects analysis of variance, determine if there is a statistically significant difference between the means, and calculate a Tukey HSD CD and 2η when appropriate. Answers are provided on the page following the assignment. Assignment 12.2 This assignment is a data set from a one-way within-subjects design that includes a theoretical research scenario relating to the data. Students are to calculate a within-subjects analysis of variance, determine if there is a statistically significant difference between the means, and calculate a Tukey HSD CD and 2η if needed. Students are also expected to interpret the findings and write a paragraph describing the results following the style of the Publication Manual of the American Psychological Association. Assignment 12.3 This assignment is a set of 15 multiple choice questions that can be used as a homework assignment, in-class assignment, or quiz. The questions are a varied sample of the information covered in this chapter. Answers are provided on the page following the assignment.
Chapter 12. One-Factor Within-Subjects Analysis of Variance
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 12.1 Assume that the following data sets represent the scores of subjects who were given each level of the independent variable indicated. For each data set find X and s, then complete a within-subjects analysis of variance. Determine if the differences between the means are statistically significant with α = .05. When appropriate, find the Tukey HSD CD for post-hoc tests, and calculate 2η .
Data Set A
1AX 2AX 3AX
61 64 60 59 66 59 57 67 63 58 69 64 61 64 58
Data Set B
1AX 2AX 3AX
89 78 79 82 82 85 80 79 82 86 81 76 84 79 75 89 81 77 Data Set C
1AX 2AX
91 112 90 110 93 99 99 104 92 100
Chapter 12. One-Factor Within-Subjects Analysis of Variance
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 12.2 Complete a one-factor within-subjects analysis of variance for the following problem. Determine if the differences between the means are statistically significant with α = .05. If needed, find the Tukey HSD CD for post hoc comparisons and the value of 2η . Describe the results in a paragraph following the style of the Publication Manual of the American Psychological Association. A psychologist interested in the effect of caffeine consumption on working memory (the amount of information one can remember at a given time) hypothesized that caffeine ingestion would decrease working memory function. To test this hypothesis students were asked to report to the research lab once a week for three weeks. On one of their visits the students were given a drink with no caffeine, on a different visit they were given a drink with caffeine equivalent to that found in 1.5 cups of coffee, and on a third visit, they were given a drink that contained caffeine equivalent to that found in 3 cups of coffee. The order in which the subjects received the three conditions was varied. After the subjects consumed the drink and following a waiting period of 20 minutes, they were asked to completed a working memory type task involving a “concentration type” computer game. Sixteen face-down cards were visible on the computer monitor. Using the mouse, the subjects could turn over two cards at a time, as they searched for a matched pair. The subjects were timed to see how long it took to identify all 8 pairs. The shorter the time it took to complete the task, the larger their working memory was estimated to be. The times obtained in seconds are given in the table below.
Caffeine Condition (A)
None (A1) Moderate (A2) High (A3)
22 26 28
16 17 24
38 36 41
28 32 31
24 30 32
34 33 36
Chapter 12. One-Factor Within-Subjects Analysis of Variance
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 12.3 Read each of the questions carefully and then select the best answer.
1. If an experimenter used a one-factor within-subjects design with four levels of the independent variable, then each subject would be tested and measured under ____ levels of the independent variable.
A. one B. two C. three D. four
2. The effect of the independent variable is reflected in the ____ of a one-factor
within-subjects analysis of variance. A. SSTotal B. ASS C. SSS D. A SSS ×
3. A psychologist used a one-factor within-subjects design with three levels of the
independent variable and a total of 13 subjects. For this design, the A Sdf × equals ____.
A. 13 B. 24 C. 26 D. 39
4. To obtain the MSA in a one-factor within-subjects analysis of variance, the ____ is
divided by the ____. A. A SSS × ; dfA B. SSS; dfA C. SSA; A Sdf × D. SSA; dfA
Chapter 12. One-Factor Within-Subjects Analysis of Variance
5. In a one-factor within-subject analysis of variance, the F statistic is obtained by
dividing ____ by ____. A. A SMS × ; MSA B. MSS; MSA C. MSA; A SMS × D. MSA; dfA
6. An experimenter calculated an analysis of variance on a one-factor within-
subjects and found SSA = 40.00, A SSS × = 88.00, SSS = 44.00, dfA = 2, dfS = 11 and
A Sdf × = 22. Given these values, MSA for this analysis equals ____. A. 2.00 B. 4.00 C. 20.00 D. 44.00
7. Suppose you calculated a one-factor within-subjects analysis of variance and
found MSA = 60.00, A SMS × = 15.00, and MSS = 10.00. Given these values, Fobs for this analysis equals ____.
