Investigation of the Ability of Normality Tests to Prevent Issues in Downstream Tests
The validity of many parametric statistical procedures depends on the normality assumption which is often checked using tests of normality. Researchers have studied the type I error rate and power of the standard normality tests for different alternative hypotheses to suggest the most powerful normality tests under different situations.
Although several statistical procedures are somewhat robust against the violation of normality, extreme violations of normality assumption can result in inflated type-I error rate or loss of power in the downstream tests. However, the commonly used normality tests may not be very useful to check this since the power of these tests depends strongly on the sample size. In this simulation-based study, we attempt to understand how well the normality tests are able to detect such issues in downstream tests. We combine a power (and type-I error) analysis of the commonly used normality tests with a power (and type-I error) analysis of the downstream tests for different kinds of departures from normality to explore the ability of the normality tests to prevent issues such as inflated type-I error rate or loss of power in the downstream tests.