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A Chi-square test is a common test for nominal (categorical) data. One application of a Chi-square test is a test for independence. In this case, the null hypothesis is that the occurrence of the outcomes for the two groups is equal. For example, you have two user groups ( e.g., male and female, or young and elderly). And you have nominal data for each group, for example, whether they use mobile devices or which OS they use.

So, your data look like this. If your data of the two groups came from the same participants ( i.e., the data were paired), you should use the McNemar's test.

Let's use the examples above. First, prepare the data.

Data X^2) Likelihood Ratio 7.7592 1 0.0053440 Pearson 7.5000 1 0.0061699 Phi-Coefficient: 0.354 Contingency Coeff.: 0.333 Cramer's V: 0.354 For a 2×2 table, you can also calculate the odds ratio. The odds ratio is how the probability of the phenomena is affected by the dependent variable. This can be calculated as ad / bc. Running a McNemar's exact test is pretty similar to Chi-square. Question 2 (post-treatment) Yes No Question 1 Yes a b (pre-treatment) No c d More precisely, you need to use a binomial test rather than McNemar's test if b+ c in the 2×2 table is small.

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