Use of a t-statistic as an approximation to the exact distribution of the wildcoxon signed ranks test statistic

An approximation to the exact distribution of the Wilcoxon signed ranks test statistic based on the one-sample t-test applied to ranks is compared with the usual normal approximation. A second approximation based on a linear combination of the normal statistic and the t-statistic is introduced. The normal approximation tends to result in a conservative test in the tails, while the Student's t approximation tends to be liberal. The average of the two statistics provides a test that usually has an alpha level as close as possible to the α-levels .05, .025, .01 and .005, for values of n < 50 (only cases examined).