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1. Now we're going to ask the question, does the sex of the person observing balance time have a relationship to balance time? First, randomly pick 10 male observers and 10 female observers. Say what method you used to randomly pick the observers. Analyze the data using nested anova, with sex of the observer as the groups, individual observers as the subgroups, and log transformed balance time as the measurement variable. Report the F-statistic, degrees of freedom, and P-value for the groups and subgroups, and report the percentage of variation explained by each level. What do you conclude? Based on this information, how would you design a future set of observations on balance time?
2. It seems plausible that if there's an effect of the observer's sex on balance time, there might be an interaction between the sex of the observer and the sex of the balancer. So using the entire data set (not just the ones you analzyed in question 1), randomly pick 40 measurements of log-transformed balance time for each combination of observer sex and balancer sex. Say what method you used to randomly pick the observers. Use this online two-way anova calculator to do a two-way anova. (Don't worry about "weighted" vs. "unweighted" analysis, you're doing a balanced design so the two methods are identical.) Report the three P-values and give your interpretation of the results. If any of the P-values are significant, give your speculation about why there might be the difference you found.
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