1. Chapter 4: Designing Studies
Section 4.2
Experiments
The Practice of Statistics, 4th edition – For AP*
STARNES, YATES, MOORE

2. Chapter 4 Designing Studies
4.1 Samples and Surveys
4.2 Experiments
4.3 Using Studies Wisely

3. Section 4.2 Experiments After this section, you should be able to…
Learning Objectives
After this section, you should be able to…
DISTINGUISH observational studies from experiments
DESCRIBE the language of experiments
APPLY the three principles of experimental design
DESIGN comparative experiments utilizing completely randomized designs and randomized block designs, including matched pairs design

4. Observational Study versus Experiment
Experiments
Definition:
An observational study observes individuals and measures variables of interest but does not attempt to influence the responses.
An experiment deliberately imposes some treatment on individuals to measure their responses.
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.
When our goal is to understand cause and effect, experiments are the only source of fully convincing data.
The distinction between observational study and experiment is one of the most important in statistics.

5. Why Observational Studies?
Cheaper
Faster
Can examine long-term effects
Hypothesis-generating
Sometimes, experimental studies are not ethical (e.g., randomizing subjects to smoke)

6. Example: The scatterplot below illustrates how the number of firefighters sent to fires (X) is related to the amount of damage caused by fires (Y) in a certain city.
The scatterplot clearly displays a fairly strong positive relationship between the two variables. Would it, then, be reasonable to conclude that sending more firefighters to a fire causes more damage?
Of course not! So what is going on here?
There is a third variable in the background—the seriousness of the fire—that is responsible for the observed relationship. More serious fires require more firefighters, and also cause more damage.

7. Here, the seriousness of the fire is a lurking variable.
 A lurking variable is a variable that is not among the explanatory
or response variables in a study, but could substantially affect your
interpretation of the relationship among those variables.
In particular, as in our example, the lurking variable might have an effect on both the explanatory and the response variables. This common effect creates the observed association between the explanatory and response variables, even though there is no causal link between them. We call this situation common response. 

8. Does Caffeine Affect Pulse Rate
Many students regularly consume caffeine to help them stay alert. Thus, it seems plausible that taking caffeine might increase an individual’s pulse rate. Is this true? One way to investigate this is to have volunteers measure their pulse rates, drink some cola with caffeine, measure their pulses again after 10 minutes and calculate the increase in pulse rate.
Alternate Example
Experiment
Unfortunately, even if every student’s pulse rate went up, we couldn’t attribute the increase to caffeine. Perhaps the excitement of being in an experiment made their pulse rates increase. Perhaps it was the sugar in the cola and not the caffeine. Perhaps their teacher told them a funny joke during the 10 minute waiting period and made everyone laugh! In other words, there are many variables that are potentially confounded with caffeine.

9. Observational Study versus Experiment
Observational studies of the effect of one variable on another often fail because of confounding between the explanatory variable and one or more lurking variables.
Experiments
Definition:
An explanatory variable explains or influences changes in responses
A response variable measures an outcome of a study
A lurking variable is a variable that is not among the explanatory or response variables in a study but that may influence the other variables in the study giving the impression of an association between them. Sometimes call common response.
Confounding occurs when two variables are associated in such a way that their effects on a response variable cannot be distinguished from each other.
Well-designed experiments take steps to avoid confounding.

10. The Language of Experiments
An experiment is a statistical study in which we actually do something (a treatment) to people, animals, or objects (the experimental units) to observe the response. Here is the basic vocabulary of experiments.
Experiments
Definition:
A specific condition applied to the individuals in an experiment is called a treatment. If an experiment has several explanatory variables, a treatment is a combination of specific values of these variables.
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.
Types of variables:
an explanatory variable explains or influences changes in a response variable
a response variable measures an outcome of a study

11. The Language of Experiments
Sometimes, the explanatory variables (those variables which may influence change in a response) in an experiment are called factors.
Many experiments study the joint effects of several factors. In such an experiment, each treatment is formed by combining a specific value (often called a level) of each of the factors.

12. A Louse-y Situation Experiment
A study published in the New England Journal of Medicine (March 11, 2010) compared two medicines to treat head lice: an oral medication called ivermectin and a topical lotion containing malathion. Researchers studied 812 people in 376 households in seven areas around the world. Of the 185 randomly assigned to ivermectin, 171 were free from head lice after two weeks compared to only 151 of the 191 households randomly assigned to malathion.
Alternate Example
Experiment
Problem: Identify the experimental units, explanatory and response variables, and the treatments in this experiment.
Solution: The experimental units are the households, not the individual people, since the treatments were assigned to entire households, not separately to individuals within the household. The explanatory variable is type of medication and the response variable is whether the household was lice-free. The treatments were ivermectin and malathion.

