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In testing for a correlation using nominal data, which test should be utilized?

  1. Pearson's R

  2. Spearman's Rho

  3. Chi-squared test

  4. Mann-Whitney test

The correct answer is: Chi-squared test

When dealing with nominal data, the most appropriate statistical test to use is the Chi-squared test. This test assesses the association between two categorical variables by comparing the observed frequencies in each category to the frequencies that would be expected if there were no association between the variables. Nominal data consists of categories without any intrinsic ordering (such as gender, color, or type of animal), making it unsuitable for tests that assume continuous or ordinal data. Thus, the Chi-squared test is specifically designed to evaluate relationships between categorical variables, making it the fitting choice in this scenario. In contrast, Pearson's R and Spearman's Rho are used for continuous or ordinal data. Mann-Whitney is a non-parametric test for comparing two independent samples and also requires ordinal or continuous data. Therefore, the Chi-squared test stands out as the correct approach for analyzing correlations within nominal data.