A. 4.00 B. 6.00 C. 1.50 D. 0.67
8. An experimenter used a one-factor within-subjects design with four levels of the
independent variable. For this design, the null hypothesis for the analysis of variance is ____.
A. 1 2 3 4 5
μ μ μ μ μA A A A A= = = =
B. 1 2 3
μ μ μA A A= =
C. 1 2 3 4
μ μ μ μA A A A= = =
D. the Aμ ’s are not all equal
9. Suppose the null hypothesis for a one-factor within-subjects analysis of variance is true. In this situation, you would expect the value of Fobs to be ____ and the null hypothesis should ____.
A. about zero; not be rejected. B. about 1.00; not be rejected. C. very large; be rejected. D. very large; not be rejected
Chapter 12. One-Factor Within-Subjects Analysis of Variance
10. An experimenter failed to reject the null hypothesis in a one-factor within-
subjects analysis of variance. Thus, she concluded that A. the variances of each of the treatment conditions were equal. B. the treatment means differed because of the effect of the independent
variable. C. the variances of each of the treatment conditions were unequal. D. any differences between the treatment means were due only to sampling
error.
11. An experimenter would need to use the Tukey HSD test for post hoc comparisons with a one-factor within-subjects analysis of variance if
A. two levels of an independent variable were manipulated and Fobs was nonsignificant.
B. two levels of an independent variable were manipulated and Fobs was statistically significant.
C. four levels of an independent variable were manipulated and Fobs was nonsignificant.
D. four levels of an independent variable were manipulated and Fobs was statistically significant.
12. A psychologist reported the results of a one-factor within-subjects analysis of
variance as F(3, 33) = 3.47, p < .05. From this report you would know that ____ subjects were used in the study and the differences among the treatment condition means were ____.
A. 12; nonsignificant B. 12; statistically significant C. 34; nonsignificant D. 34; statistically significant
13. A researcher reported the results of a one-factor within-subjects analysis of
variance as F(4, 45) = 2.04, p > .05. Which of the following statements is true about this study?
A. The value of Fobs was nonsignificant. B. The Tukey HSD test was needed to find which pairwise comparisons were
statistically significant. C. There were 45 subjects in the study. D. H0 was
1 2 3 4μ μ μ μA A A A= = = .
Chapter 12. One-Factor Within-Subjects Analysis of Variance
14. A one-factor within-subjects design ____ a one-factor between-subjects design.
A. is usually less sensitive to the effects of the independent variable than B. is not affected by practice on a task as is C. usually requires fewer subjects than does D. is not open to the effects of multiple treatments as is
15. A change in a subject’s performance on the measure of the dependent variable in
a one-factor within-subjects design due to simply repeating the performance of the task is called ____ effect.
A. a practice B. a repetition C. the sensitivity D. the within-subjects
Chapter 12. One-Factor Within-Subjects Analysis of Variance
Assignment 13.1 This assignment assists students in learning the symbols and definitions discussed in this chapter. The assignment helps students become comfortable with statistical notation and formulas. For some students, completing this assignment more than once is necessary to assure they remember the meaning of each symbol and formula. Assignment 13.2 This assignment has students look at scatterplots to estimate the correlation coefficient that is associated with the graph. Answers are provided on the page following the assignment. Assignment 13.3 Given small data sets, students are to calculate the Pearson correlation coefficient, determine whether the relationship is statistically significant, and when appropriate, calculate r 2. Answers are provided on the page following the assignment. Assignment 13.4 Given small data sets, students are to calculate the Spearman rank-order correlation coefficient and determine whether the relationship is statistically significant. Assignment 13.5 This assignment is a set of 15 multiple choice questions that can be used as a homework assignment, in-class assignment, or quiz. The questions are a varied sample of the information covered in this chapter. Answers are provided on the page following the assignment.
