Under certain conditions,the t test for the Pearson correlation is robust with respect to violations of normality and homogeneity of variance.

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The t test for Pearson correltation is robust under certain assumptions such as the sample size is sufficiently large and the data is not heavily skewed or have extreme outliers. Therefore, it is often used in practice even if the normality and homogeneity of variance assumptions are not fully met. However, if the sample size is small or there are significant deviations from the assumptions, alternative nonparametric tests may be more appropriate.

Under Certain Conditions,the T Test for the Pearson Correlation Is