On Comparing Correlated Means in the Presence of Incomplete Data

Two statistics are proposed for testing the hypothesis of equality of the means of a bivariate normal distribution with unknown common variance and correlation coefficient when observations are missing on both variates. One of the statistics reduces to the one proposed by Bhoj (1978, 1984) when the unpaired observations on the variates are equal. The distributions of the statistics are approximated by well known distributions under the null hypothesis. The empirical powers of the tests are computed and compared with those of some known statistics. The comparison supports the use of one of the statistics proposed in this paper.     

A Test for the Equality of Variances in the Paired Case with Incomplete Data

A modification of the numbers of degrees of freedom which makes the F ratio test of the equality of two variances applicable also in the paired case with incomplete data is suggested. Monte Carlo simulation studies indicate that the suggested test is reasonably powerful in many cases.     

On Testing Equality of Means in the Paired Case with Incomplete Data on Both Responses

Several non iterative tests for the equality of two correlated means with missing data on both responses are compared by means of Monte Carlo studies. The main results are that a test due to LIN and STIVERS (1974) is to be preferred when the number of complete pairs is large, a WELCH type statistic with degrees of freedom modified in this paper when the correlation between the two responses is known to be low, and one of four suggested, one in this paper, maximum likelihood based tests when the number of complete pairs is small and there is no large variance inequality believed to exist.     

On Testing Equality of Means of Correlated Variates with Missing Data on One Response

A statistic is proposed for testing the hypothesis of equality of the means of a bivariate normal distribution with unknown common variance and correlation coefficient when observations are missing on one of the variates. The distribution of the statistic is approximated by a normal distribution under the null hypothesis. The empirical powers of the statistic are computed and compared with those of the conventional paired t and the other known statistics. The power comparisons support the use of the proposed test.     

Testing Equality of Correlated Means in the Presence of Unequal Variances and Missing Values

Several statistics are proposed for testing the hypothesis of equality of the means of bivariate normal distribution with unknown variances and correlation coefficient when observations are missing on both variatea. The null distributions of the statistics are approximated by well-known distributions. The empirical sizes and powers of the statistics are computed and compared with paired t test and some of the known statistics based on available data. The comparisons support the use of two of the statistics proposed in this paper.