Normality Tests - When Marketers
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
Z tests - These explicitly require
normally-distributed variables because Z scores are drawn from the normal
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
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.