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by by

Allan G. BlumanAllan G. Bluman

SLIDES PREPARED SLIDES PREPARED

BY BY

LLOYD R. JAISINGHLLOYD R. JAISINGH

MOREHEAD STATE UNIVERSITYMOREHEAD STATE UNIVERSITY

MOREHEAD KYMOREHEAD KY

Elementary Elementary Statistics Statistics

A Step by Step ApproachSixth Edition

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Topic 1Topic 1

Chapter One: The Nature of Chapter One: The Nature of Probability and StatisticsProbability and Statistics

WCB/McGraw-Hill

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1-31-3 OutlineOutline

1-1 Introduction 1-2 Descriptive and Inferential

Statistics 1-3 Variables and Types of Data 1-4 Data Collection and

Sampling Techniques

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1-41-4 OutlineOutline

1-5 Observational and

experimental studies

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1-51-5 ObjectivesObjectives

Demonstrate knowledge of all statistical terms.

Differentiate between the two branches of statistics.

Identify types of data.

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1-61-6 ObjectivesObjectives

Identify the measurement level for each variable.

Identify the four basic sampling techniques.

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1-71-7 ObjectivesObjectives

Explain the importance of computers and calculators in statistics.

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1-81-8 1-1 Introduction1-1 Introduction

StatisticsStatistics consists of conducting studies to collect, organize, summarize, analyze, and draw conclusions.

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1-91-91-2 Descriptive and Inferential 1-2 Descriptive and Inferential

StatisticsStatistics

DataData are the values (measurements or observations) that the variables can assume.

Variables whose values are determined by chance are called random variablesrandom variables.

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1-101-101-2 Descriptive and Inferential 1-2 Descriptive and Inferential

StatisticsStatistics

A collection of data values forms a data set.data set.

Each value in the data set is called a data valuedata value or a datumdatum.

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StatisticsStatistics

Descriptive statisticsDescriptive statistics consists of the collection, organization, summation, and presentation of data.

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StatisticsStatistics

A populationpopulation consists of all subjects (human or otherwise) that are being studied.

A samplesample is a subgroup of the population.

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StatisticsStatistics

Inferential statisticsInferential statistics consists of generalizing from samples to populations, performing hypothesis testing, determining relationships among variables, and making predictions.

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Example: Attendance & Grades

A study conducted at Manatee Community College revealed that students who attended class 95% to 100% of the time usually received an A in the class. Students who attended class 80% to 90% of the time usually received a B or C in the class. Students who attended class less than 80% of the time usually received a D or an F or eventually withdrew from the class.

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Example: Attendance & Grades

Answer the following questions:1. What are the variable under study?2. What are the data in the study?3. Are descriptive, inferential, or both types of

statistics used?4. What is the population under study?5. Was a sample collected? If so, from where?6. From the information given, comment on the

relationship between the variables.

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1-161-16 1-3 Variables and Types of Data1-3 Variables and Types of Data

Qualitative variablesQualitative variables are variables that can be placed into distinct categories, according to some characteristic or attribute. For example, gender (male or female).

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Quantitative variablesQuantitative variables are numerical in nature and can be ordered or ranked. Example: age is numerical and the values can be ranked.

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1-181-18 1-3 Variables and Types of Data1-3 Variables and Types of Data

Discrete variablesDiscrete variables assume values that can be counted.

Continuous variablesContinuous variables can assume all values between any two specific values. They are obtained by measuring.

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Classification of Variables

Data

Qualitative Quantitative

Discrete Continuous

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1-201-20 1-3 Variables and Types of Data1-3 Variables and Types of Data

The nominal level of measurementnominal level of measurement classifies data into mutually exclusive (non-overlapping), exhausting categories in which no order or ranking can be imposed on the data.

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1-211-21 1-3 Variables and Types of Data1-3 Variables and Types of Data

The ordinal level of measurementordinal level of measurement classifies data into categories that can be ranked; precise differences between the ranks do not exist.

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1-221-22 1-3 Variables and Types of Data1-3 Variables and Types of Data

The interval level of measurementinterval level of measurement ranks data; precise differences between units of measure do exist; there is no meaningful zero.

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1-231-231-3 Variables and Types of Data1-3 Variables and Types of Data

The ratio level of measurementratio level of measurement possesses all the characteristics of interval measurement, and there exists a true zero. In addition, true ratios exist for the same variable.

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Examples of Measurement Scale

Nominal Ordinal Interval Ratio

Zip code Grade Exam score Height

Gender Rating scale IQ exam Weight

Eye color Ranking of tennis players

Temperature Age

Nationality Salary

Major field

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Example: Transportation Safety

The chart shows the number of job-related injuries for each of the transportation industries for 1998.