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 13.1 The purpose of this assignment is to help you to become more comfortable in knowing the meaning of important terms covered in Chapter 13. For each item in the table below, either the term or the definition is given. Complete the following table with the missing information. For example, the term correlation coefficient is provided in the left column. In the right column, write the definition for the term. It is best to complete this page without looking at your notes or textbook. Once you have completed it, refer back to your notes and textbook to verify you are correct.
Term Definition (also include formula as appropriate)
A change in one variable is related to a consistent change in another variable
Correlation coefficient
A distribution in which two scores are obtained from each subject
A graph of a bivariate distribution. The X value is plotted on the horizontal axis and the Y variable is plotted on the vertical axis
A relationship between two variables that can be described by a straight line
Positive relationship
Negative relationship
Pearson correlation coefficient
The value of ( )( )X X Y Y− −∑ for variables X and Y
Outlier
The value of r2 indicating the common variance of variables X and Y
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 13.2 Five scatterplots are shown below. For each scatterplot, estimate the correlation of the relationship between the X and Y variables. The X variable is represented on the abscissa and the Y variable on the ordinate. The Pearson r for each data set is given on the answer sheet.
Answers for Assignment 13.2 Remember, the purpose of this assignment is for you to practice looking at scatterplots and estimating correlation coefficients. The values listed below are actual correlation coefficients, so your answers may be good estimates, but not exactly match the values listed below.
Data Set 1: r = +0.76 Data Set 2: r = –0.92 Data Set 3: r = –0.34 Data Set 4: r = +1.00 Data Set 5: r = 0.00 ( Note: although the X and Y scores for this data set are perfectly related, they are not linearly related, hence the Pearson correlation between them is 0.)
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 13.3 For each of the data sets given below, calculate the Pearson correlation coefficient using the definitional formula. Determine if the relationship between the two variables is statistically significant at the .05 level. If appropriate, calculate r2 , then answer the questions that follow.
Set A Set B X Y X Y 5 5 3 7 4 5 4 7 8 7 5 5 9 7 6 5 6 3 7 5 7 5 8 3 3 3 9 3
Set C Set D
X Y X Y 3 3 5 7 4 3 4 3 5 5 8 5 6 5 9 5 7 5 6 5 8 7 7 3 9 7 3 7
Set E Set F
X Y X Y 6 5 5 3 7 3 7 3 3 7 6 5 8 7 8 5 9 3 4 5 5 5 9 7 4 5 3 7
1. Compare the means and SSX and SSY for each data set to each other data set. 2. As you notice, the means for each group are the same, as are the SS. Thus, why is
there a difference in the correlation coefficient for each data set? 3. What is the critical value for each data set? How do they compare?
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 13.4 The data sets below present ordinal data representing ranked scores. For each data set, find the Spearman rank-order correlation coefficient and determine if the two variables are significantly related at the .05 level.
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 13.5 Read each of the questions carefully and then select the best answer.
1. Two variables are said to covary when A. a change in one of the variables is accompanied by a consistent change in
the other variable. B. both variables have the same mean and standard deviation. C. as one variable increases, the other may increase or decrease. D. a change in one of the variables may or may not be accompanied by a
change in the other variable.
2. Supposed you have obtained two set of scores on a group of subjects. You notice that as the score on one of the variables increases, the score on the other decreases. This relationship represents a ____ or ____ relationship between the variables.
A. negative; direct B. positive; direct C. positive; inverse D. negative; inverse
3. The term in the numerator of the Pearson correlation coefficient is the
A. standard deviation of the X variable multiplied by the standard deviation of the Y variable.
B. SSX plus the SSY. C. square root of the cross products of X and Y. D. cross products of X and Y.
4. Suppose you obtain a value of r = +.68. The + indicates the ____ of the
relationship of the two variables. A. strength B. direction, direct or inverse C. statistical significance D. degree
5. If you had two sets of scores that were completely unrelated, then you would
expect robs calculated on those variables to be A. a large positive value. B. about equal to zero. C. greater than 1.00. D. a large negative value.
6. Which of the values of robs listed below would represent the strongest association
between two variables? A. +10.00 B. –.60 C. –.89 D. +.75
7. Suppose there is a negative correlation between the amount of daily exercise a
person engages in and his or her blood pressure. Given this relationship, you would expect that
A. greater daily exercise is associated with lower blood pressure. B. greater daily exercise is associated with higher blood pressure. C. there is no relationship between amount of daily exercise and blood
pressure. D. the more a person exercises, the higher his or blood pressure will be.
