Suppose the Wilcoxon signed-rank test was used on seven pairs of data. If the calculated test statistic for a two-tailed test was found to be 5, at α = 0.05 we can conclude that
A) the null hypothesis should not be rejected and there is no evidence that the median of the differences differs from zero.
B) the null hypothesis should be rejected and that the groups are not all the same.
C) the alternative hypothesis should not be rejected and the median of the differences is not zero.
D) as T = 5 Tcr = 2, we support the alternative hypothesis.
E) the groups are different, as T = 5 Tcr = 2.

Question

Suppose the Wilcoxon signed-rank test was used on seven pairs of data. If the calculated test statistic for a two-tailed test was found to be 5, at α = 0.05 we can conclude that
A) the null hypothesis should not be rejected and there is no evidence that the median of the differences differs from zero.
B) the null hypothesis should be rejected and that the groups are not all the same.
C) the alternative hypothesis should not be rejected and the median of the differences is not zero.
D) as T = 5 > Tcr = 2, we support the alternative hypothesis.
E) the groups are different, as T = 5 > Tcr = 2.

Quizplus · Accepted Answer

The Wilcoxon signed-rank test is a non-parametric test used to compare two related samples to assess whether their population mean ranks differ. It is used when the assumptions of the paired t-test are not met. The test statistic calculated (T = 5) needs to be compared against critical values from the Wilcoxon signed-rank test distribution, which depend on the sample size and the chosen significance level (α = 0.05). Without specific critical values provided for comparison, the statement about T being greater than a critical value (Tcr = 2) cannot be directly evaluated. However, typically, a smaller T value indicates a stronger evidence against the null hypothesis. The correct interpretation, without specific critical values or a detailed table, is to not make a conclusion about rejecting the null hypothesis based solely on the T value without the context of critical values or a p-value. Therefore, the most appropriate conclusion given the information is that there is no direct evidence provided to reject the null hypothesis, implying there is no evidence that the median of the differences differs from zero.

Suppose the Wilcoxon Signed-Rank Test Was Used on Seven Pairs