1. Get out your homework and materials for notes!
If you have your parent letter signed and/or supplies, please place it on my desk.

2. CHAPTER 4: Designing Studies
4.2 Experiments

3. Experiments
DISTINGUISH between an observational study and an experiment.
EXPLAIN the concept of confounding.
IDENTIFY the experimental units, explanatory and response variables, and treatments in an experiment.
EXPLAIN the purpose of comparison, random assignment, control, and replication in an experiment.
DESCRIBE a completely randomized design for an experiment.
DESCRIBE the placebo effect and the purpose of blinding in an experiment.
INTERPRET the meaning of statistically significant in the context of an experiment.
EXPLAIN the purpose of blocking in an experiment.
DESCRIBE a randomized block design or a matched pairs design for an experiment.

4. Observational Study vs. Experiment
Observational study - observes individuals and measures variables of interest but does not attempt to influence the responses.
Experiment - deliberately imposes some treatment on individuals to measure their responses.
When our goal is to understand cause and effect, experiments are the only source of fully convincing data.
In contrast to observational studies, experiments don’t just observe individuals or ask them questions. They actively impose some treatment in order to measure the response. The distinction between observational study and experiment is one of the most important concepts in statistics.

5. Observational Study vs. Experiment
Observational studies of the effect of an explanatory variable on a response variable often fail because of confounding between the explanatory variable and one or more other variables. Well-designed experiments take steps to prevent confounding.
Confounding occurs when two variables are associated in such a way that their effects on a response variable cannot be distinguished from each other.

6. AP Exam Tip
If you are asked to identify a possible confounding variable, you must:
1. Explain how it is associated with the explanatory variable.
2. explain how it affects the response variable.

7. Check Your Understanding, p. 237
1. Does reducing screen brightness increase battery life in laptop computers? To find out, researchers obtained 30 new laptops of the same brand. They chose 15 of the computers at random and adjusted their screens to the brightest setting. The other 15 laptop screens were left at the default setting—moderate brightness. Researchers then measured how long each machine’s battery lasted. Was this an observational study or an experiment? Justify your answer.
Experiment, because a treatment (brightness of screen) was imposed on the laptops.

8. Check Your Understanding, p. 237
2. Does eating dinner with their families improve students’ academic performance? According to an ABC News article, “Teenagers who eat with their families at least five times a week are more likely to get better grades in school. This finding was based on a sample survey conducted by researchers at Columbia University.
Was this an observational study or experiment? Justify your answer.
Observational Study because students were not assigned to eat a particular number of meals with their family per week.

9. Check Your Understanding, p. 237
2. Does eating dinner with their families improve students’ academic performance? According to an ABC News article, “Teenagers who eat with their families at least five times a week are more likely to get better grades in school. This finding was based on a sample survey conducted by researchers at Columbia University.
What are the explanatory and response variables?
Explanatory: number of meals per week eaten with family
Response: GPA

10. Check Your Understanding, p. 237
2. Does eating dinner with their families improve students’ academic performance? According to an ABC News article, “Teenagers who eat with their families at least five times a week are more likely to get better grades in school. This finding was based on a sample survey conducted by researchers at Columbia University.
Explain clearly why such a study cannot establish a cause-and- effect relationship. Suggest a variable that may be confounded with whether families eat dinner together.
There are probably other variables that influence the response variable. For example, students who have part-time jobs may not be able to eat many meals with their families and may not have much time to study, leading to lower grades.

11. Ants Can Count
FnoU

12. The Language of Experiments
Here is the basic vocabulary of experiments:
A specific condition applied to the individuals in an experiment is called a treatment. If an experiment has several explanatory variables (factors), a treatment is a combination of levels of these factors.
The experimental units are the smallest collection of individuals to which treatments are applied. When the units are human beings, they often are called subjects.

13. Example, p. 239
What are the effects of repeated exposure to an advertising message? The answer may depend on both the length of the ad and on how often it is repeated. An experiment investigated this question using 120 undergraduate students who volunteered to participate. All subjects viewed a 40-minute television program that included ads for a digital camera. Some subjects saw a 30- second commercial; others, a 90-second version. The same commercial was shown either 1, 3, or 5 times during the program. After viewing, all the subjects answered questions about their recall of the ad, their attitude toward the camera, and their intention to purchase it.

