Math 58B – Intro to Biostatistics Spring 2009 Jo Hardin Lab

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Math 58B – Intro to Biostatistics Spring 2009 Jo Hardin Lab Powered By Docstoc
					                                                                          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).

				
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