A comparison of the independent-samples t-test and the paired-samples t-test when the observations are nonnegatively correlated pairs

An account of the behavior of the independent-samples t-test when applied to homoschedastic bivariate normal data is presented, and a comparison is made with the paired-samples t-test. Since the significance level is not violated when applying the independent-samples t-test to data which consist of positively correlated pairs and since the estimate of the variance is based on a larger number of 'degrees of freedom', the results suggest that when the sample size is small, one should not worry much about the possible existence of weak positive correlation. One may do better, powerwise, to ignore such correlation and use the independent-samples t-test, as though the samples were independent.