14. Experimental Subjects: 120 undergraduate students
What are the effects of repeated exposure to an advertising message? The answer may depend on both the length of the ad and on how often it is repeated. An experiment investigated this question using 120 undergraduate students who volunteered to participate. All subjects viewed a 40-minute television program that included ads for a digital camera. Some subjects saw a 30-second commercial; others, a 90-second version. The same commercial was shown either 1, 3, or 5 times during the program. After viewing, all the subjects answered questions about their recall of the ad, their attitude toward the camera, and their intention to purchase it.
For the advertising study, identify the experimental units or subjects, explanatory and response variables, the factors, and the treatments.
Experimental Subjects: 120 undergraduate students
Response variables: recall of the ad, attitude about the digital camera and whether they intend to
purchase it
Skip explanatory for a minute.

15. What are the effects of repeated exposure to an advertising message
What are the effects of repeated exposure to an advertising message? The answer may depend on both the length of the ad and on how often it is repeated. An experiment investigated this question using 120 undergraduate students who volunteered to participate. All subjects viewed a 40-minute television program that included ads for a digital camera. Some subjects saw a 30-second commercial; others, a 90-second version. The same commercial was shown either 1, 3, or 5 times during the program. After viewing, all the subjects answered questions about their recall of the ad, their attitude toward the camera, and their intention to purchase it.
For the advertising study, identify the experimental units or subjects, explanatory and response variables, the factors, and the treatments.
Factor B: Repetitions (Explanatory variable)
1 time 3 times 5 times
Factor A:
Length
(Explanatory Variable)
30-sec
90-sec
Treatment 1 Treatment 2 Treatment 3
Treatment 4 Treatment 5 Treatment 6

16. For the advertising study, identify the experimental units or subjects, explanatory and response variables, the factors, and the treatments.
Factor B: Repetitions
3 levels
1 time 3 times 5 times
30-sec
90-sec
Treatment 1 Treatment 2 Treatment 3
Treatment 4 Treatment 5 Treatment 6
Factor A:
Length
2 levels
Treatment 5 = 90-sec commercial 3 times during the program.

17. For the advertising study, identify the experimental units or subjects, explanatory and response variables, the factors, and the treatments.
Factor B: Repetitions
1 time 3 times 5 times
30-sec
90-sec
Treatment 1 Treatment 2 Treatment 3
Treatment 4 Treatment 5 Treatment 6
Factor A:
Length
Hint: # of treatments = # levels for Factor A x # of levels for Factor B
EX: 2 x 3 = 6

18. How to buy happiness
ow_to_buy_happiness
Think about the # of factors and # of treatments. Watch until about 4: factors: amount of money and how it is spent.

19. Example, p. 240
A bad experiment: A high school regularly offers a review course to prepare students for the SAT. This year, budget cuts will allow the school to offer only an online version of the course. Suppose the group of students who take the online course earn an average increase of 45 points in their math scores from a pre-test to the actual SAT test. Can we conclude that the online course is effective?

20. Increase in math scores
Example, p. 240
A bad experiment: A high school regularly offers a review course to prepare students for the SAT. This year, budget cuts will allow the school to offer only an online version of the course. Suppose the group of students who take the online course earn an average increase of 45 points in their math scores from a pre-test to the actual SAT test. Can we conclude that the online course is effective?
Students
Online Course
Increase in math scores
This experiment has a very simple design:
Closer look showed that the students in the online course were in advanced math classes. Students could have increased their score due to the new knowledge from their advanced math classes.
What is something that may cause confounding?

21. How to Experiment Badly
Many laboratory experiments use a design like the SAT online course example:
Experimental Units
Treatment
Measure Response
In the lab environment, simple designs often work well.
Field experiments and experiments with animals or people deal with more variable conditions.
Outside the lab, badly designed experiments often yield worthless results because of confounding.

22. How to Experiment Well
Most well designed experiments compare two or more treatments. Comparison alone isn’t enough, if the treatments are given to groups that differ greatly, bias will result. The solution to the problem of bias is random assignment.
In an experiment, random assignment means that experimental units are assigned to treatments using a chance process.
The remedy for confounding is to perform a comparative experiment in which some units receive one treatment and similar units receive another.

23. Principles of Experimental Design
The basic principles for designing experiments are as follows:
1. Comparison. Use a design that compares two or more treatments.
2. Random assignment. Use chance to assign experimental units to treatments.
3. Control. Keep other variables that might affect the response the same for all groups.
4. Replication. Use enough experimental units in each group so that any differences in the effects of the treatments can be distinguished from chance differences between the groups.
Randomized comparative experiments are designed to give good evidence that differences in the treatments actually cause the differences we see in the response.
2. Random assignment - Doing so helps create roughly equivalent groups of experimental units by balancing the effects of other variables among the treatment groups.

