Sampling and ExperimentsSections 6.1 - 6.3
Cathy Poliak, [email protected] in Fleming 11c
Department of MathematicsUniversity of Houston
Lecture 16 - 2311
Cathy Poliak, Ph.D. [email protected] Office in Fleming 11c (Department of Mathematics University of Houston )Sections 6.1 - 6.3 Lecture 16 - 2311 1 / 21
Outline
1 Simple Random Sample
2 Observational Studies vs. Experiments
3 Experiments
4 Types of Experimental Designs
5 Principle of Experimental Design
Cathy Poliak, Ph.D. [email protected] Office in Fleming 11c (Department of Mathematics University of Houston )Sections 6.1 - 6.3 Lecture 16 - 2311 2 / 21
Popper Set Up
Fill in all of the proper bubbles.
Make sure your ID number is correct.
Make sure the filled in circles are very dark.
This is popper number 12.
Cathy Poliak, Ph.D. [email protected] Office in Fleming 11c (Department of Mathematics University of Houston )Sections 6.1 - 6.3 Lecture 16 - 2311 3 / 21
Popper #12 Questions
Identify the type of sampling used in the following situations:
a) Convience Sample b) Volunteer Samplec) Stratified Sample d) Simple Random Sample
1. A radio talk show wanted to know whether Houstonians think Texasshould continue to use the death penalty. The station asked for listenersto call in and give their opinion.
2. To judge the appeal to American adults of a proposed television sitcom,a sample of 10 people from each of three different age groups wasselected and those chosen were asked to rate a pilot show.
3. Subscribers to the magazine Sound Alive were assigned numbers.Thirty numbers were selected at random. The subscribers with thechosen numbers were asked to rate a new compact disk player for a"What Subscribers Think" column. (Assume all chosen did respond)
Cathy Poliak, Ph.D. [email protected] Office in Fleming 11c (Department of Mathematics University of Houston )Sections 6.1 - 6.3 Lecture 16 - 2311 4 / 21
How to take a Simple Random Sample (SRS)
We select an SRS by labeling all the individuals in the populationand using software or a table of random digits to select a sampleof the desired size.
In R: sample(1:N,n) where N = the number of individuals in thepopulation and n = the number of individuals in the sample.
A table of random digits is a long string of the digits 0 - 9 whereeach entry in the table is equally likely to be any of the 10 digitsand the entries are independent of each other. See the appendixin your textbook for this table.
Cathy Poliak, Ph.D. [email protected] Office in Fleming 11c (Department of Mathematics University of Houston )Sections 6.1 - 6.3 Lecture 16 - 2311 5 / 21
Example
You have been hired by a company that is planning to build a newapartment complex for students in a college town. They want you tocollect information about preferences of potential customers for theircomplex. Most of the college student who live in an apartment live inone of the 10 complexes.
Ashley Oaks Bay Pointe Beau JardinBrownstone Cambridge Chauncey VillageCountry View Del-Lynn Fairway KnollsGeorgetown
Select a simple random sample of 2 of the following complexes startingat line 137 using the Random Digits Table.
Cathy Poliak, Ph.D. [email protected] Office in Fleming 11c (Department of Mathematics University of Houston )Sections 6.1 - 6.3 Lecture 16 - 2311 6 / 21
Another Example of Sampling
It is believed that 75% of all apartment dwellers in a large city deadbolttheir doors in addition to locking them as an added precaution againstburglary. Describe how you would select ans SRS of 20 apartmentdwellers to survey if there are 50 complexes in the city and eachcomplex has 250 residents.
Cathy Poliak, Ph.D. [email protected] Office in Fleming 11c (Department of Mathematics University of Houston )Sections 6.1 - 6.3 Lecture 16 - 2311 7 / 21
Observation versus experiment
An observational study observes individuals and measuresvariables of interest but does not attempt to influence theresponses.
I Example: A pharmacy student would like to know if there is adifference in results from a specific brand of drug and its equivalentgeneric prescription. She randomly selects 50 people who take thedrug hand has them complete a questionnaire regarding theirsymptoms and improvements after taking the specific brand orgeneric equivalent.
An experiment deliberately imposes some treatment onindividuals in order to observe their responses.
I The editor of a magazine is wondering if the type of font used in thearticles affects the reading speed of the subscribers of themagazine. Hes asks 10 subscribers to read 4 articles each withdifferent fonts. If the reading speed increases with a particular font,hew will use it in the next publication.
Cathy Poliak, Ph.D. [email protected] Office in Fleming 11c (Department of Mathematics University of Houston )Sections 6.1 - 6.3 Lecture 16 - 2311 8 / 21
Popper #12 Questions
Are each of these an a) experiment or b) observational study.4. Nordic mobiles from early-1980s may hike brain tumor risk.
Long-term users of some first generation cell phones primarilyused in Nordic countries face up to 80 percent greater risk ofdeveloping brain tumors than those who did not use the phones, anew Swedish study shows.
5. Work in mice paves way to new drugs. Studies of the ginsengberry may someday bear fruit for millions of Americans who sufferfrom obesity and its life-threatening complications. If new work inmice can be duplicated in people, researchers predict thedevelopment of novel drugs that deflate spare tires, while wardingoff diabetes.
Cathy Poliak, Ph.D. [email protected] Office in Fleming 11c (Department of Mathematics University of Houston )Sections 6.1 - 6.3 Lecture 16 - 2311 9 / 21
Experiments
A study is an experiment when we actually do something topeople, animals, or objects in order to observe the response.
