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# Normality Tests - When Marketers  Need Them

Normality is a requirement in most parametric tests done in marketing. These would include statistical tests that involve the normal distribution, the t distribution, the chi-square distribution, and the F distribution. In fact, any test that is not a nonparametric test usually has some requirement of normality.

Parametric statistical tests that require normality include the t test, the z test, ANOVA, correlation, covariance, regression, the chi-square test of independence, and the chi-square test of population variance, and F tests. Each requires normality as follows:

Z tests - These explicitly require normally-distributed variables because Z scores are drawn from the normal distribution.

t - tests - Each of the two populations being compared must be normally distributed.

ANOVA - Each of the two or more populations from which samples are drawn must be normally distributed.

Regression - The residuals must be normally distributed.

chi-square tests - Require samples drawn from normally-distributed populations.

F tests - Since the F distribution is the ratio of chi-squared variables divided by their individual degrees of freedom, and the chi-square distribution required normally-distributed variables, F tests also require normally-distributed variables.

The F distribution is the ratio of two independent chi-squared variables divided by their respective degrees of freedom, and since the chi-square distribution requires a normal distribution, the F distribution is also going to require a normal distribution.

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