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Math 58B – Intro to Biostatistics Spring 2009 Jo Hardin Lab Assignment 7 Swinging Arms (from Spurrier, Edwards, and Thombs, Statistics: Learning by Doing) “Power walking is an important form of aerobic exercise, especially for middle-aged and elderly individuals. What are the eﬀects of diﬀerent walking styles on walking speed and heart rate? Research questions like these are typical to the ﬁeld of exercise physiology, where formal experimental design and statistical analysis have been instrumental in important discoveries made in recent years.” • Import the class data (assume we have two variables, wlktime1 and wlktime2). Create a new variable that is the paired diﬀerences between the two variables: > diffwlk <- wlktime1 - wlktime2 Using histograms, check whether you think a normal distribution is a reasonable description of the three diﬀerent variables. Also give summary statistics (means and standard deviations) of the three variables. • Using the t.test command, complete a paired t-test on the data. You probably need to type: > ?t.test in order to make sure you have the correct type of test. (Note, you should decide the directionality of the test before looking at the data!!!). Also, report (and interpret) the appropriate conﬁdence interval. • Repeat the above task but now assume that the groups are actually independent samples. Assume the variance is equal in the two groups. • Repeat the above task but now assume that the groups are actually independent samples. Assume the variance is not equal in the two groups. • Deﬁne the relative eﬃciency of the paired sample approach to the independent samples approach to be: 2(s2 + s2 ) 1 2 R= s2 d R is roughly the the ratio of the total number of subjects for an independent comparison to the total number of subjects for a paired comparison needed to obtain conﬁdence intervals for the diﬀerence in population means of equal width. What is the R value for these data? • Given the results from your analyses above, conclude which type of test and conﬁdence interval you should report (be speciﬁc about both the t-test / t CI results as well as the relative eﬃciency results).
"Math 58B – Intro to Biostatistics Spring 2009 Jo Hardin Lab "