Hypothesis Testing and Small Sample Sizes
One of the biggest breakthroughs during the last 40 years has been the derivation of inferential methods that perform well when sample sizes are small. Indeed, some practical problems that seemed insurmountable only a few years ago have been solved. But to appreciate this remarkable achievement, we must first describe the shortcomings of conventional techniques developed during the first half of the 20th century—methods that are routinely used today. At one time it was generally thought that these standard methods are insensitive to violations of assumptions, but a more accurate statement is that they seem to perform reasonably well (in terms of Type I errors) when groups have identical probability curves, or when performing regression with variables that are independent. If, for example, we compare groups that happen to have different probability curves, extremely serious problems can arise. Perhaps the most striking problem is described in Chapter 7, but the problems described here are very serious as well and are certainly relevant to applied work.
KeywordsNull Hypothesis Central Limit Theorem Sample Variance Actual Probability Probability Coverage
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