In a Wilcoxon signed rank sum test for matched pairs with n = 35, the rank sums of the positive and negative differences are 380 and 225, respectively. The value of the standardised test statistic z is:
A) 1.689.
B) 1.065.
C) 1.206.
D) 1.400.

Question

Quizplus · Accepted Answer

The formula for the standardised test statistic in a Wilcoxon signed rank sum test for matched pairs is:

z = (T - μT) / σT

where T is the smaller of the rank sum of the positive and negative differences, μT is the expected value of T under the null hypothesis (which is n(n+1)/4 = 35*36/4 = 315), and σT is the standard deviation of T under the null hypothesis (which is sqrt(n(n+1)(2n+1)/24) = sqrt(35*36*71/24) ≈ 18.46).

Plugging in the given values, we get:

T = 225
μT = 315
σT = 18.46

So:

z = (225 - 315) / 18.46 ≈ -4.871

Since this z-value is negative, we need to look at the cumulative distribution function of the standard normal distribution (which is the distribution of z under the null hypothesis) to find the p-value. The area to the left of -4.871 is essentially zero, so the p-value is very small. This means we can reject the null hypothesis at conventional levels of significance and conclude there is a significant difference between the positive and negative differences.

From the options given, the closest value of z is 1.065 (option B), which is the standardised test statistic for a one-tailed test with a p-value of about 0.143. Since we are not told the direction of the difference between the positive and negative differences, we cannot be sure whether this is the correct choice, but it is the best choice given.

In a Wilcoxon Signed Rank Sum Test for Matched Pairs