Which test: Compare MORE THAN TWO INDEPENDENT groups (Unpaired, Unmatched, Different respondent groups)

Which stat test
When the research objective is to compare more than 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
[Unless where otherwise indicated] One dependent variable and one independent categorical variable (more than two levels)
 
Examples: 
  1. Are the means / frequencies of more than two independent groups of respondents significantly different?

When the dependent variable is BINOMIAL / BINARY / DICHOTOMOUS
  1. Chi-square (χ²) Test of Independence
  2. Fisher’s Exact test
 
When the dependent variable is NOMINAL
  1. Chi-square (χ²) Test of Independence
  2. Fisher’s Exact test
  3. Factorial logistic regression (for more than one independent variable)
When the dependent variable is ORDINAL / RANK-DATA
  1. Kruskal-Wallis test
  2. Median-Test
  3. Jonckheere-Terpstra test
  4. Chi-square (χ²) Test of Independence
  5. Ordered logistic regression (for more than one independent variable)
 
When the dependent variable is INTERVAL and passed the assumption of normality (parametric data)
  1. One-way (Independent) ANOVA
  2. Analysis of Covariance (ANCOVA) (when adding a covariate)
  3. Factorial ANOVA (for more than one independent variable)
  4. Factorial ANCOVA (when adding more than one covariate)
  5. MANOVA, and MANCOVA (with more than one dependent variable)
 
When the dependent variable is INTERVAL but failed the assumption of normality (non-parametric data)
  1. Kruskal-Wallis test
  2. Median test
  3. Jonckheere-Terpstra test 
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