Chapter 3 producing data *Now we will draw conclusions about large groups by taking samples

Observational Study Observes individuals and measures variables of interest but does not attempt to influence the responses Example: Record the number of students wearing school colors on spirit day

Experiment Imposes some treatment on individuals in order to observe their responses. Use when the goal is to determine cause and effect Example: Offer extra credit to anyone wearing school colors tomorrow

CONFOUNDED – Two variables whose effect on the response cannot be distinguished. *Can’t tell which variable causes response.* Welfare -> Does offering mandatory job training help women get off welfare? Or is it self-motivation?

**The design of a sample is the method used to choose sample.** 3.1 Designing Samples Population- the entire group of individuals that we want information about Example: all high school students Sample- a part of the population that we actually examine in order to gather information Example: 25 students in Prob. And Stat. **The design of a sample is the method used to choose sample.**

Types of Samples 1. Voluntary Response Sample - People choose themselves by responding - Usually Bias (Bias-> Favor a certain side) - Usually negative * Bad sample design * Example: Call-in Opinion Poll (Talk-Back 16) 2. Convenience Sample - Interviewer chooses sample - Choose easiest to reach individuals Example: Mall: Lotion, buff nails, flat iron

3. Simple Random Sample -> SRS - Consists of n individuals from the population chosen in a way that every set of n individuals has an equal chance to be the sample selected - Drawing names out of a hat To pick a random sample 1. Assign # to each individual (01 -> 24) 2. Use Table B: Random Digits (back of book), start on given line and pick 2 digit numbers

2. Turn to Table B in your book. 3. Using line 115, pick 6 students. Example 1: There are 27 students in the class and I want an SRS of 6 students. 1. Assign students 01 -> 27 2. Turn to Table B in your book. 3. Using line 115, pick 6 students. 61041 77684 94322 24709 73698 14526 31893 32592 What if you wanted an SRS of 7?

Example 2: 225 workers, use line 121 to pick an SRS of 5 077 148 168 052 102

5. Stratified Random Sample 4. Probability Sample Gives each member of the population a known chance to be selected Example: Choosing 1 student from class (1 in 24 chance) 5. Stratified Random Sample - Used for sampling from large populations spread out over wide area 1.) Divide population into groups of similar individuals (strata) 2.) Choose a separate SRS in each stratum and combine the SRS’s to form sample. Example: Divide class into girls and boys and take SRS

6. Multistage Sample Break into groups, then break up those groups, and so on - Then, take stratified sample from ALL groups Example: Divided class into boys and girls, then divide each group into juniors and seniors, then divide only child vs. siblings.

Cautions about sample surveys 1. Undercoverage -> When some groups in the population are left out of the process of choosing the sample 2. Nonresponse ->When an individual chosen for the sample can’t be contacted or refuses to cooperate 3. Response Bias -> Lie about illegal or unpopular behavior 4. Wording of questions -> Words may be confusing or misleading *The larger the random sample, the more accurate the results.*

3.2 Designing Experiments Experimental Units - the individuals on which the experiment is done (called subjects when they are human) Treatment- the specific experimental condition that is applied to the units Factor- explanatory variable in an experiment Level- specific value of a factor Example 1: 60 people are given 3 different doses of a new drug (50 mg, 100 mg, 150 mg) to determine pain relief Experimental units -> 60 people Treatment -> drug (single factor with 3 levels, 20 subjects for each level)

Diagram the Experiment Example 2: 60 people are given new drug to relieve pain. The patients are given gel caps in doses of 50 mg, 100 mg, and 150 mg. The drug is given on an empty stomach and with food. 2 factors - > gel caps with 3 levels and time of day with 2 levels Gel Caps 50 mg 100 mg 150 mg empty stomach Time of day with food 1 2 3 4 5 6

DESIGNING THE EXPERIMENT Randomized Comparative Experiment 20 patients-> 50 mg Random 20 patients ->100 mg Pain Assignment Relief 20 patients -> 150 mg *Do experiment twice, once on an empty stomach and once with food to get all six treatments.

Comparative Experiment- impose treatment and record result UNITS -> TREATMENT -> RESPONSE **when humans or animals are units, there is always a lurking variable** Placebo Effect - favorable response to dummy treatment - “in their head”, but not really Control Group - the group of patients who receive the placebo

Principles of Experimental Design 1. CONTROL the effects of lurking variables on the response by comparing several treatments 2. Use RANDOMIZATION to randomly assign experimental units to treatments. 3. Use REPLICATION in an experiment on many units to reduce chance variation

STATISTICALLY SIGNIFICANT When an observed effect is so large that it would rarely occur by chance, it is called statistically significant. This provides evidence that the treatments actually cause these effects. ***Doesn’t happen “by chance”.***

Matched Pairs Design for Experiments - Combines matching with randomization Compares 2 treatments Take pair of evenly matched units and randomly assign 1 treatment to one subject and 2nd treatment to other subject “Pair” is single subject that receives both treatments randomly. Example: Coke vs. Pepsi taste test

Block Design for Experiments - Group of similar units where treatment is carried out separately within each group - Subjects are grouped by characteristics that are expected to affect the response to the treatment. - Corresponds to stratified random sample Examples: Medical treatments, block by gender Biggest loser competitions, block by weight

Cautions about Experimentation 1. Unconscious Bias – if subjects and/or testers know which treatment they are receiving, the results may be bias **To avoid this, do a Double Blind Experiment in which neither the subject nor the tester knows which treatment the subject receives.** 2. Lack of Realism -cannot realistically duplicate the conditions you want (subjects know it is experiment)