When You Need To Do A Test For Normality On Your Data

Before you perform any statistical test on samples that you've
drawn, you should check if your data is normally distributed. If your
data is not normally distributed, many well-known statistical methods
will produce totally invalid results. Here's a list of statistical
tools that required normally distributed data samples (NDDS)
samples.Normality is a requirement in most parametric statistical
procedures done in marketing. These would include statistical methods
that involve the normal dist., the t distribution, the chi-square
distribution, and the F distribution. In fact, any test that is
parametric test usually has some requirement of normality.Parametric
statistical procedures 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 - Normality is
explicitly required of the variables because Z scores are drawn from
the norm. dist.t - tests - Normailty is a requirement of each of the
two populations being compared.ANOVA - Normailty is a requirement of
each of the two or more populations being compared.Regression - The
residuals must be normally distributed.Chi-Square tests - Require
NDDS.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 normality of its variables, F tests
also require normality in its variables.The F distribution is the
ratio of two independent chi-squared variables divided by their
respective degrees of freedom, and the chi-square distribution require
NDDS, then the F distribution is also going to require NDDS.If you
find that your data sample is not distributed according to the normal
curve, you cannot use the above parametric statistical procedures. The
alternative in this case is nonparametric testing. Nonparametric tests
have no requirements about the distribution of the underlying
population. My blog contains a number of articles about how to perform
the above tests in Excel and also how to perform all of the major
nonparametric tests in Excel.