Cochran's Q Test

Cochran's Q test is a nonparametric test of whether the proportion of a binary outcome differs across three or more related conditions measured on the same subjects.

코크란 Q 검정은 같은 대상을 셋 이상의 조건에서 측정한 이분형 결과의 비율이 조건마다 다른지를 검정하는 비모수 검정이다.

How do I compare the success rates of the same participants across three or more conditions?

같은 참가자들의 성공률을 세 가지 이상의 조건에서 어떻게 비교하나요?

Cochran's Q test extends McNemar's test to three or more matched conditions, testing whether the proportion of a yes/no outcome is the same across conditions measured on the same subjects. A significant Q, referred to a chi-square distribution with k − 1 degrees of freedom, is usually followed by pairwise McNemar tests with a multiplicity correction.

When to use Cochran's Q Test

• The same subjects give a binary response under three or more conditions
• Comparing pass rates, endorsement or detection across matched items or time points
• Repeated-measures designs where the outcome is coded 0/1

When to use something else

• Only two related conditions: use McNemar's test
• Continuous or ordinal repeated outcomes: use the Friedman test or repeated measures ANOVA

Assumptions and requirements

• Each condition is a column coded 0/1
• Subjects independent of one another
• Complete responses for every condition (subjects with missing values are removed)
• Enough subjects whose responses vary across conditions for the chi-square approximation

What the analysis reports

• Cochran's Q statistic
• Degrees of freedom (k − 1)
• p-value
• Bar chart of the proportion of 1s in each condition

How to report it

Cochran's Q test showed that the proportion of [outcome] differed significantly across the [k] conditions, Q([df]) = [value], p = [value].

Related methods

• McNemar's Test
• Friedman Test
• Bonferroni Correction

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