Statistical Analysis for Education and Psychology Researchers

Friedman’s

Chi-square

adjusted

for ties—

7.6

where: N=number of subjects (or sets of matched subjects);

k=number of conditions (repeated measures);

Rj=rank sum of the conditions (i.e., sum of the rank for each repeated measure);

gi=number of different rank values for the ith subject;

tij=number of observations of the jth rank value in the ith subject.

Consider, for example, the first subject in Table 7.7. There are 3 different rank

values, that is gi=3, these rank values are 3.5 (two observations), 2 (one

observation) and 1 (one observation), therefore;

If there are no tied values in the ranked data then, and therefore

the denominator for becomes Nk(k+1).

For all 6 subjects in Table 7.7

the numerator is given

by: 12(22.5^2 +11^2 +13^2 +13.5^2 )−3×36× 4×(4+1)^2 =942. The denominator is given

by: 6×4(5)+(24–30)/ 3=118 so, 942/118=7.983. This is evaluated using χ^2

distribution with k−1 degrees of freedom. The table of critical values of χ^2 is

shown in Table 2, Appendix A4. In this example, 7.983 with 3 df and alpha set to

5 per cent is greater than the tabled critical value (7.82).

Interpretation

Given the significant test statistic, the null-hypothesis of different modes of
representation of spatial perspectives having similar levels of success on the
representation tasks can be rejected, and we can conclude that the average ranks
(medians) for the four conditions differ significantly. Task performance would seem to
depend upon the nature of the task (matching, drawing, verbal and making) and looking
at Table 7.7 the highest mean rank was for the matching condition (higher rank score

Inferences involving rank data 243