Which test: Compare a single group distribution to a hypothetical / known distribution (goodness-of-fit tests)

When the research objective is to compare a single group distribution to a hypothetical / known distribution (goodness-of-fit tests), we have a choice among different statistical procedures, depending on the following variable characteristics:

 
Number of variables
One dependent variable
 
Examples: 
  1. Does our sample data distribution fit the binomial / normal / poisson curve?
  2. Is our interval-measured sample distribution significantly different from a normal distribution (goodness-of-fit for normality)?
  3. Is the 10%/20%/20%/30%/20% age proportions in our sample significantly different from the known population’s age proportions? 

When the dependent variable is BINOMIAL / BINARY / DICHOTOMOUS
  1. One-sample Binomial test 
  2. Chi-square goodness-of-fit test
  3. G-Test
 
When the dependent variable is NOMINAL
  1. Chi-square goodness-of-fit test
  2. G-Test
 
When the dependent variable is ORDINAL / RANK-DATA
  1. Kolmogorov-Smirnov goodness-of-fit test
  2. Shapiro-Wilke
  3. Anderson-Darling goodness-of-fit test
 
When the dependent variable is INTERVAL and passed the assumption of normality (parametric data)
The key objective here is to confirm whether our assumed normality is indeed correct…. so we technically use non-parametric procedures!
  1. Kolmogorov-Smirnov goodness-of-fit test
  2. Shapiro-Wilke goodness-of-fit test
  3. Anderson-Darling goodness-of-fit test

When the dependent variable is INTERVAL but failed the assumption of normality (non-parametric data)
  1. Kolmogorov-Smirnov goodness-of-fit test
  2. Shapiro-Wilke goodness-of-fit test
  3. Anderson-Darling goodness-of-fit test
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