When using the Wilcoxon signed-rank test, reject the null hypothesis only when the _____ of the two calculated statistics is equal to or _____ than the critical value.
A) smaller; less
B) larger; less
C) smaller; greater
D) larger; greater

Question

Quizplus · Accepted Answer

The Wilcoxon signed-rank test is a non-parametric paired test used to compare two related samples. The test is based on ranking the differences between the paired observations and taking into account their signs. The null hypothesis is that there is no significant difference between the paired observations.

When using the Wilcoxon signed-rank test, the decision to reject or fail to reject the null hypothesis is based on the calculated test statistic and the critical value from the Wilcoxon signed-rank table. The test statistic is the smaller of the sum of the ranks of the positive differences and the sum of the ranks of the negative differences.

To reject the null hypothesis, we need to compare the calculated test statistic with the critical value from the table. The critical value is determined by the sample size, significance level, and one- or two-tailed test.

Therefore, we reject the null hypothesis only when the smaller of the two calculated statistics is equal to or less than the critical value. This corresponds to choice A: smaller; less.

When Using the Wilcoxon Signed-Rank Test, Reject the Null Hypothesis