13. Growing Tomatoes Experiment
Does adding fertilizer affect the productivity of tomato plants? How about the amount of water given to the plants? To answer these questions, a gardener plants 24 similar tomato plants in identical pots in his greenhouse. He will add fertilizer to the soil in half of the pots. Also, he will water 8 of the plants with 0.5 gallons of water per day, 8 of the plants with 1 gallon of water per day and the remaining 8 plants with 1.5 gallons of water per day. At the end of three months he will record the total weight of tomatoes produced on each plant.
Alternate Example
Experiment
Problem: Identify the explanatory and response variables, experimental units, and list all the treatments.
Solution: The two explanatory variables are amounts of fertilizer and water. The response variable is the weight of tomatoes produced. The experimental units are the tomato plants. There are 6 treatments:
fertilizer, 0.5 gallon (2) fertilizer, 1 gallon
(3) fertilizer, 1.5 gallons (4) no fertilizer, 0.5 gallons
(5) no fertilizer, 1 gallon (6) no fertilizer, 1.5 gallons

14. A farm-product manufacturer wants to determine if the yield of a crop is different when the soil is treated with three different types of fertilizers. Fifteen similar plots of land are planted with the same type of seed but are fertilized differently. At the end of the growing season, the mean yield from the sample plots is compared.
Experimental units?
Factors?
Levels?
Response variable?
How many treatments?
Plots of land
Type of fertilizer
Fertilizer types A, B, & C
Yield of crop 3

15. A consumer group wants to test cake pans to see which works the best (bakes evenly). It will test aluminum, glass, and plastic pans in both gas and electric ovens.
Experiment units?
Factors?
Levels?
Response variable?
Number of treatments?
Cake batter
Two factors - type of pan & type of oven
Type of pan has 3 levels (aluminum, glass, & plastic & type of oven has 2 levels (electric & gas)
How evenly the cake bakes 6

16. Experiments are the preferred method for examining the effect of one variable on another. By imposing the specific treatment of interest and controlling other influences, we can pin down cause and effect. Good designs are essential for effective experiments, just as they are for sampling. Many laboratory experiments use a design like the following:
Experiment
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.

17. 100% of daily vitamins & essential oils!
SO WHAT MAKES A GOOD EXPERIMENT?
I’ve developed a new rabbit food,
Hippity Hop.
Makes fur soft & shiny!
Hippity Hop
Rabbit Food
Increases energy!
100% of daily vitamins & essential oils!

18. Can I just make these claims?NO
What must I do to make you believe these claims?
Do an experiment
Who (what) should I test this on?
Rabbits
What do I test?
The type of food

19. I plan to test my new rabbit food. What are my experimental units?
What is my factor?
What is the response variable?
Rabbits
Type of food
How well they grow

20. I’ll use my pet rabbit, Lucky!
Hippity Hop
Discuss the need for a comparison group.
Since Lucky’s coat is shinier & he has more energy, then Hippity Hop is a better rabbit food!

21. WOW! Lucky is bigger & shinier so Hippity Hop is better!
Old Food
Hippity Hop
Now I’ll use Lucky & my friend’s rabbit, Flash. Lucky gets Hippity Hop food & Flash gets the old rabbit food.
Discuss the need for replication.
WOW! Lucky is bigger & shinier so Hippity Hop is better!

22. The Hippity Hop rabbits have scored higher so it’s the better food!
Old Food
Hippity Hop
The first five rabbits that I catch will get Hippity Hop food and the remaining five will get the old food.
Discuss the need for random assignment to treatment groups.
The Hippity Hop rabbits have scored higher so it’s the better food!

23. How to Experiment Well: The Randomized Comparative Experiment
The remedy for confounding is to perform a comparative experiment in which some units receive one treatment and similar units receive another. 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.
Experiments
Definition:
In an experiment, random assignment means that experimental units are assigned to treatments at random, that is, using some sort of chance process.

