Abstract
A computer-simulation study examined the one-sample Student t test under violation of the assumption of independent sample observations. The probability of Type I errors increased, and the probability of Type II errors decreased, spuriously elevating the entire power function. The magnitude of the change depended on the correlation between pairs of sample values as well as the number of sample values that were pairwise correlated. A modified t statistic, derived from an unbiased estimate of the population variance that assumed only exchangeable random variables instead of independent, identically distributed random variables, effectively corrected for nonindependence for all degrees of correlation and restored the probability of Type I and Type II errors to their usual values.
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