Chapter 4: Causation: Can We Say What Caused the Effect? Sections 4.1 & 4.2: Association and Confounding / Observations v.s.

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1 Stat 300: Intro to Probability & Statistics Textbook: Introduction to Statistical Investigations Name: American River College Chapter 4: Causation: Can We Say What Caused the Effect? Sections 4.1 & 4.2: Association and Confounding / Observations v.s. Experiments Example 1: An area of research in biomechanics and gerontology concerns falls and fall-related injuries, especially for elderly people. Recent studies have focused on how individuals respond to large postural disturbances (e.g., tripping, induced slips). One question is whether subjects can be instructed to improve their recovery from such perturbations. Suppose researchers want to compare two such recovery strategies, lowering (making the next step shorter, but in normal step time) and elevating (using a longer or normal step length with normal step time). Subjects will have first been trained on one of these two recovery strategies, and they will be asked to apply it after they feel themselves tripping. The researchers will then induce the subject to trip while walking (but harnessed for safety), using a concealed mechanical obstacle. (a) Identify the observational units and the two variables in this study. Classify each variable as categorical or quantitative. Observational Units: Variable 1: Variable 2: Definition: When we have two variables in a study we often consider one the explanatory variable and the other the response variable. Often the research study is looking for evidence that the explanatory variable causes changes in the response variable. (b) Which variable is being considered the explanatory variable and which the response variable?

2 Stat 300 Text: Intro. to Statistical Investigations Section 4.1 & 4.2 Page 2 of 5 Example 2: Sports teams prefer to play in front of their own fans rather than at the opposing team s site. Having a sell-out crowd should provide even more excitement and lead to an even better performance, right? Well, consider the Oklahoma City Thunder, a National Basketball Association team, in its second season ( ) after moving from Seattle. This team had a win-loss record that was actually worse for home games with a sell-out crowd (3 wins and 15 losses) than for home games without have a sell-out crowd (12 wins and 11 losses). (These data were noted in the April 20, 2009 issue of Sports Illustrated in the Go Figure column.) (a) Identify the observational units and the explanatory and response variables in this study. Observational units: Explanatory: Response: (b) Organize the data into a 2 2 table of counts, with the explanatory variable groups in columns: Win Loss Total Smaller crowd Sell-out crowd Total (c) Calculate the proportion of wins for each group. Identify them with appropriate symbols. [Hint: Are these a parameter or a statistic?] These are called the conditional distributions of the game outcome variable for the two different categories of the crowd size variable. The relationship between two categorical variables can be displayed visually in a segmented bar graph. Each category of the explanatory variable has a bar with a height of 100%, but these bars contain segments whose length corresponds to the conditional proportions. (Excel calls this a 100% stacked column chart.)

3 Stat 300 Text: Intro. to Statistical Investigations Section 4.1 & 4.2 Page 3 of 5 (d) Produce a segmented bar graph to display these conditional proportions. (e) Do these proportions, and the segmented bar graph, suggest an association (relationship) between the two variables? Explain. (f) Is it reasonable to conclude that a sell-out crowd caused the team to play worse? If not, provide an alternative explanation that plausibly explains the observed association. [Hint: the Thunder were less likely to win with a sell-out crowd. What are three possible explanations for this difference?] Definition: A confounding variable is one whose potential effects on a response variable cannot be distinguished from those of the explanatory variable. o A confounding variable is related to both the explanatory and response variable. o Because of the potential for confounding variables, one cannot legitimately draw cause-and-effect conclusions from observational studies. g) Identify a confounding variable in this study, and explain how this confounding variable is related to both the explanatory and response variable.

4 Stat 300 Text: Intro. to Statistical Investigations Section 4.1 & 4.2 Page 4 of 5 Definition: An observational study passively records information on the observational units without intervention. An experiment actively intervenes and imposes the explanatory variable on the observational (aka experimental) unit. (g) Is the OK City Thunder study an observational study or an experiment? Key idea: When confounding variables are present, we are not able to draw any cause-andeffect conclusions between our explanatory variable and our response variable. Observational studies always have the potential for confounding variables. Therefore, never draw causeand-effect conclusions from observational studies. Example 1 continued: (c) Explain how you could design this study as an experiment. Suppose 24 subjects have agreed to participate in this study: Females: Alisha, Alice, Betty, Martha, Audrey, Mary, Barbie, Anna Males: Matt, Peter, Shawn, Brad, Michael, Kyle, Russ, Patrick, Bob, Kevin, Mitch, Marvin, Paul, Pedro, Roger, Sam (d) Would it be reasonable to give the females the lower strategy and the males the elevating strategy? Why or why not? If not, what would you do instead? How can you decide whether this is effective? The Randomizing Subjects applet allows us to simulate this random assignment a large number of times to observe the long-run behavior. (e) Moral:

5 Stat 300 Text: Intro. to Statistical Investigations Section 4.1 & 4.2 Page 5 of 5 Scope of Conclusions permitted depending on study design (from Ramsey and Schafer) Assignment of units to groups By random assignment No random assignment Selection of units from population Random sampling Not random sampling A random sample is selected from one population; units are then randomly assigned to different treatment groups A groups of study units is found; units are then randomly assigned to treatment groups Random samples are selected from existing distinct populations Collections of available units from distinct groups are examined Þ Þ Inferences to populations can be drawn Potential for sampling bias ß Can draw cause and effect conclusions ß Potential for confounding variables (f) But we still have the question that even with a randomized comparative experiment, we still may get an unlucky random assignment and the difference we observed between the groups occurred just by chance. How can we eliminate this as a possible explanation? Example 3: Many studies have shown that women who smoke while pregnant tend to have babies who weigh significantly less at birth, on average, than women who do not smoke while pregnant. (a) Identify the population of interest in these studies. (b) Identify and classify the explanatory variable and the response variable. (c) Do you think these studies were observational or experimental? Justify your answer. (d) Can you identify a potential confounding variable that provides an alternative explanation to concluding that smoking while pregnant causes lower birthweight in babies?