8. ____ provides the coefficient of determination.
A. robs
B. r
C. r2
D. r r×
9. If you had two set of scores for which robs = +.60, then you would know that ____
percent of the variance in the scores of one of the variables is associated with the variance in the scores of the other variable.
A. 60 B. 40 C. 36 D. zero
10. Suppose you know that there is a strong negative correlation between the amount
of daily exercise and blood pressure. From simply knowing this relationship, which of the following is an appropriate conclusion to reach?
A. People should exercise more in order to decrease their blood pressure. B. Blood pressure and amount of daily exercise are related, but we do not
know what causes the relationship. C. People with high blood pressure generally exercise more than people with
low blood pressure. D. People with high blood pressure should exercise more in order to decrease
11. The null hypothesis for a test of statistical significance of the Pearson correlation
coefficient is ____. A. 0r = B. 0r ≠ C. ρ 0= D. ρ 0≠
12. A psychologist reported the results of a correlational study as r(25) = –.473. rcrit (25) = .381. Based on this information you would know that the H0 was ____ and was ____.
A. ρ 0= ; rejected. B. ρ 0= ; not rejected. C. ρ 1= ; rejected. D. ρ 1= ; not rejected.
13. An experimenter reported the results of a correlational study as r (19) = +.341, p >
.05. Which of the following statements is true of this result? A. H0 was ρ 1= . B. rcrit was .341. C. H0 was ρ 1≠ . D. robs was not statistically significant at the .05 level.
14. If two sets of scores are at the ____ level of measurement, then the Spearman
correlation coefficient, rs , is appropriate to determine if there is a relationship between them.
A. nominal B. ordinal C. interval D. ratio
15. An experimenter reported the results of a study using the Spearman correlation
coefficient as rs (23) = +.71, p < .05. From this report you would know that H0 was ____ and was ____.
A. Sρ 0= ; not rejected B. Sρ 0= ; rejected C. Sρ 1= ; rejected D. Sρ 1= ; not rejected
Regression Analysis: Predicting Linear Relationships Assignment 14.1 This assignment assists students in learning the symbols, definitions, and formulas discussed in this chapter. The assignment helps students become comfortable with statistical notation and formulas. For some students, completing this assignment several times is necessary to assure they remember the meaning of each symbol and formula. Assignment 14.2 Students are to find the least squares regression line for six small data sets. These data sets were used to calculate the Pearson r in Assignment 13.3. Answers are provided on the page following the assignment. Assignment 14.3 This assignment presents a research scenario and a small data set. Students are to find the least squares regression line, the residual for each pair of scores, and interpret the regression line. Answers are provided on the page following the assignment. Assignment 14.4 This assignment is a set of 15 multiple choice questions that can be used as a homework assignment, in-class assignment, or quiz. The questions are a varied sample of the information covered in this chapter. Answers are provided on the page following the assignment.
Chapter 14. Regression Analysis: Predicting Linear Relationships
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 14.1 The purpose of this assignment is to help you to become more comfortable in recognizing what each statistical symbol and formula in Chapter 14 represents. For each item in the table below, either the term or definition is given. Complete the following table with the missing information. For example, for the term standard error of estimate, provide the definition in the appropriate column. Once you have completed it, refer back to your notes and textbook to verify you are correct.
Term Definition (also include a symbol or formula as appropriate)
Standard error of estimate
Y bX a= +
Linear relationship
The value of Y predicted from X using a linear regression equation
Slope of a straight line
Predicting the value of Y scores using several X variables
The tendency of an extreme score to be less extreme on a second measure
Y-intercept
Least-squares regression line
The value of Y Y ′−
Chapter 14. Regression Analysis: Predicting Linear Relationships
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 14.2 For each of the data sets given below, calculate a least-squares regression line for predicting Y from X. Then, using this regression line, find Y’ for each value of X. Use the Y’ values to find SSResidual for each data set.
