# Which test: Compare TWO INDEPENDENT groups for differences (Unpaired, Unmatched, Different respondent group)

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:**

- 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**

- Chi-square (χ²) Test of Independence
- Fisher’s Exact test

**When the dependent variable is NOMINAL**

- Chi-square (χ²) Test of Independence
- Fisher’s Exact test

**When the dependent variable is ORDINAL / RANK-DATA**

- (Wilcoxon) Mann-Whitney test
- Wald-Wolfowitz Runs test
- Kolmogorov-Smirnov Z test
- Moses Extreme test
- 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**

**)**

- (Wilcoxon) Mann-Whitney test
- Wald-Wolfowitz Runs test
- Kolmogorov-Smirnov test
- Moses Extreme test
- Chi-square (χ²) Test of Independence

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