1. Producing Data: Samples and Experiments
Chapter 4

2. Simple Random Sample number the population
use a method to randomly select the desired sample size from entire population
Advantages: every member of population always has equal chance of being selected
Disadvantages: sample may not be representative of population with small sample

3. Cluster Random Sample divide population into clusters
use a method to randomly select one or more clusters
use all subjects in chosen cluster(s)
Advantages: can work well if population is easy to divide or there are established clusters
Disadvantages: selected clusters may not be representative of population

4. Stratified Random Sample
divide population into strata
use a method to randomly select a sample from each strata
Advantages: guarantees representation from each strata
Disadvantages: strata (of interest) may be difficult to determine

5. Systematic Random Sample
use sample size and population size to determine (estimate) “magic number”
use a method to randomly select number using “magic number” as range; add to determine corresponding selections
Advantages: allows rapid method to select from large population
Disadvantages: not everyone has equal chance of being chosen

6. Multi-Stage Random Sample (FYI)
use a method (simple, cluster, stratified) to randomly select (large) groups
use a method (simple, cluster, stratified) to randomly select (smaller) groups
repeat until participants are chosen

7. Warm up
A sociologist wants to know the opinions of employed adult women about government funding for day care. She obtains a list of the 520 members of a local business and professional women’s club and mails a questionnaire to 100 of these women selected at random. Only 48 questionnaires are returned. What is the population in this study? What is the sample?

8. Role of Good Sampling Design
Any conclusion will be unreliable if the method of collecting data is flawed.
A poor design systematically favors certain outcomes or results and thus provides biased results.

9. Flaws in sample surveys
undercoverage
a sampling design that misses a part of the population
nonresponse bias
when a significant part of the population refuses to participate in the survey
response bias
anything that influences the response of the participant; i.e. wording of the question, the person conducting the survey, etc.

10. Role of mathematics in sampling
Results will differ from sample to sample. This phenomenon is called sampling variability.
Since we deliberately use randomization, sample results obey the laws of probability allowing reliable results.
The degree of accuracy can be improved by increasing the size of the sample.

11. Brownie Experiment Follow-Up
Why was it necessary to assign a Roman numeral for each type of brownie rather than leave the types of brownies with their brand names?
Why was it necessary to roll a die to decide the Roman numeral assigned for each type of brownie?

12. Brownie Experiment Follow-Up
When assigning the Roman numerals for each brownie type, the numbers 1,2,3 were assigned “I”, the numbers 4,5,6 were assigned “II”. Describe another method to randomly assign the Roman numerals.
Describe how the brownies were cut before eating. Why were the brownies cut in this way?

13. Brownie Experiment Follow-Up
Describe the procedure used to give the brownies to the person tasting. Please explain the reasons why each step was used.
We are limited to the type of brownies available in a store. If we wanted to better compare if one brand was better than another, describe what conditions would be preferred.

14. Discussion example 1
One school board member noticed that students in band tended to be in the top 25% of their school. She compiled a list from each high school’s band director and took a random sample of 25 students from each school’s band. She then took a random sample of 25 students from each high school that wasn’t in band. She found a slightly higher average G.P.A. of student’s in band.

15. Discussion example 1
Will this study give evidence that being in band causes an increase in a students G.P.A?
Will this study help her generalize that student’s in band tend to have a slightly higher G.P.A. than students not in band?

16. Vocabulary from example 1
Observational study
a study based on data collected from individuals that meet a determined criteria
Lurking variable
an outside factor that is not the explanatory nor response variable
prevents causal relationships from being established in observational studies

17. Discussion example 2
Another school board member is surprised the increase is so slight. First, he s each band director and asks for a list of 30 students. He then accesses each high school’s roster takes the first 40 listed striking any student’s name has already has. He found the average G.P.A. of student’s in band to be more significant than the first study.

18. Discussion example 2
Will this study give evidence that being in band causes an increase in a students G.P.A?
Will this study help her generalize that student’s in band tend to have a slightly higher G.P.A. than students not in band?

19. Discussion example 3
Walmart is considering buying a gasoline additive that is suppose to improve gas mileage. They found 30 employees in Texas that drive the same car. Fifteen employees are randomly selected to receive the additive, the remaining fifteen are given a bottle with just gas. Each employee is given a set route around the city to drive. The gas mileage is recorded by an onboard computer which shows the additive gives the driver 12% better gas mileage.

20. Discussion example 3
Will this study give evidence that using the additive will give a car better gas mileage?

21. Vocabulary from example 3
Experiment
a planned study where deliberate conditions are imposed to see how the response variable will change
Confounding variable
a variable associated (noncausal) with the explanatory variable that affects the response variable
makes it difficult to tell if the treatment affected the response variable significantly

22. Lurking versus confounding
Observation study
Experiment ? x y x y ? z z
Lurking
Confounding

23. Randomized comparative experiments
Goal of an experiment: collect statistically significant evidence for a cause-and-effect relationship.

