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

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Presentation on theme: "+ The Practice of Statistics, 4 th edition – For AP* STARNES, YATES, MOORE Chapter 4: Designing Studies Section 4.2 Experiments."— Presentation transcript:

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

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

3 + Section 4.2 Experiments 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 Learning Objectives 3

4 + ADHD Linked to Lead and Mom’s Smoking (February 1, 2007): A mother’s smoking during pregnancy and exposure to lead significantly increases her child’s risk for developing attention deficit hyperactivity disorder (ADHD), say researchers. In fact, as many as one third of cases of ADHD in children are linked to exposure to tobacco smoke and lead before birth, giving moms yet another reason to quit smoking during pregnancy. 4

5 + ADHD Linked to Lead and Mom’s Smoking (February 1, 2007): For the study, researchers from Cincinnati Children’s Hospital Medical Center surveyed over 4,700 children between the ages of 4 and 15 and their parents. Over 4 percent of the children included had ADHD. The researchers found that those children whose mother smoked during pregnancy were over twice as likely to develop ADHD than a child whose mother had not smoked. In addition, a child who had been exposed to lead, giving them high lead blood levels, were four times as likely to have ADHD, as compared to a child with low lead levels in his blood. 5

6 + ADHD Linked to Lead and Mom’s Smoking (February 1, 2007): Based on this study, should we conclude that smoking during pregnancy causes an increase in the likelihood that a child develops ADHD? Explain. 6

7 + Experiments Observational Study versus Experiment In contrast to observational studies, experiments don’t just observe individuals or ask them questions. They activelyimpose some treatment in order to measure the response. 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. 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. 7

8 + Comparing: Watch and record what happens NO treatments applied NO Cause and Effect can be claimed Apply a treatment to subjects Finding cause and effect is the GOAL Observational StudyExperiment 8

9 + Types of variables: May help explain or influence changes in a response variable These are also called factors Example: How much you study explains your score on a test Measures the outcome of a study Example: measuring level of energy after counting how many hours of sleep you got Explanatory Variable Response Variable 9

10 + 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. Note: Each lurking variable can turn into a confounding variable if the experiment is designed poorly!! 10

11 + Check your understanding (p233) # 1 – Experiment: the treatment of screen brightness was imposed #2 – observational study: no treatment was assigned #3 – Explanatory: # of meals per week eaten with family Response: GPA 11

12 + Experiment or Study? A teacher wants to compare the effectiveness of computer software for teaching biology with that of a textbook presentation. She gives a biology pretest to a group of high school juniors, then randomly divides them into two sub-groups. One group uses the computer, and the other studies the text. At the end of the year, she tests all the students again and compares the increase in biology test scores in the two groups. Experiment or study? Justify your answer. 12

13 + Experiment or Study? One study of cell phones and the risk of brain cancer looked at a group of 469 people who have brain cancer. The investigators matched each cancer patient with a person of the same age, gender, and race who did not have brain cancer, then asked about the use of cell phones. Result: “Our data suggest that the use of handheld cellular phones is not associated with the risk of brain cancer.” Experiment or study? Justify your answer. 13

14 + 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. 14

15 + Vocabulary of Experiments (p234) Identify the experimental units, explanatory and response variables, and the treatments in the Careerstart experiment Experimental Units: 14 middle schools in Forsyth County, NC Explanatory variable: If the school used the CareerStart program with its students Response Variable: test scores, attendance, behavior, student engagement, and graduation rates Treatments: (1) standard middle school curriculum (2) standard curriculum plus CareerStart 15

16 + Example: A louse-y situation Experimental Units: the 376 households Explanatory variable: type of medication Response Variable: if the household was lice-free Treatments: (1) ivermectin (2) malathion 16

17 + Example: Growing Tomatoes Experimental Units: 24 tomato plants Explanatory variable: (1) if fertilizer is applied (2) amount of water Response Variable: weight of tomatoes Treatments: (1) fertilizer, 0.5 gallon (2) fertilizer, 1 gallon (3) fertilizer, 1.5 gallons (4) no fertilizer, 0.5 gallon (5) no fertilizer, 1 gallon (5) no fertilizer, 1.5 gallons 17

18 + Experiments Does caffeine affect pulse rate? 1. Measure pulse rate 2. Give students caffeine 3. Wait for a certain amount of time 4. Measure the pulse rate 5. Compare final and initial pulse rates Are there problems? Lurking variables? 18