Industry Number of InjuriesRailroad 4520Intercity bus 5100Subway 6850Trucking 7144Airline 9950

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Example: Transportation Safety

Answer the following questions:1. What are the variable under study?2. Categorize each variable as quantitative or

qualitative.3. Categorize each quantitative variable as

discrete or continuous.4. Identify the level of measurement for each

variable.

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1-271-271-4 Data Collection and Sampling 1-4 Data Collection and Sampling Techniques Techniques

Data can be collected in a variety of ways. One of the most common methods is through

the use of surveys. Surveys can be done by using a variety of

methods - Examples are telephone, mail questionnaires,

personal interviews, surveying records and direct observations.

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1-281-281-4 Data Collection and Sampling 1-4 Data Collection and Sampling Techniques Techniques

To obtain samples that are unbiased, statisticians use four methods of sampling.

Random samplesRandom samples are selected by using chance methods or random numbers.

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Example

A lottery draw is a good example of simple random sampling. A sample of 6 numbers is randomly generated from a population of 45, with each number having an equal chance of being selected.

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Systematic samplesSystematic samples are obtained by numbering each value in the population and then selecting the kth value.

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Example

If a systematic sample of 500 students were to be carried out in a university with an enrolled population of 10,000, the sampling interval would be:

I = N/n = 10,000/500 =20 All students would be assigned sequential numbers.

The starting point would be chosen by selecting a random number between 1 and 20. If this number was 9, then the 9th student on the list of students would be selected along with every following 20th student. The sample of students would be those corresponding to student numbers 9, 29, 49, 69, ........ 9929, 9949, 9969 and 9989.

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1-321-321-4 Data Collection and Sampling 1-4 Data Collection and Sampling Techniques Techniques

Stratified samplesStratified samples are selected by dividing the population into groups (strata) according to some characteristic and then taking samples from each group.

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Example

The committee of a company of 1,000 employees wishes to assess any reaction to the re-introduction of security system into the company. To ensure a representative sample of employees from all departments, the committee uses the stratified sampling technique.

In this case the strata are the departments. Within each strata the committee selects a sample. So, in a sample of 100 employees, all departments would be included. The employees in the sample would be selected using simple random sampling or systematic sampling within each strata

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1-341-341-4 Data Collection and Sampling 1-4 Data Collection and Sampling Techniques Techniques

Cluster samplesCluster samples are selected by dividing the population into groups and then taking samples of the groups.

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Example

Suppose an organization wishes to find out which lung cancer treatment doctors are recommending in across Malaysia. It would be too costly and take too long to survey every doctor, or even some doctors from every hospital. Instead, 100 hospitals are randomly selected from all over Malaysia.

These hospitals are considered to be clusters. Then, every doctor in these 100 hospitals is surveyed. In effect, doctors in the sample of 100 hospitals represent all doctors in Malaysia.

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Cluster vs. Stratified

Cluster sampling is different from stratified random sampling, because in the latter sampling technique, some units are selected from each group.

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1-5 Observational and Experimental Studies

In an observational study, the researcher merely observes what is happening or what has happened in the past and tries to draw conclusions based on these observations.

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1-5 Observational and Experimental Studies

In an experimental study, the researcher manipulates one of the variables and tries to determine how the manipulation influences other variables.

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1-5 Observational and Experimental Studies

The independent variable (explanatory variable) in an experimental study is the one that is being manipulated by the researcher.

The resultant variable is called the dependent variable (outcome variable).

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1-5 Observational and Experimental Studies

A confounding variable is one that influences the dependent or outcome variable but cannot be separated from the independent variable.

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Example: Observational or Experimental Study?

(a) Subjects were randomly assigned to two groups, and one group was given an herb and the other group a placebo. After 6 months, the numbers of respiratory tract infections each group had were compared.

Experimental Study

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Example: Observational or Experimental Study?

(b) A researcher stood at a busy intersection to see if the color of the automobile that a person drives is related to running red lights.

Observational Study

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Example: Observational or Experimental Study?

(c) A researcher finds that people who are more hostile have higher total cholesterol levels than those who are less hostile.

Observational Study

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Example: Observational or Experimental Study?

(d) Subjects are randomly assigned to four groups. Each group is placed on one of four special diets – a low-fat diet, a high-fish diet, a combination of low-fat diet and high-fish diet, and a regular diet. After 6 months, the blood pressures of the groups are compared to see if diet has any effect on blood pressure.

Experimental Study

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