A Non-Parametric Sequential Signed-Rank Test and Comparison with the Sequential T-Test

Sequential analysis is a method of statistical inference whose characteristic feature is that the number of observations required by the procedure is not determined in advance of the experiment. The decision to terminate the experiment depends, at each stage, on the results of the observations previously made. So far the general sequential t-test (without truncation) is a standard test for the mean of a normal distribution. A truncated sequential t-test has been developed by Suich and Iglewicz (1970). The difference between these two tests is that the former has a fixed critical value whenever the type I error (α) and type II error (β) are given while the latter has different boundaries whenever the sample size changes. A non-parametric sequential signed-rank test was published in December (Miller, 1970). This test works for testing the mean of a symmetric distribution. It seems that the sequentila signed-rank test is more convenient and robust than other sequential tests, especially under a distribution with thicker tails. The purpose of this paper therefore is to explain and compare the three sequential tests under three different distributions; that is, the normal distribution, the double exponential distribution (with thicker tails than the normal distribution), and the uniform distribution (with no tails). The results of these tests indicate that the non-parametric test may not be as powerful as the truncated t-test for some non-normal data. Examples will be given to explain the use of the tests to make them easier to understand. Since the ASN (average sample number) and power are two important quantitative values for the sequential test, in section III, the comparison is therefore based on these two values. Monte Carlo methods will be used to investigate the power and stopping time distribution for each test