Using R for Introductory Statistics : John Verzani

Using R for introductory statistics 232sample sizes are the same. We get a larger p-value, though, as the degrees of freedomdecrease.8.6.2 Matched samplesThere are times when two samples depend on each other in some way, for example,samples from twin studies, where identical or fraternal twins are used as pairs, so thatgenetic or environmental factors can be controlled. For this, the usual two-sample t-test isnot applicable. We mention two examples.■ Example 8.10: Twin studies An industry-sponsored clinical trial(http://www.hairtoday.com/html/propeciatwins.cfm) demonstrates that Finasterideinhibits male-pattern hair loss. How did the researchers show this? They used twotreatment groups: one received a Finasteride treatment, the other a placebo. Arandomized, double-blind study was performed. Hair loss was measured by photographs,hair counts, and questionnaires.What was different about this study was the use of identical twins for the treatmentgroups. For each pair of twins, one was randomly assigned to the treatment group and theother to the control group. This allowed the researchers to “control” for geneticdifferences—differences that might be so great that the true effect of the Finasteridetreatment could be hidden. The researchers statedAs identical twins share the same genetic makeup, comparison betweenthe responses of each subject in a twin pair, when one receives drug andthe other receives placebo, allows for rigorous examination of the effectsdue to drug treatment in a limited number of subjects.■ Example 8.11: Pre- and post-tests Outcomes assessment is an attempt to measurewhether a certain action actually does what it is intended to do. For example, does astatistics book actually work for teaching R? Or, does a statistics class make youunderstand the difference between mere sampling variation and a true effect? One way toassess the effectiveness of something is with a pre-test and a post-test. If the scores aremarkedly better on the post-test, then we may be able to attribute the change to theteaching.Imagine a class takes a pre-test and a post-test. Each student has two test scores, X i forthe first test and the matching Y i for the second. How can we test whether there is adifference in the means? We might be tempted to use the t-test, but we should be careful,as the two samples are not independent. This assumption of independence was usedimplicitly when computing the standard error in the test statistic. Besides, what is reallyimportant is the change in the scores X i −Y i .For paired data, even if there are large variations within the samples, we can still test adifference in the means by using a one-sample test applied to the data, X i −Y i .Significance tests for paired samplesIf the two sample X 1 , X 2 , …, X n and Y 1 , Y 2 , …, Y n are matched so that the differencesX i −Y i are an i.i.d. sample, then the significance test of hypotheses