The following are basic vocabulary of experiments.I Experimental units are the individuals on which the experiment is
done. When the units are people, they are called subjects.I A treatment is the specific experimental condition applied to the
units.I Factors are the explanatory variables in an experiment. Note that
factors my have several levels.I A placebo is a dummy treatment that can have no physical effect.
When the subjects respond to a placebo treatment, we call this theplacebo effect
In practice, experiments can give good evidence for the factor(s)causing the response.
Cathy Poliak, Ph.D. [email protected] Office in Fleming 11c (Department of Mathematics University of Houston )Sections 6.1 - 6.3 Lecture 16 - 2311 10 / 21
Example of an Experiment
From:New England Journal of Medicine 1989; 321:129-135, July 20,1989, the tile is: "Nealy five decades of research now link aspirin to theprevention of heart attacks." This came from a large medicalexperiment involving 22,000 male physicians. One group of about11,000 physicians took an aspirin every second day, while the rest tooka placebo. After several years the study found that subjects in theaspirin group had significantly fewer heart attacks than the subjects inthe placebo group.
Who are the experimental subjects in this study?
Identify the factor and its levels.
Identify the response variable.
Cathy Poliak, Ph.D. [email protected] Office in Fleming 11c (Department of Mathematics University of Houston )Sections 6.1 - 6.3 Lecture 16 - 2311 11 / 21
Example of an Experiment
A company that produces healthy food called "Healthnut" wants todetermine if their food relates to weight loss. This company asked 100people to participate in this experiment and followed them for 6months. Half of the people (50) were given the company’s food theother half were given regular food. After 6 months they weighed theparticipants to determine the average percent of weight loss betweenthe two groups.
1. What is the explanatory variable (the factor)?
a) The people who eat the food. c) The percent of weight loss.b) The type of food. d) Healthnut.
2. What is the response variable?
a) The people who eat the food. c) The percent of weight loss.b) The type of food. d) Healthnut.
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Diagram of Experiment
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Suppose we add in Amount of Exercise as anotherFactor
Factor 1: Type of food; Healthnut or RegularFactor 2: Amount of daily exercise; 0 min, 30 min or 60 minResponse: Percent of Weight loss
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Parts of an Experiment Design
1. The design of an experiment describes the response variables,the factors and the layout of the treatments, with comparison asthe leading principle.
2. The rule used to assign the subjects to the treatments. How canwe assign individuals to treatments in a way that is not biased?
These experiments are called randomized comparativeexperiments. They are designed to give good evidence that thedifferences in the treatments actually causes the differences we see inthe response.
Cathy Poliak, Ph.D. [email protected] Office in Fleming 11c (Department of Mathematics University of Houston )Sections 6.1 - 6.3 Lecture 16 - 2311 15 / 21
Types of Experiment Designs
In a Completely randomized experimental design (CRD), all thesubjects are allocated at random among all the treatments.
A blocked design occurs when groups of experimental units aresimilar, it is often a good idea to gather them together into blocks.This design is used if we cannot control something important (asin age or gender).
A matched pairs design compares two treatments. If possible insome matched pair designs, each subject receives bothtreatments in a random order. In others. the pairs are chosen sothat the subjects are as closely matched as possible. Matchedpairs design is an example of of block designs.
Cathy Poliak, Ph.D. [email protected] Office in Fleming 11c (Department of Mathematics University of Houston )Sections 6.1 - 6.3 Lecture 16 - 2311 16 / 21
Examples of Randomized Comparative Experiments
Completely Randomized Design: Suppose we want to knowhow levels of exercise affects weight loss. Weight is the responsevariable. There are three levels of exercise: none, moderate, andextreme. In this experiment we have 30 subjects, thus the 30subjects will be randomly selected into the three levels of exercise10 in each level. Then measure the percent of weight loss.
Blocked design: There are 15 males and 15 females. Becausemales and females have different body types we will use genderas a blocking variable. Then randomly select the 15 males intoeach of the three levels and the 15 females into each of the threelevels. Then compare the weight loss among gender.
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Diagram of Blocked Design
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The Principles of Experimental Design
The fundamental principle of experimental design is control. Thereare three fundamental priciple of control:
1. Comparison2. Randomization3. Blindness (blind or double-blind),
We want a control group to manage the effects of lurking variables.
Cathy Poliak, Ph.D. [email protected] Office in Fleming 11c (Department of Mathematics University of Houston )Sections 6.1 - 6.3 Lecture 16 - 2311 19 / 21
Does the Difference Make a Difference?
We usually say after the experiment that there is a statisticallysignificant difference between the factor levels.
Statistically significant means that when an observed differenceis too large for us to believe that it is likely to have occurrednaturally.
We well see in later chapters how large that difference has to be.
Cathy Poliak, Ph.D. [email protected] Office in Fleming 11c (Department of Mathematics University of Houston )Sections 6.1 - 6.3 Lecture 16 - 2311 20 / 21
Example
Many colleges and universities have developed "calculus reform"courses which substantially alter the way that calculus is taught. thegoal is that the reform courses help students to understandfundamental calculus concepts better than traditionally taught coursedo.a. If you simply compare scores on a standardize calculus test
between students in traditional classes and those in reform classes,will you be able to conclude that any differences you might find areattributable to the teaching style? Why or why not?
b. Describe how you might design an experiment to assess whetherthe goal is being met.
Cathy Poliak, Ph.D. [email protected] Office in Fleming 11c (Department of Mathematics University of Houston )Sections 6.1 - 6.3 Lecture 16 - 2311 21 / 21
