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Multiple Paired Binary Variables

On the previous page we noticed that not every option was chosen equally often. To test if these differences are significantly different we can use a Cochran's Q test. This is a so-called omnibus test, so if it is significant it needs to be followed up by a post-hoc test. As usual we end the testing with an effect size.

3a. Test for differences: Cochran's Q test

The Cochran's Q test starts similar as a Pearson chi-square test by squaring the differences between the observed and the expected proportions, but then divides this by the sum of the number of successes multiplied by the number of failures for each case.

In the example the Cochran's Q value is 19.38 and has a significance of .000228. This indicates that there is a very low chance (.000228 is usually considered low, the threshold is usually set at .05 or lower) to obtain a Q value of 19.38 or even higher in a sample, if in the population there would be no differences. This is so low that most likely in the populations each variable is not chosen equally often. We could report this similar as a Pearson chi-square test:

Cochran's Q test indicated that there are differences between the proportions among the four options of visited cinemas, χ²(3, N = 150) = 19.38, p < .001.

Now that we found out there are differences in proportions of success we would like to know which ones are then different. This will be the topic for the next page.

3+ binary

Introduction

Impression

Visualisation

Test

Post-hoc

Effect size

Reporting

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