Set A Set B X Y X Y 5 5 3 7 4 5 4 7 8 7 5 5 9 7 6 5 6 3 7 5 7 5 8 3 3 3 9 3
Set C Set D
X Y X Y 3 3 5 7 4 3 4 3 5 5 8 5 6 5 9 5 7 5 6 5 8 7 7 3 9 7 3 7
Set E Set F
X Y X Y 6 5 5 3 7 3 7 3 3 7 6 5 8 7 8 5 9 3 4 5 5 5 9 7 4 5 3 7
Chapter 14. Regression Analysis: Predicting Linear Relationships
Answers for Assignment 14.2 (Note. Some answers are given to 2 or 3 decimal places to facilitate checking computations. Your answers may differ slightly from those given here due to rounding differences.) Set A X = 6.0 Xs = 2.16 XSS = 28 b = +0.571
Y = 5.0 Ys = 1.63 XYCP = 16 a = +1.6 Regression Line:
0.571 1.6Y X′ = + +
ResidualSS = 6.857 Y Xs =g 1.17 Set B X = 6.0 Xs = 2.16 XSS = 28 b = –0.714
Y = 5.0 Ys = 1.63 XYCP = –20 a = +9.3 Regression Line:
0.714 9.3Y X′ = − +
ResidualSS = 1.714 Y Xs =g 0.59 Set C X = 6.0 Xs = 2.16 XSS = 28 b = +0.714
Y = 5.0 Ys = 1.63 XYCP = 20 a = +0.7 Regression Line:
0.714 0.7Y X′ = + +
ResidualSS = 1.714 Y Xs =g 0.59 Set D X = 6.0 Xs = 2.16 XSS = 28 b = –0.214
Y = 5.0 Ys = 1.63 XYCP = –6 a = +6.3 Regression Line:
0.214 6.3Y X′ = − +
ResidualSS = 14.714 Y Xs =g 1.72 Set E X = 6.0 Xs = 2.16 XSS = 28 b = –0.357
Y = 5.0 Ys = 1.63 XYCP = –10 a = +7.1 Regression Line:
0.357 7.1Y X′ = − +
ResidualSS = 12.429 Y Xs =g 1.58 Set F X = 6.0 Xs = 2.16 XSS = 28 b = 0.0
Y = 5.0 Ys = 1.63 XYCP = 0 a = +5.0 Regression Line:
0.0Y ′ = X + 5
ResidualSS = 16.000 Y Xs =g 1.79
Chapter 14. Regression Analysis: Predicting Linear Relationships
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 14.3 A group of students in a research course hypothesized that there is a relationship between students’ academic dedication to college and their involvement in extracurricular activities such as belonging to an organization or team. Academic dedication is a student’s ability to focus on activities and behaviors that assure academic success. For example, a student who is high in academic dedication would forego attending a party to complete a written report. The research students obtained a measure of academic dedication and of extracurricular involvement from a group of 10 subjects. The scores obtained are given below. Calculate the least squared regression line for predicting academic dedication from extracurricular involvement from these scores. Is there a predictive relationship between involvement in extracurricular activities and academic dedication? Explain your answer.
Is it appropriate to conclude from these results that encouraging students to be active in extracurricular activities will cause an increase in their academic dedication? Explain your answer.
Chapter 14. Regression Analysis: Predicting Linear Relationships
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 14.4 Read each of the questions carefully and then select the best answer.
1. When two variables are linearly related, A. if the X variable equals zero, then the Y variable must also equal zero. B. the X and Y variables must be normally distributed. C. a change in the X variable is accompanied by a constant change in the Y
variable. D. the Y variable remains constant when the X variable changes.
2. Which of the following equations is the general equation for a straight line
relating variables X and Y? A. Y = bX + a. B. Y = bX – a. C. Y = b(X + a). D. Y = b(X – a).
3. The ____ is the amount of change in the Y variable that accompanies a constant
amount of change in the X variable. A. Y-intercept of a straight line B. covariation of X and Y C. slope of a straight line D. correlation coefficient
4. Suppose you perform a correlational study on the relationship between variables
X and Y, and find the equation relating the variables is Y = –1.3X + 8.1. In this equation, = –1.3 is the ____ and 8.1 is the ____.
A. Y-intercept; slope B. slope; Y-intercept C. X-intercept; slope D. slope; X-intercept
5. Suppose you perform a correlational study on the relationship between variables
X and Y, and find the equation relating the variables is Y = –4.6X + 9.3. From this equation we know that
A. the line has a positive slope and intersects the Y axis at +9.3. B. the X and Y variables are not linearly related. C. the line has a slope of +9.3 and intersects the Y axis at –4.6. D. the line has a slope of –4.6 and intersects the Y axis at +9.3.
