Statistical Methods for Psychology

results for Mahon’s data is shown below. You will see that the Linear-by-Linear Association

measure of 5.757 is the same as the that we calculated using (N 2 1) r^2.

Chi-Square Tests

Asymp. Sig.

Value df (2-sided)

Pearson Chi-Square 9.459a 4 .051

Likelihood Ratio 9.990 4 .041

Linear-by-Linear

Association 5.757 1 .016

N of Valid Cases 126

a2 cells (20.0%) have expected count less than 5. The

minimum expected count is 4.50.

There are a number of other ways to approach the problem of ordinal variables in a

contingency table. In some cases only one of the variables is ordinal and the other is nomi-

nal. (Remember that dichotomous variables can always be treated as ordinal without af-

fecting the analysis.) In other cases one of the variables is clearly an independent variable

while the other is a dependent variable. An excellent discussion of some of these methods

can be found in Agresti, 1996 and 2002.

10.5 Kendall’s Coefficient of Concordance (W)

All of the statistics we have been concerned with in this chapter have dealt with the rela-

tionship between two sets of scores (Xand Y). But suppose that instead of having two

judges rank a set of objects, we had six judges doing the ranking. What we need is some

measure of the degree to which the six judges agree. Such a measure is afforded by

Kendall’s coefficient of concordance (W).

Suppose, as an example, that we asked six judges to rank order the pleasantness of

eight colored patches, and obtained the data in Table 10.4. If all of the judges had agreed

that Patch B was the most pleasant, they would all have assigned it a rank of 1, and the col-

umn total for that patch across six judges would have been 6. Similarly, if A had been

ranked second by everyone, its total would have been 12. Finally, if every judge assigned

the highest rank to Patch H, its total would have been 48. In other words, the column totals

would have shown considerable variability.

x^2

Section 10.5 Kendall’s Coefficient of Concordance (W) 309

0

0.4

0.6

0.8

Percent dropout

1

Number of traumatic events

234

Figure 10.2 Scatterplot of Mahon’s data on dropout data

Kendall’s
coefficient of
concordance (W)