When the research objective is to compare a single group mean or frequency to a hypothetical / known value or proportion (such as an action standard or a norm), we have a choice among different statistical procedures, depending on the following variable characteristics:
Number of variables:
One dependent variable
- Is our mean customer satisfaction score significantly different from the industry average (or action standard) of e.g. 4.6?
- Is the 54/46 gender proportion in our sample significantly different from the population’s age proportions of 51/49?
- One-sample Binomial test
- Chi-square (χ²) goodness-of-fit test
When the dependent variable is NOMINAL
When the dependent variable is ORDINAL / RANK-DATA
- Wilcoxon signed rank test (also referred to as the “One sample median test”)
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 signed rank test (also referred to as the “One sample median test”