The last section dealt with chi-square and its use with one group. However, chi-square has wide application, and it can be used with two or more groups. To distinguish between the use of chi-square with one group and with two or more groups, we shall use the terms chi-square (I) and chi-square (II). The question we ask in discussing chi-square (II) is: do two or more groups differ in respect to some characteristics? In other words, do the number of frequencies that fall into each category for one group differ significantly from the number that fall into each category for another group or groups? The requirements for chi-square (II) are:
Nominal data
Two or more groups
Independent observations
Adequate sample size
No more than 20% of expected frequencies can be smaller than five.
When expected frequencies are very small, use the Fisher exact probability test (Siegel, 1956), not the chi-square (II).
Two-tail test only
The method for finding chi-square (II) differs from that for chi-square (I) in the way the expected frequencies are found. You have no prior basis for computing the expected frequencies, so they are derived from the data. This involves setting up a contingency table. The formula however, is the same as that for (I).