Cochran’s Q with Pairwise McNemar for Dichotomous Multiple Responses Data: a Practical Approach

Abstract

When utilizing single-response questions for a survey, researchers often overlook the possibility that an item can have a smorgasbord of viable answers. It results in the loss of information as it forces the respondents to select a best-of-fit option. A multiple-responses question allows the respondent to select any number of answers from a set of preformatted options. The ability to capture a flexible number of responses allows collectively exhaustive concepts to manifest for deductive verification. This paper explores the practical use of Cochran’s Q test and pairwise McNemar test to examine the proportion of responses derived from the results of Multiple Responses Analysis (MRA). This includes Cochran’s Q operation on MRA data table using a simulated data set. Cochran’s Q test detects if there is a difference in the proportion of multiple concepts. In the case of a significant result, it would require a post hoc analysis to pinpoint the exact difference in pairwise proportions. This pairwise difference can be detected by utilizing pairwise McNemar test with Bonferroni Correction. This paper serves as a reference for researchers and practitioners who need to examine the proportion of collectively exhaustive concepts collected from a multiple responses item.