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: 
  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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