The Lin-Mudholkar test is based on the fact that the mean and variance of a random sample are independently distributed, if and only if, the parent population is normal (Lin and Mudholkar, 1980).
The test is sensitive only to departures from normality due to skewness. As shown by Lin and Mudholkar (1980), the procedure is generally much more powerful at detecting skewness than is the coefficient of Skewness.
The procedure has little power in detecting non-normal symmetrical distributions. For example, uniform or platykurtic distributions will pass this test easily. Therefore, other tests, such as Anderson-Darling, should also be consulted if there is a concern for this type of departure from normality.
A minimum sample size of 10 is recommended for this procedure.