COCHRAN Q TEST

Cochran's Q Test on dichotomous data for k-related samples

H = COCHRANQTEST(X) performs the non-parametric Cochran's Q-test on the hypothesis that the K columns of N-by-K matrix have the same number of successes and failures. H==0 indicates that the null hypothesis cannot be rejected at the 5 significance level. H==1 indicates that the null hypothesis can be rejected at the 5% level.

X should contain dichotomous values (success/fail, left/right, yes/no, true/false, 0/1, etc.), where one value indicates a success and the other value denotes a failure. The K columns correspond to K related observations; the N rows correspond to N distinct cases. Note that the coding of success and failure does not matter. The highest value will be treated as a success. Also note that cases that comprise only successes or failures do not have an effect on the test statistic.

X can be cell array of (two different) strings (e.g., 'YES' and 'NO').

H = COCHRANQTEST(...,ALPHA) performs the test at the significance level (100*ALPHA)%. ALPHA must be a scalar between 0 and 1.

[H,P] = COCHRANQTEST(...) returns the p-value, i.e., the probability of observing the given result, or one more extreme, by chance if the null hypothesis is true. Small values of P cast doubt on the validity of the null hypothesis.

[H,P,STATS] = COCHRANQTEST(...) returns a structure with the following fields:
'Q' -- the value of the test statistic
'df' -- the degrees of freedom of the test
'fail' -- the value regarded as a fail
'pass' -- the value regarded as a success
'Npass' -- the sum of successes for each column
'Ne' -- the number of effective cases (i.e., the number of cases that do show differences on the K observations)

COCHRANQTEST(...) without output arguments prints a string saying whether the null-hypothesis should be rejected at significance level APLHA.

The Cochran Q test is useful for comparing related samples measured on a categorical (nominal) scale. For K=2 this test equals the McNemar test for two related samples.

Version 2.2, okt 2007