Chapter 4 Designing Studies Section 4 2 Experiments

+ Chapter 4: Designing Studies Section 4. 2 Experiments The Practice of Statistics, 4 th edition – For AP* STARNES, YATES, MOORE

+ Chapter 4 Designing Studies n 4. 1 Samples and Surveys n 4. 2 Experiments n 4. 3 Using Studies Wisely

+ Section 4. 2 Experiments Learning Objectives After this section, you should be able to… ü DISTINGUISH observational studies from experiments ü DESCRIBE the language of experiments ü APPLY the three principles of experimental design ü DESIGN comparative experiments utilizing completely randomized designs and randomized block designs, including matched pairs design

Study versus Experiment Definition: Experiments 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. + n Observational 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. 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.

Soy Good For You? n Does Taking Hormones Reduce Heart Attack Risk After Menopause? n The Miracle of Vitamin D – Sound Science or Hype? n Texting While Driving n Owning More Cars Leads to a Longer Life Experiments n Is + n Examples

Study versus Experiment Definition: A lurking variable is a variable that is not among the explanatory or response variables in a study but that may influence the response variable. 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. Experiments 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. + n Observational

Language of 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. Sometimes, the explanatory variables 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. 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. + n The

n Louse-y Situation 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 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. Experiment n. A + Alternate Example 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.

n Tomatoes 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. Experiment n Growing + Alternate Example Problem: Identify the explanatory and response variables, experimental units, and list all the treatments. Solution: The two explanatory variables are fertilizer and water. The response variable is the weight of tomatoes produced. The experimental units are the tomato plants. There are 6 treatments: (1) 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

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. Experiment n to Experiment Badly + n How Example, page 236 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. Over the past 10 years, the average SAT score of students in the classroom course was 1620. The online group gets an average score of 1780. That’s roughly 10% higher than the long- time average for those who took the classroom review course. Is the online course more effective? Students -> Online Course -> SAT Scores

n 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. 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. Experiment n Does + Alternate Example

Many laboratory experiments use a design like the one in the online SAT 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. Experiment n to Experiment Badly + n How

n 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. n 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. Definition: In an experiment, random assignment means that experimental units are assigned to treatments at random, that is, using some sort of chance process. Experiments to Experiment Well: The Randomized Comparative Experiment + n How

n More Caffeine n Suppose you have a class of 30 students who volunteer to be subjects in the caffeine experiment described earlier. n Problem: Explain how you would randomly assign 15 students to each of the two treatments. Solution: Using 30 identical slips of paper, write A on 15 and B on the other 15. Mix them thoroughly in a hat and have each student select one paper. Have each student who received an A drink the cola with caffeine and each student who received a B to drink the cola without caffeine. + Experiment Alternate Example

Randomized Comparative Experiment + n The Group 1 Experimental Units 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. Treatment 1 Compare Results Random Assignment Group 2 Treatment 2

Diets n A health organization wants to know if a low-carb or low-fat diet is more effective for long-term weight loss. The organization decides to conduct an experiment to compare these two diet plans with a control group that is only provided with brochure about healthy eating. Ninety volunteers agree to participate in the study for one year. n Problem: Outline a completely randomized design for this experiment. Write a few sentences describing how you would implement your design. Group 1 30 Subjects 90 Volunteers Random Assignment Group 2 30 Subjects Group 3 30 Subjects Experiment n Dueling + Alternate Example Treatment 1 Low Carb Treatment 2 Low Fat Treatment 3 Control Compare Weight Loss

Randomized comparative experiments are designed to give good evidence that differences in the treatments actually cause the differences we see in the response. Principles of Experimental Design 1. 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. 2. 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. 3. 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. Experiments n Principles of Experimental Design + n Three

More Caffeine Experiment n + Alternate Example Problem: Explain how to use all three principles of experimental design in the caffeine experiment. Solution: Control: There should be a control group that receives non-caffeinated cola. Also, the subjects in each group should receive exactly the same amount of cola served at the same temperature. Also, each type of cola should look and taste exactly the same and have the same amount of sugar. Subjects should drink the cola at the same rate and wait the same amount of time before measuring their pulse rates. Try to control lurking variables. Randomization: Subjects should be randomly assigned to one of the two treatments. This should roughly balance out the effects of the lurking variables we cannot control, such as body size, caffeine tolerance, and the amount of food recently eaten. Replication: We want to use as many subjects as possible to help make the treatment groups as equivalent as possible. This will give us a better chance to see the effects of caffeine, if there any. n

Read the description of the Physicians’ Health Study on page 241. Explain how each of the three principles of experimental design was used in the study. A placebo is a “dummy pill” or inactive treatment that is indistinguishable from the real treatment. Experiments n The Physicians’ Health Study + n Example:

What Can Go Wrong? 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. n Good experiments, therefore, require careful attention to details to ensure that all subjects really are treated identically. 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. Whenever possible, experiments with human subjects should be double-blind. 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. Experiments n + n Experiments:

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. n 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. n If they are, we call them statistically significant. 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. Experiments n + n Inference

Distracted Drivers Perform 10 repetitions of your simulation and report the number of drivers in the cell phone group who failed to stop Experiments Is talking on a cell phone while driving more distracting than talking to a passenger? Read the Activity on page 245. + n Activity: Teacher: Right-click (control-click) on the graph to edit the counts. In what percent of the class’ trials did 12 or more people in the cell phone group fail to stop? Based on these results, how surprising would it be to get a result this large or larger simply due to chance involved in random assignment? Is this result statistically significant?

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. 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. Experiments n + n Blocking 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 (lurking variables) among the experimental units. Randomization will average out the effects of the remaining lurking 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.

n. A Texting? cell phone company is considering two different keyboard designs (A and B) for its new line of cell phones. Researchers would like to conduct an experiment using subjects who are frequent texters and subjects who are not frequent texters. The subjects will be asked to text several different messages in 5 minutes. The response variable will be the number of correctly typed words. Experiment n Better + Alternate Example Problem: (a) Explain why a randomized block design might be preferable to a completely randomized design for this experiment. (b) Outline a randomized block experiment using 100 frequent texters and 200 novice testers.

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. 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. Experiments n Design + n Matched-Pairs

Consider the Fathom dotplots from a completely randomized design and a matched-pairs design. What do the dotplots suggest about standing vs. sitting pulse rates? Experiments n Standing and Sitting Pulse Rate + n Example:

+ Section 4. 2 Experiments Summary In this section, we learned that… ü We can produce data intended to answer specific questions by observational studies or experiments. ü In an experiment, we impose one or more treatments on a group of experimental units (sometimes called subjects if they are human). ü The design of an experiment describes the choice of treatments and the manner in which the subjects are assigned to the treatments. ü The basic principles of experimental design are control for lurking variables, random assignment of treatments, and replication (using enough experimental units). ü Many behavioral and medical experiments are double-blind.

+ Section 4. 2 Experiments Summary, con’t In this section, we learned that… ü Some experiments give a placebo (fake treatment) to a control group that helps confounding due to the placebo-effect. ü 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. ü 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.

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