The endurance data set contains data from a 1983 paper [KM83] testing the effects of vitamin C on grip strength and muscular endurance. This data set is also available from Oz DASL (https://www.statsci.org/data), where the following description is given.
The effect of a single 600 mg dose of ascorbic acid versus a sugar placebo on the muscular endurance (as measured by repetitive grip strength trials) of fifteen male volunteers (19-23 years old) was evaluated. The study was conducted in a double-blind manner with crossover. Three initial maximal contractions were performed for each subject, with the greatest value indicating maximal grip strength. Muscular endurance was measured by having the subjects squeeze the dynamometer, hold the contraction for three seconds, and repeat continuously until a value of 50% maximum grip strength was achieved for three consecutive contractions. Endurance time was defined as the number of repetitions required to go from maximum grip strength to the initial 50% value. Subjects were given frequent positive verbal encouragement in an effort to have them complete as many repetitions as possible. a) Use a paired t-test to compare the two treatments. Is there a significant difference? b) Now repeat the analysis, but first take the logarithm of each endurance measurement before doing the analysis c) Since the difference of logarithms is the logarithm of the quotient, repeat the analysis using the quotient of the two measurements in place of the difference. d) Let's try one more transformation. This time use the reciprocal of each endurance measurement. e) Now analyze these data using the sign test. f) We have several different analyses, each with a different p-value. How do we decide which is the "right" analysis?