Normality is the assumption that the underlying residuals are normally distributed, or
While a residual plot, or normal plot of the residuals can identify non-normality, you can
formally test the hypothesis using the Shapiro-Wilk or similar test.
The null hypothesis states that the residuals are normally distributed, against the alternative
hypothesis that they are not normally-distributed. If the test p-value is less than the
predefined significance level, you can reject the null hypothesis and conclude the residuals are
not from a normal distribution. If the p-value is greater than the predefined significance level,
you cannot reject the null hypothesis.
Violation of the normality assumption only becomes an issue with small sample sizes. For large
sample sizes, the assumption is less important due to the central limit theorem, and the fact
that the F- and t-tests used for hypothesis tests and forming confidence intervals are quite
robust to modest departures from normality.