Chapter 4 Designing Studies

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

2. Section 4.2Experiments 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

3. Experiments • Observational Study versus Experiment 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. Definition: An observational study observes individuals and measures variables of interest butdoes 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.

4. Experiments • Observational Study versus Experiment EXAMPLES • In a health study, women who took hormones seemed to reduce their risk of heart attack by 35% to 50%. The risks of taking hormones appeared small compared with benefits. Observational study or Experiment? • A study randomly assigned elderly women to either soy or placebo to test the proposed benefits of soy like lower rates osteoporosis. The study showed that soy did not lower rate of osteoporosis. Observational study or Experiment? .

5. Experiments • 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. 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.

6. Experiments • Observational Study versus Experiment EXAMPLE • While experiments showed that soy did not lower the risk of osteoporosis in elderly women, observational studies show lower rates of osteoporosis in Asian cultures in which soy is a major dietary component. What are potential confounding variables in the observational studies?

7. Experiments • 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. 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.

8. Experiments • The Language of Experiments EXAMPLES • 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 households randomly assigned to ivermectin, 171 were free from head lice after two weeks compared with only 151 of the 191 households randomly assigned to malathion. • What are the experimental units? • What the explanatory & response variables? • What are the treatments? • A gardener plants 24 similar tomato plants in identical plots in his greenhouse. He will add fertilizer to the soil in half the pots. Also, he will water 8 of the plants with 0.5 gallon of water per day, 8 of the plants with 1 gallon of water per day, and the remaining 8 plants with 1.5 gallon of water per day. At the end of three months, he will record the total weight of tomatoes produced on each plant. • What are the experimental units? • What the explanatory & response variables? • What are the treatments?

9. Experiment • How to Experiment Badly • 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. 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

10. Experiment • How to Experiment Badly • 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.

11. Summary of Statistical Studies • How to Analyze & Critique a Statistical Study • Ask yourself these questions when you read about a study: • What is the population of interest? • Is this an experiment or observational study? • What was the sampling method? • SRS? • Convenience? • Voluntary response? • Stratified random sample? • Cluster sample? • Is the sample likely to be representative of the population of interest? • Are there any obvious sources of bias? • Undercoverage? • Nonresponse? • Response bias? • Wording of questions? • Other? • Are there any potential confounding variables?

12. Summary of Statistical Studies • How to Analyze & Critique a Statistical Study EXAMPLES • Many students regularly consume caffeine to help them stay alert. Thus, it seems plausible that taking caffeine might increase an individual’s pulse rate. A group of students wanted to test out this theory. At lunch, the asked the 10 other students at their lunch table to participate in their study. The students’ pulse rates were measured, then they drank some cola with caffeine, and after 10 minutes their pulse rates were measured again. Analyze & critique this study. • What is the population of interest? • Is this an experiment or observational study? • What was the sampling method? • Is the sample likely to be representative of the population of interest? • Are there any obvious sources of bias? • Are there any potential confounding variables?