Comparison of observed and estimated cell counts
We test for independence with the hypotheses:
H0 : X and Y are independent
HA : X and Y are dependent
The test asks whether the observed and estimated cell counts are 'sufficiently close' — are the observed counts consistent with the counts estimated under independence?
Male | Female | Total | |
---|---|---|---|
A | 20 (11.59) |
60 (68.41) |
80 |
B | 9 (13.47) |
84 (79.53) |
93 |
C | 2 (5.94) |
39 (35.06) |
41 |
Total | 31 | 183 | 214 |
Possible test statistic?
A simple summary of how close the observed counts, nxy, are to the estimated cell counts, exy, is the sum of the squared differences,
Unfortunately this would be a bad test statistic — its distribution depends not only on the numbers of rows and columns in the table, but also on the number of individuals classified — the overall total for the table. A better test statistic is presented in the next page.