What test should be used for 3 or more independent samples of nominal data?

When dealing with three or more independent samples of nominal data, the appropriate statistical test to use is the Chi square for k independent samples. This test is specifically designed to evaluate whether there are significant differences in the distribution of categorical outcomes across several groups.

In the context of nominal data, the Chi square test assesses how often each category's observed frequency differs from what would be expected under the null hypothesis, which posits no association between the groups. By analyzing the data this way, researchers can determine if the proportions from different groups are significantly different from each other.

In contrast, the other tests listed are not suitable for this type of analysis. Friedman ANOVA is used for repeated measures on ordinal data. The correlation coefficient calculates the relationship between two continuous variables, making it irrelevant for nominal data comparisons. McNemar's test is applied in specific situations involving paired nominal data, making it unsuitable for independent samples. Therefore, using the Chi square test for k independent samples is the correct choice for analyzing three or more independent samples of nominal data.