Statistical Analysis for Education and Psychology Researchers

3 Assign each ranked difference score either +ve or −ve indicating the sign of the
difference it represents.
4 The test statistic T is either i) for small samples, n≤15, the smaller sum of the rank
signed differences regardless of whether it is + or − (that is compute the sum of the
positive ranked differences and the sum of the negative ranked differences and choose
the smaller of the two sums), or ii) with a large sample approximation, T+, the sum of
the positive ranked differences.

In this example there are only 8 subjects for analysis (two have zero differences and are
thus eliminated) and therefore the test statistic, T, is 1.5 because this is the smaller of the
two rank totals in Table 7.4. This test statistic is compared with tabled critical values (see
Table 5, Appendix A4). Should n be >25 then the following large sample approximation
should be used:

Z-

score

approx

imatio

n for

sampli

ng

distrib

ution

of T,

Wilcox

on

Signed

Ranks

test—

7.3

The large sample test is a good approximation even with samples as small as 10.

Interpretation

Small sample test

If for a chosen number of observation pairs and a chosen alpha level the observed test
statistic, T (rank sum total), is larger than the tabled critical value then statistical
significance has not been attained at the selected alpha level. In this example 1.5<4
(critical value from Table 5, Appendix A4 with n=8, two-tailed test and alpha=0.05) the
result is therefore significant at the 5 per cent level. The null hypothesis can be rejected
and we conclude that teachers’ sharing behaviour is not the same in poorest and best
relationship situations. Higher scores (more frequent sharing behaviour) were found
predominantly in the best relationship situations. The exact sampling distribution is
tabled in some statistical texts in which case T+ should be used, see for example Siegel

Inferences involving rank data 229