# Which test: Compare a single group mean or frequency to a hypothetical / known value or proportion

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

**Examples:**

- 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
- G-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”

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