Cochran's Q Test
Computes Cochran's Q test, the extension of McNemar's test to three or more binary treatments measured on the same subjects. Imagine asking each person whether they approve of three different products (yes/no): the test checks whether the approval proportion differs across products, respecting the fact that they're the same respondents. It's effectively the dichotomous-response version of the Friedman test. The Q statistic approximately follows a chi-square. Enter the subjects with 0/1 treatments.
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Cochran's Q Test
Computes Cochran's Q test, the extension of McNemar's test to three or more binary treatments measured on the same subjects. Imagine asking each person whether they approve of three different products (yes/no): the test checks whether the approval proportion differs across products, respecting the fact that they're the same respondents. It's effectively the dichotomous-response version of the Friedman test. The Q statistic approximately follows a chi-square. Enter the subjects with 0/1 treatments.
McNemar for three or more yes-or-no answers
McNemar's test compares two paired yes-or-no answers. But what about when there are three, four or more conditions measured on the same people? Asking each evaluator whether they approve of three different ads, for example. Cochran's Q test generalizes McNemar precisely to that case of multiple related dichotomous treatments.
The statistic looks at the approval totals of each treatment and measures how much they vary among themselves, relative to the variability of the subjects themselves. If all treatments had the same approval rate, the column totals would be similar and Q would stay small; marked differences between treatments inflate Q, which approximately follows a chi-square with degrees of freedom equal to the number of treatments minus one.
Enter the data as a matrix of zeros and ones: each row is a subject, each column a treatment, with 1 for success and 0 for failure. The tool returns the Q statistic and the degrees of freedom. Think of it as the dichotomous sibling of the Friedman test: both handle repeated measures, one with ranks, the other with binary responses.
Related Tools
McNemar's Test (Paired)
Computes McNemar's test, used to compare two paired proportions — when the same subjects are measured twice (before and after, or by two methods). Unlike the two-proportion test, which treats the groups as independent, McNemar looks only at the cases that switched classification (the discordant cells b and c of the 2×2 table), ignoring those that stayed the same. The continuity-corrected version follows a chi-square with 1 degree of freedom. Enter the two discordant counts.
Paired t-Test
Computes the paired t-test, used when you measure the same subjects twice — before and after a treatment, or by two methods. It works with the differences of each pair and tests whether the mean difference is compatible with zero. By removing the variability between subjects, it's usually far more powerful than comparing two independent groups. The tool returns the t statistic, the degrees of freedom and the two-sided p-value. Enter the two paired series.
Sign Test (Paired)
Computes the sign test, the simplest and most robust paired test of all. It completely ignores the magnitude of the differences between pairs and looks only at the sign: how many times the value went up and how many it went down. Under the hypothesis of no effect, ups and downs should balance out, like heads and tails, and the p-value comes straight from a binomial distribution. Because it uses so little information, it's less powerful than Wilcoxon, but it makes almost no assumptions. Enter the two paired series.
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