19 + Experiment How to Experiment Badly Experiments are the preferred method for examining the effectof one variable on another. By imposing the specific treatmentof interest and controlling other influences, we can pin downcause and effect. Good designs are essential for effectiveexperiments, 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 19

20 + Experiment How to Experiment Badly Many laboratory experiments use a design like the one in theonline 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. 20

21 + Experiments How to Experiment Well: The RandomizedComparative 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 experimentscompare two or more treatments. Comparison alone isn’t enough, if the treatments are given togroups 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. 21

22 + Experiments The Randomized Comparative Experiment 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. Experimental Units Random Assignment Group 1 Group 2 Treatment 1 Treatment 2 Compare Results 22

23 + Example: Dueling Diets Here is a basic outline: To implement the design, use 90 equally sized slips of paper. Label 30 of the slips “1”, 30 of the slips “2” and 30 of the slips “3”. Then, mix them up in a hat and have each subject draw a number without looking. The number that each subject chooses will be the group he or she is assigned to. At the end of the year, the amount of weight loss will be recorded for each subject and the mean weight loss will be compared for the three treatments. Diagram: 23

24 + Control groups – Do you need one? The primary purpose of a control group is to provide a baseline for comparing the effects of the other treatments. Most control groups receive inactive treatments that might be called a placebo. However, some control groups receive active treatments depending on the design of the experiment. Some designs do not have a control group. This is appropriate when researchers want to compare the effectiveness of several treatments and not compare them to an inactive treatment. 24

25 + Experiments Three Principles of Experimental Design Randomized comparative experiments are designed to givegood evidence that differences in the treatments actuallycause the differences we see in the response. 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. Principles of Experimental Design 25

26 + More caffeine 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. If all of these lurking variables are controlled, they will not be confounded with caffeine or be an additional source of variability in pulse rates. 26

27 + More Caffeine 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 are any. 27

28 + Experiments Example: The Physicians’ Health Study Read the description of the Physicians’ Health Study on page241. Explain how each of the three principles of experimentaldesign was used in the study. A placebo is a “dummy pill” or inactive treatment that is indistinguishable from the real treatment. 28

29 + Experiments Experiments: What Can Go Wrong? The logic of a randomized comparative experiment dependson our ability to treat all the subjects the same in every wayexcept for the actual treatments being compared. Good experiments, therefore, require careful attention todetails 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. 29

30 + Check your understanding (p244) #1 – No – it is possible that women who thought they were getting an ultrasound would have different reactions to pregnancy than those who knew that they had not received an ultrasound. #2 – No. While the people weighing the babies at birth may not know which group the mother was in, the mothers know whether or not they had the ultrasound. This means that the mothers may have affected the outcome since they knew if they had received the treatment or not. #3 – An improved design would be one in which all mothers are treated as if they had an ultrasound, but for some mothers the ultrasound was fake. 30

31 + Experiments Inference for Experiments In an experiment, researchers usually hope to see a differencein the responses so large that it is unlikely to happen justbecause of chance variation. We can use the laws of probability, which describe chancebehavior, to learn whether the treatment effects are larger thanwe would expect to see if only chance were operating. 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. 31

32 + Experiments Activity: Distracted Drivers Is talking on a cell phone while driving more distracting than talking to a passenger? Read the Activity on page 245. Perform 10 repetitions of your simulation and report the number of drivers in the cell phone group who failed to stop 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? 32

33 + Experiments Blocking Completely randomized designs are the simplest statistical designsfor experiments. But just as with sampling, there are times when thesimplest 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. 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. 33

34 + Example: Chocolate Chip Cookies A randomized block design might be preferable because cookies might bake differently depending on which rack they are on. Diagram: 34

35 + Experiments Matched-Pairs Design A common type of randomized block design for comparing twotreatments is a matched pairs design. The idea is to create blocks bymatching 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. 35

36 + Blocked/Paired Design This design is beneficial when you think there might be lurking variables present Control what you can, block on what you can’t control, and randomize to create comparable groups 36

37 + Section 4.2 Experiments 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. Summary 37

38 + Section 4.2 Experiments 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. Summary, con’t 38

39 + Experiments Example: Standing and Sitting Pulse Rate Consider the Fathom dotplots from a completely randomizeddesign and a matched-pairs design. What do the dotplotssuggest about standing vs. sitting pulse rates? 39

40 + Looking Ahead… 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… 40

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