Chapter 14. Regression Analysis: Predicting Linear Relationships
6. Suppose you perform a correlational study on the relationship between variables X and Y, and find the equation relating the variables is Y = +1.5X + 10. From this equation, the value of Y will be ____when X = 20.
A. 40 B. –40 C. 35 D. 45
7. The value of ____ is minimized by the least squares regression line. A. 2( )Y Y ′Σ + B. 2( )Y Y ′Σ − C. 2( )Y Y ′Σ + D. ( )Y Y ′Σ −
8. If Y = 30, X = 10, and b = +2.0, then the Y-intercept of the least squares regression line between variables X and Y is ____.
A. +50 B. –10 C. –50 D. +10
9. Suppose you perform a correlational study on the relationship between variables
X and Y, and find the least square linear regression equation relating the variables is Y ′ = 2X + 50. From this equation, the value of Y ′ will be ____ when X = 10.
A. 70 B. 30 C. –30 D. –70
10. The error in predicting a person’s Y score from a linear regression line is
A. how much the actual Y score differs from Y ′ . B. how much the Y ′ differs from the X score used to make the prediction. C. how much the Y ′ differs from the mean of the predicted scores, Y ′ . D. how much the Y ′ differs from the actual scores, Y .
11. The ____ is the difference between the actual value of a Y score and the Y ′ value
predicted from a linear regression line. A. estimated error B. prediction residue C. residual D. standard error of estimate
Chapter 14. Regression Analysis: Predicting Linear Relationships
12. In linear regression, the SSResidual is equal to A. 2( )X Y ′Σ + . B. 2( )Y Y ′Σ − . C. 2( )X Y ′Σ − . D. 2( )Y Y ′Σ − .
13. In linear regression, the symbol Y Xs g is used to represent
A. the standard error of estimate for predicting Y from X. B. the standard error of estimate for predicting X from Y. C. the standard error of estimate for predicting X ′ from Y. D. the standard error of the mean for predicting Y from X.
14. The values of Y Xs g and Ys will be equal in linear regression when
A. r for the X and Y variables is either +1.00 or -1.00. B. r for the X and Y variables is zero. C. X and Y are equal. D. Ys equals Xs .
15. An experimenter reported that r(25) = +.18, p > 0.05 for variables X and Y. In this
study, the best prediction of a Y score from an X score is ____. A. the value of X B. the value of Y – Y ′ C. .18 D. the value of Y
Chapter 14. Regression Analysis: Predicting Linear Relationships
Nonparametric Statistical Tests Assignment 15.1 This assignment has students calculate a chi-square test of independence. Answers are provided on the page following this assignment. Assignment 15.2 This assignment has students completing a Mann-Whitney U test on four data sets. Answers are provided on the page following this assignment. Assignment 15.3 This assignment has students completing the Wilcoxon signed-ranks test on four data sets. Answers are provided on the page following this assignment. Assignment 15.4 This assignment is a set of 15 multiple choice questions that can be used as a homework assignment, in-class assignment, or quiz. The questions are a varied sample of the information covered in this chapter. Answers are provided on the page following the assignment.
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 15.1 For each of the following contingency tables, calculate the expected frequencies and 2χ . Indicate whether 2χ is statistically significant at the .05 level. The values in each cell represent observed frequencies.
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 15.3 Each of the following data sets represents scores obtained from a between-subjects design with two levels of the independent variable. For each set, determine if there is a statistically significant difference using the Mann-Whitney U test. Assume that for each set, the scores do not meet the assumptions necessary for a parametric test.
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 15.4 Each of the following data sets represents scores obtained from a within-subjects design with two levels of the independent variable. For each set,. determine if there is a statistically significant difference using the Wilcoxon Signed-Ranks test. Assume that for each set, the scores do not meet the assumptions necessary for a parametric test.
Name: Class: Date: From Kiess and Green’s Statistical Concepts for the Behavioral Sciences, 4/e Assignment 15.5 Read each of the questions carefully and then select the best answer.
1. Nonparametric tests are typically used for statistical analysis of data when A. the measurement of the dependent variable is either interval or ratio in
nature. B. the measurement of the dependent variable is either nominal or ordinal in
nature. C. the population distributions for the samples involved are normal. D. the variances of the population distributions for the samples involved are
equal.
