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

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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).

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