Keywords: paired t test, transformation, outliers
The effect of a single 600 mg dose of absorbic 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.
Data File (tab-delimited text)
|Keith, R. E., and Merrill, E. (1983). The effects of vitamin C on maximum grip strength and muscular endurance. Journal of Sports Medicine and Physical Fitness, 23, 253-256.|
This data illustrates dramatically the importance of correct scaling. On the original scale, the difference in Endurance between Vitamin C and the Placebo is not even nearly significant (P = 0.5). On a log-scale (i.e., analyze log(Endurance)) the difference is borderline significant (P = 0.07). On a reciprocal scale, the difference is clearly significant (P = 0.03). A Box-Cox likelihood analysis suggests a power -0.2 transformation, with log also acceptable, but residual plots do not clearly distinguish between the log and reciprocal scales.
There are two Endurance values much higher than the other values. If these are removed as outliers, then the log(Endurance) is very significantly greater for the Placebo group. (The two points do not show up as formally as outliers using externally studentized residuals, possibly because of masking.)