2. A ____ table is a table arranged in rows and columns used in the chi-square test of independence.
A. data display B. marginal frequency C. expected frequency D. contingency
3. The chi-square test of independence compares
A. the observed frequencies and the expected frequencies of the occurrence of an event or behavior of interest.
B. the sample means of three or more independent groups. C. the sample means from three or more levels of a within-subjects design. D. the sample medians of three or more independent groups.
4. Suppose you performed a chi-square test of independence on a 2 3× contingency
table. What would be an appropriate alternative hypothesis for this analysis? A. The μ A ’s are not all equal. B. The row and column variables are related in the population sampled. C.
1 2 3μ μ μA A A= = .
D. The distribution of scores for population A is different from the distribution of scores from population B.
5. Which of the following formulas provides the degrees of freedom for a 3 4× chi-
square test of independence? A. (r + 1)(c + 1). B. (r – 1) + (c – 1). C. (r – 1)(c – 1). D. (r – 1)2(c – 1).
6. Suppose you ran a chi-square test of independence on a 2 2× contingency table.
If the null hypothesis is true for this chi-square analysis, then you would expect A. that the observed and expected frequencies in a cell would be about equal. B. that the observed and expected frequencies in a cell would be very
different from each other. C. the sample means for each of the populations sampled to be about equal to
each other. D. the cell means should be about equal to each other.
7. Suppose you ran a chi-square test of independence on a 2 2× contingency table.
If the null hypothesis is true for this chi-square analysis, then you would expect A. reject the null hypothesis and accept the alternative. B. fail to reject the null hypothesis and not accept the alternative. C. fail to reject H0: 1 2 3
μ μ μA A A= = . D. conclude the observed and expected cell frequencies differ significantly
from each other.
8. Suppose the results of a chi-square test of independence are summarized as 2χ (2, N = 180) = 11.46, p <.05. From this report you would know that the total number of participants involved was ____ and the null hypothesis was
A. 181; rejected. B. 180; not rejected. C. 179; rejected. D. 180; rejected.
9. The Mann-Whitney U test is a nonparametric test that may be used to analyze
data from a ____ design with ____ levels of the independent variable. A. within-subjects; three or more B. between-subjects; two C. between-subjects; three or more D. within-subjects; two
10. To calculate the U statistic, you would find the
A. number of times that the rank of a score in one group precedes the rank of a score in the other group.
B. ratio of MSA to MSError. C. expected and observed frequencies in a contingency table. D. smaller of the two sums of ranks of the two treatment conditions.
11. Suppose you performed a Mann-Whitney U test on two equivalent groups of
participants. The null hypothesis for this test would be A.
1 2μ μA A= .
B. The population distribution of 1A scores is not identical to the population distribution of the 2A scores.
C. The row and column variables are not independent in the population.. D. The population distribution of 1A scores is identical to the population
distribution of the 2A scores.
12. Suppose you performed a Mann-Whitney U test on two equivalent groups of participants of size n1 = 15 and n2 = 16, respectively. The value of Uobs was 47. Ucrit for this test is 70 at the .05 level. In this situation you would
A. reject both H0 and H1. B. fail to reject H0. C. reject H0 and accept H1. D. not accept H1.
13. Suppose an experimenter had a one-factor within-subject design with two levels
of the independent variable and the dependent variable measured at an ordinal level. What statistical test should this person use to analyze the data from this study?
A. t test for related scores. B. Wilcoxon signed-ranks test. C. Chi-square test of independence. D. Mann-Whitney U test.
14. If you ran a Wilcoxon signed-ranks test on a set of scores, the alternative
hypothesis for the test would be A. the µA’s are not all equal. B. the population distributions of the related A1 and A2 conditions are not
identical. C. the row and column variables are not independent in the population. D. the population distributions of the related 1A and 2A conditions are
identical.
15. Suppose you used a Wilcoxon signed-ranks test to analyze a set of 26 related scores and found Tobs was 62. Tcrit for 26 pairs of scores is 98 at the .05 level. In this situation, you
A. found a nonsignificant difference between the treatment conditions. B. reject both H0 and H1. C. made a mistake because Tobs must always be greater than 75. D. found a statistically significant difference between the treatment
