Cochran Test
The Cochran test is a variation of the x2 test where the categories along the top of the contingency table are treatments and those along the left side are blocks as shown in the table below. he blocks may be individuals, groups of similar individuals, or levels of the treatment.
| Treatment | 1 | 2 | 3 | Total |
| Block 1 | X11 | X12 | … | R1 |
| 2 | X21 | R2 | ||
| 3 | … | R3 | ||
| Total | C1 | C2 | C3 | N |
The values within the table are 1 or 0 for success or failure. The hypotheses for this test are
Ho: the treatments are equally effective
HA: the treatment are not equally effective
The test statistic is calculated by
where c is the number of columns in the table.
The test statistic is compared to the x2 distribution. The critical value is taken from the x2 table with (c-1) degrees of freedom and the desired alpha level. If the test statistic is greater than the critical value, the null hypothesis that the treatments are equally effective is rejected.