Modified t Tests and Confidence Intervals for Asymmetrical Populations

Abstract This article considers a procedure that reduces the effect of population skewness on the distribution of the t variable so that tests about the mean can be more correctly computed. A modification of the t variable is obtained that is useful for distributions with skewness as severe as that of the exponential distribution. The procedure is generalized and applied to the jackknife t variable for a class of statistics with moments similar to those of the sample mean. Tests of the correlation coefficient obtained using this procedure are compared empirically with corresponding tests determined using Fisher's z transformation and the usual jackknife estimate.

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