There are at least three fundamental concerns when using the mean to summarize data and compare groups. The first is that hypothesis testing methods based on the mean are known to have relatively poor power under general conditions. One of the earliest indications of why power can be poor stems from a seminal paper by John Wilder Tukey published in 1960. Roughly, the sample variance can be greatly inflated by even one unusually large or small value (called an outlier), which in turn can result in low power when using means versus other measures of central tendency that might be used. A second concern is that control over the probability of a Type I error (when the true hypothesis is wrongly rejected) can be poor. ...
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