24. Completely Randomized Design
In a completely randomized design, the treatments are assigned to all the experimental units completely by chance.
Some experiments may include a control group that receives an inactive treatment or an existing baseline treatment.
Group 1
Group 2
Treatment 1
Treatment 2
Compare Results
Random Assignment
Experimental Units

25. Example, p revised
This year, the high school has enough budget money to compare the online SAT course with the classroom SAT course. Fifty students have agreed to participate in an experiment comparing the two instructional methods.
Changed the example a little

26. Example, p revised
This year, the high school has enough budget money to compare the online SAT course with the classroom SAT course. Fifty students have agreed to participate in an experiment comparing the two instructional methods.
AP Exam Common Error: Many students lose credit because they fail to adequately describe how they assign the treatments to experimental units in an experiment. Most important, the method must be RANDOM.
What are some ways we can assign the treatments? Technology, Random Digit Table, Slips or paper, etc.

27. Example, p. 243
A well-designed experiment: Does regularly taking aspirin help protect people against heart attacks? The Physicians’ Health Study was a medical experiment that helped answer this question. In fact, the Physicians’ Health Study looked at the effects of two drugs: aspirin and beta-carotene. Researchers wondered whether beta-carotene would help prevent some forms of cancer. The subjects in this experiment were 21,996 male physicians. There were two explanatory variables (factors), each having two levels: aspirin (yes or no) and beta-carotene (yes or no). One-fourth of the subjects were assigned at random to each of the four treatments.

28. Example, p. 243
A well-designed experiment: Does regularly taking aspirin help protect people against heart attacks? The Physicians’ Health Study was a medical experiment that helped answer this question. In fact, the Physicians’ Health Study looked at the effects of two drugs: aspirin and beta-carotene. Researchers wondered whether beta-carotene would help prevent some forms of cancer. The subjects in this experiment were 21,996 male physicians. There were two explanatory variables (factors), each having two levels: aspirin (yes or no) and beta-carotene (yes or no). One-fourth of the subjects were assigned at random to each of the four treatments.
Explain how the four principles of experimental design was used in the Physicians’ Health Study.
1. Comparison:
Used active treatments and placebo to compare.

29. Example, p. 243 2. Random assignment:
A well-designed experiment: Does regularly taking aspirin help protect people against heart attacks? The Physicians’ Health Study was a medical experiment that helped answer this question. In fact, the Physicians’ Health Study looked at the effects of two drugs: aspirin and beta-carotene. Researchers wondered whether beta-carotene would help prevent some forms of cancer. The subjects in this experiment were 21,996 male physicians. There were two explanatory variables (factors), each having two levels: aspirin (yes or no) and beta-carotene (yes or no). One-fourth of the subjects were assigned at random to each of the four treatments.
Explain how the four principles of experimental design was used in the Physicians’ Health Study.
2. Random assignment:
Randomly assigned to the four treatments.

30. Example, p. 243
A well-designed experiment: Does regularly taking aspirin help protect people against heart attacks? The Physicians’ Health Study was a medical experiment that helped answer this question. In fact, the Physicians’ Health Study looked at the effects of two drugs: aspirin and beta-carotene. Researchers wondered whether beta-carotene would help prevent some forms of cancer. The subjects in this experiment were 21,996 male physicians. There were two explanatory variables (factors), each having two levels: aspirin (yes or no) and beta-carotene (yes or no). One-fourth of the subjects were assigned at random to each of the four treatments.
Explain how the four principles of experimental design was used in the Physicians’ Health Study.
3. Control:
Same gender and occupation. (Also, the subjects followed the same schedule of pill taking.)

31. Example, p. 243 4. Replication: Over 5000 subjects per treatment.
A well-designed experiment: Does regularly taking aspirin help protect people against heart attacks? The Physicians’ Health Study was a medical experiment that helped answer this question. In fact, the Physicians’ Health Study looked at the effects of two drugs: aspirin and beta-carotene. Researchers wondered whether beta-carotene would help prevent some forms of cancer. The subjects in this experiment were 21,996 male physicians. There were two explanatory variables (factors), each having two levels: aspirin (yes or no) and beta-carotene (yes or no). One-fourth of the subjects were assigned at random to each of the four treatments.
Explain how the four principles of experimental design was used in the Physicians’ Health Study.
4. Replication:
Over 5000 subjects per treatment.

32. Homework – Due Monday
P #45, 48, 50, 54, 57, 60, 62, 63