When the research objective is to compare two independent groups, which means they are unpaired, unmatched, and thus different respondent groups, we have a choice among different statistical procedures, depending on the following variable characteristics:

Number of variables
One dependent variable and one independent categorical variable (two levels or groups)

Examples:
1. Are the means / frequencies of two independent groups of respondents (e.g. males vs. females) significantly different on the scores of the dependent variable?

When the dependent variable is BINOMIAL / BINARY / DICHOTOMOUS

When the dependent variable is NOMINAL

When the dependent variable is ORDINAL / RANK-DATA
1. (Wilcoxon) Mann-Whitney test
2. Wald-Wolfowitz Runs test
3. Kolmogorov-Smirnov Z test
4. Moses Extreme test
5. Chi-square (χ²) Test of Independence

When the dependent variable is INTERVAL and passed the assumption of normality (parametric data)

When the dependent variable is INTERVAL but failed the assumption of normality (non-parametric data)
1. (Wilcoxon) Mann-Whitney test
2. Wald-Wolfowitz Runs test
3. Kolmogorov-Smirnov test
4. Moses Extreme test
5. Chi-square (χ²) Test of Independence
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