# 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:**

- Does our sample data distribution fit the binomial / normal / poisson curve?
- Is our interval-measured sample distribution significantly different from a normal distribution (goodness-of-fit for normality)?
- Is the 10%/20%/20%/30%/20% age proportions in our sample significantly different from the known population’s age proportions?

- One-sample Binomial test
- Chi-square goodness-of-fit test
- G-Test

**When the dependent variable is NOMINAL**

**When the dependent variable is ORDINAL / RANK-DATA**

- Kolmogorov-Smirnov goodness-of-fit test
- Shapiro-Wilke
- 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!

- Kolmogorov-Smirnov goodness-of-fit test
- Shapiro-Wilke goodness-of-fit test
- Anderson-Darling goodness-of-fit test

**When the dependent variable is INTERVAL but failed the assumption of normality (non-**

**parametric data**

**)**

- Kolmogorov-Smirnov goodness-of-fit test
- Shapiro-Wilke goodness-of-fit test
- Anderson-Darling goodness-of-fit test

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