24. The Randomized Comparative Experiment
Experiments
Definition:
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
Experimental Units
Random Assignment

25. Place the numbers in a hat.
Old Food
Hippity Hop
Number the rabbits
The remaining rabbits get the old food. 8 5 7 3 9
The first five numbers pulled from the hat will be the rabbits that get Hippity Hop food. 6
Discuss the need for the evaluator to be blinded 2 4 5
I evaluated the rabbits & found that the rabbits eating Hippity Hop are better than the old food! 10 1 9 7 3 8

26. Hippity Hop Rabbit Food makes fur soft and shiny, & increases energy for ALL types of rabbits!
Discuss scope of inference.
Can I make this claim?

27. Principles of Experimental Design
Three Principles of Experimental Design
Randomized comparative experiments are designed to give good evidence that differences in the treatments actually cause the differences we see in the response.
Experiments
Principles of Experimental Design
Control for lurking variables that might affect the response: Use a comparative design and ensure that the only systematic difference between the groups is the treatment administered.
Random assignment: Use impersonal chance to assign experimental units to treatments. This helps create roughly equivalent groups of experimental units by balancing the effects of lurking variables that aren’t controlled on the treatment groups.
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.

28. Example: The Physicians’ Health Study
This study looked at the effects of two drugs: aspirin and beta carotene. Researchers wondered whether beta carotene would help prevent some types of cancer. The subjects 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). Combinations of these factors form the four treatments shown. ¼ of the subjects were assigned at random to each of these treatments. On odd-numbered days, the subjects took either a tablet that contained aspirin or a placebo pill. On even-numbered days, they took either a beta carotene pill or a placebo*. There were several kinds of response variables: heart attacks, certain types of cancer, and other medical outcomes. After several years, 239 of the placebo group and 139 of the aspirin group suffered heart attacks. The beta carotene, however, didn’t seem to have any significant effects
Explain how each of the 3 principles of
Experimental design was used in the
study

29. Designing Better Experiments
The logic of a randomized comparative experiment depends on our ability to treat all the subjects the same in every way except for the actual treatments being compared.
Good experiments, therefore, require careful attention to details to ensure that all subjects really are treated identically, even if that means you need to use a little deception! .
Experiments
A response to a dummy treatment is called a placebo effect. The strength of the placebo effect is a strong argument for randomized comparative experiments. .
Definition:
In a double-blind experiment, neither the subjects nor those who interact with them and measure the response variable know which treatment a subject received.
Whenever possible, experiments with human subjects should be double-blind.

30. Blocking Experiments Definition
Completely randomized designs are the simplest statistical designs for experiments. But just as with sampling, there are times when the simplest method doesn’t yield the most precise results.
Experiments
Definition
A block is a group of experimental units that are known before the experiment to be similar in some way that is expected to affect the response to the treatments.
In a randomized block design, the random assignment of experimental units to treatments is carried out separately within each block.
Form blocks based on the most important unavoidable sources of variability among the experimental units.
Randomization will average out the effects of the remaining variables and allow an unbiased comparison of the treatments.
Control what you can, block on what you can’t control, and randomize to create comparable groups.

31. Randomized block – units are blocked into homogeneous groups and then randomly assigned to treatments
Random assignment

32. Treatment B Treatment A Treatment A Treatment B
Put into homogeneous groups
Randomly assign experimental units to treatments
Randomized block design

33. EXAMPLE: Suppose a researcher is carrying out a study of the effectiveness of four different skin creams for the treatment of a certain skin disease. He has ninety subjects and plans to divide them into 3 treatment groups of thirty subjects each.
HOW COULD WE CARRY OUT A BLOCK DESIGN?
If the experimenter has reason to believe that age might be a significant factor in the effect of a given medication, he might choose to first divide the experimental subjects into age groups, such as under 30 years old, years old and over 60 years old. Then, within each age level, individuals would be assigned to treatment groups using a completely randomized design

34. Another way we could do randomized block design would be to have the subjects assessed and put in blocks of three according to how severe their skin condition is; the four most severe cases are the first block, the moderate cases in the second block, and mildest cases in the third block. The members of each block are then randomly assigned, one to each of the four treatment group

35. Matched-Pairs Design Experiments Definition
A common type of randomized block design for comparing two treatments is a matched pairs design. The idea is to create blocks by matching pairs of similar experimental units.
Experiments
Definition
A matched-pairs design is a randomized blocked experiment in which each block consists of a matching pair of similar experimental units.
Chance is used to determine which unit in each pair gets each treatment.
Sometimes, a “pair” in a matched-pairs design consists of a single unit that receives both treatments. Since the order of the treatments can influence the response, chance is used to determine with treatment is applied first for each unit.