24. Principles of Experimental Design
Control:
using comparison ensures that outside factors operate equally on all groups
comparison minimizes effects of confounding variables allowing us to accurately assess the change in the response variable

25. Principles of Experimental Design
Control:
Randomization:
use of impersonal chance equalizes unanticipated factors so that groups that should be similar in all respects.
homogenous groups reduce variability allowing better assessment of treatments

26. Principles of Experimental Design
Control:
Randomization:
Replication:
perform the experiment on as many subjects to reduce chance variation in the results

27. Designing Experiments: vocab
Vocabulary shift from algebra to statistics
algebra statistics
Independent  Explanatory variable
Dependent  Response variable
Explanatory variable also called a “factor.”

28. Experimental Design Examples
Read each design example and write a description on how each experiment should be run.
Key terms: groups, treatments, comparison, randomization

29. Completely Randomized Design
Group 1
15 babies
Treatment 1
Her product
Compare weight gain
Random Allocation
Group 2
15 babies
Treatment 2
Competitor’s
Babies will be numbered 01 to 30. Using a random number table, the first 15 selected will be in Group 1 with the remaining placed in group 2. Each babies’ weight will be measured in pounds and compared.

30. Block Design Treatment 1 Calcium Group 1 Group 2 African American men
Random assignment
Treatment 2 Placebo
Compare blood pressure
Subjects
Group 3
Group 4
Treatment 1 Calcium
Random assignment
White men
Treatment 2 Placebo
All African American men will be assigned a random number. Half the
men who have the smallest numbers will be assigned group 1, the half
with the largest numbers will be assigned group 2. The process will repeat
for the white men. The reduction in blood pressure will be compared.

31. Matched pair Design Group 1 Treatment 1 left hand Treatment 2
right hand
Compare
difference
Random Allocation
Group 2
Treatment 2
right hand
Treatment 1
left hand
A coin will be flipped to decide which hand will be measured first by each participant. Heads will squeeze the left hand first, tails will squeeze the right hand first. The different in the pounds on the scale will be compared.

32. Calcium experiment revisted
Treatment 1
Calcium
Group 1
Compare blood pressure
Random Assignment
Treatment 2
Placebo
Group 2
What potential problems might be have because we started with random assignment?
How should we alter our experiment?

33. Block Design Completely randomized experiment
African American men
Completely randomized experiment
All participants
Completely randomized experiment
White men

34. Improving the Design
A block is a group of experimental units or subjects that are known before the experiment to be similar in some way that is expected to affect the response to the treatments.
Blocks allow us to reduce the amount of variation to improve the accuracy of our conclusions by creating homogeneous groups.
single blind versus double blind

35. Improving the Design
In a matched pair design, each subject in the experiment will receive two (and only two) treatments.
The order that each subject receives both treatments is randomly selected to preserve the important aspect of randomization.

36. An example of a good design?
In order to test the effectiveness of nicotine patches, Dr. Hurt recruited 240 smokers at various locations. Volunteers were to receive a 22-mg nicotine patch for eight weeks. Almost half (46%) of the nicotine group had quit smoking at the end of the study.
Confounding variable: placebo effect

37. Example for vocabulary check
A corporation found that technology trainings were often stressful to their employees. One idea was to play background music (jazz or classical). Another idea was to have the presenter and participants dress casual rather than the usual business attire. Equivalent technology trainings over the next year were randomly assigned a particular condition. A post training survey was given to measure the stress associated with each training.
Factors? Treatments?

38. Example for vocabulary check
No music
Business attire
Casual attire
Classical music
Jazz music
Jazz Music
Factors: music, attire
Treatments: 6

39. Why a simulation?
A simulation is using a model to imitate a chance behavior based on a specific problem situation.
A simulation allows a model to be analyzed when a theoretical probability is unknown or indeterminate.

40. Elements of a simulation
Number assignment
Description of a trial
Stopping rule
Execution of simulation (marking of the number line)
Documentation of results

41. Simulation Example
Traffic Lights: Coming to school each day, Anne rides through three traffic lights, A, B, and C. The probability that any one light is green is 0.3, and the probability that it is not green is Use a simulation to answer questions below.
We must assume that the lights operate independently.
Estimate the probability that Anne will find all traffic lights to be green.
Estimate the probability that Anne will find at least one light to be not green.

42. Simulation Example Number assignment
0 – 2 green light; 3 – 9 not green
(1 – 3 green light; 4 – 0 not green)
Description of a trial/Stopping rule
A trial consists of choosing one digit at a time to represent one traffic light. After we determine if the light is green or not green, the trial ends after three lights.
Execution of simulation
Documentation of results

43. Simulation Example three green lights two or fewer
three green lights two or fewer