For sample sizes of 40 or more,the correlated groups t test is quite robust to violations of the normality assumption,even for distributions exhibiting considerable skewness.

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For sample sizes of 40 or more, the central limit theorem applies and the distributions of sample means become approximately normal, even for non-normal population distributions. Therefore, the correlated groups t test can still be considered valid and robust in these cases.

For Sample Sizes of 40 or More,the Correlated Groups T