36. Treatment A
Treatment B
Next, randomly assign one unit from a pair to Treatment A. The other unit gets Treatment B.
Pair experimental units according to specific characteristics.
This is one way to do a matched pairs design – another way is to have the individual unit do both treatments (as in a taste test).

37. We want the only influence on our units to be the treatment!
REMEMBER BLOCKING IS A WAY TO MITIGATE CONFOUNDING OR LURKING VARIABLES. THEREFORE BE SURE TO BLOCK ACCORDING TO THE OBSERVABLE POSSIBLE VARIABLE AND ADMINISTER ALL TREATMENTS RANDOMLY TO EACH BLOCK!
We want the only influence on our units to be the treatment!
Ask for 4 male & 4 female volunteers
Randomly assign to treatments – no confounding between gender & deodorant
Block by gender & randomly assign – no confounding
Block by gender – give females new deodorant & males get current – NOW have confounding!

38. Why is the same type of seed used on all 15 plots?
Example: A farm-product manufacturer wants to determine if the yield of a crop is different when the soil is treated with three different types of fertilizers. Fifteen similar plots of land are planted with the same type of seed but are fertilized differently. At the end of the growing season, the mean yield from the sample plots is compared.
Why is the same type of seed used on all 15 plots?
What are other potential extraneous OR confounding variables?
Does this experiment have a placebo? Explain
To control the factor of type of seed.
Type of soil; amount of water, sunlight, etc.
No, one would compare the three types of fertilizers
It is part of the controls in the experiment.
Type of soil, amount of water, etc.
NO – a placebo is not needed in this experiment

39. Is this an experiment? Why or why not?
Example: Four new word-processing programs are to be compared by measuring the speed with which standard tasks can be completed. One hundred volunteers are randomly assigned to one of the four programs and their speeds are measured.
Is this an experiment? Why or why not?
Yes, a treatment is imposed.
Yes, a treatment was imposed
Completely randomized
one factor, word processing program & 4 levels, the four new programs
Speed at which standard tasks can be done
What type of design is this?
Factors? Levels?
Response variable?
Completely randomized
one factor: word-processing program with 4 levels
speed

40. Example: Suppose that the manufacturer wants to test a new fertilizer against the current one on the market. Ten 2-acre plots of land scattered throughout the county are used. Each plot is subdivided into two subplots, one of which is treated with the current fertilizer, and the other with the new fertilizer. Wheat is planted and the crop yields are measured.
What type of design is this?
Why use this method?
When does randomization occur?
Matched - pairs design
Randomly assigned treatment to first acre of each two-acre plot

41. Blocking also helps reduce variability.
Randomization reduces bias by spreading any uncontrolled confounding variables evenly throughout the treatment groups.
Is there another way to reduce variability?
Blocking also helps reduce variability.
Variability is controlled by sample size. Larger samples produce statistics with less variability.

42. Inference for Experiments
In an experiment, researchers usually hope to see a difference in the responses so large that it is unlikely to happen just because of chance variation.
We can use the laws of probability, which describe chance behavior, to learn whether the treatment effects are larger than we would expect to see if only chance were operating.
If they are, we call them statistically significant.
Experiments
Definition:
An observed effect so large that it would rarely occur by chance is called statistically significant.
A statistically significant association in data from a well-designed experiment does imply causation.

43. Section 4.2 Experiments Summary In this section, we learned that…
We can produce data intended to answer specific questions by observational studies or experiments.
In an experiment, we impose one or more treatments on a group of experimental units (sometimes called subjects if they are human).
The design of an experiment describes the choice of treatments and the manner in which the subjects are assigned to the treatments.
The basic principles of experimental design are control for lurking variables, random assignment of treatments, and replication (using enough experimental units).
Many behavioral and medical experiments are double-blind.

44. Section 4.2 Experiments Summary, con’t
In this section, we learned that…
Some experiments give a placebo (fake treatment) to a control group that helps confounding due to the placebo-effect.
In addition to comparison, a second form of control is to form blocks of individuals that are similar in some way that is important to the response. Randomization is carried out within each block.
Matched pairs are a common form of blocking for comparing just two treatments. In some matched pairs designs, each subject receives both treatments in a random order.

45. Looking Ahead… In the next Section…
We’ll learn how to use studies wisely.
We’ll learn about
The Scope of Inference
The Challenges of Establishing Causation
Data Ethics
In the next Section…