On Testing Equality of Means of Correlated Variates with Incomplete Data

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. Expressions for the second and fourth central moments of the statistic are obtained. These moments are used to approximate the distribution of the statistic by a Student's t distribution under the null hypothesis. The powers of the test are computed and compared with those of the conventional paired t and the other known statistics.     

Testing Equality of Means in the Presence of Correlation and Missing Data

A statistic, derived from the combination of two dependent tests, 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 or both variates. The null distribution of the statistic is approximated by a well-known distribution. The empirical powers of the statistic are computed and compared with some of the known statistics. The comparisons support the use of the proposed test.     

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.     

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.     

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.     

Testing Equality of Means and Simultaneous Confidence Intervals in Repeated Measures with Missing Data

In this paper, repeated measures with intraclass correlation model is considered when the observations are missing at random. An exact test for the equality of the mean components and simultaneous confidence intervals (Scheffé and Bonferroni inequality types) are given for linear contrasts of the mean components when the missing observations are of a monotone type. When the missing observations are not of the monotone type, the maximum likelihood estimates are obtained numerically by iterative methods given in Srivastava and Carter (1986). These estimators are then used to obtain asymptotic tests and confidence intervals for the equality of mean components and linear contrasts, respectively. An example is given to illustrate the method.     

A Note on Testing Equality of Means when Sample Sizes are Random with Application

The problem of testing the equality of means of two normal populations is considered when independent random samples of random sizes are given with the total number of observations from both populations being a fixed number. An application in forestry is discussed.     

Proof of Safety in Toxicology Based on the Ratio of Two Means for Normally Distributed Data

The aim of toxicology testing is the safety assessment of a substance such as a new pharmaceutical compound or a pesticide relative to a vehicle or negative control. This paper is concerned with the direct safety approach when safety is expressed in terms of the ratio of population means and when the toxicological endpoint is normally distributed. The methodology for power and sample size calculation is derived for the parallel group design and results are presented for various situations.     

Missing Data and the Mixtures of Discrete and Continuous Random Variables

In many practical applications we deal with a problem of estimation of a density function of a vector x some components of which are discrete, while the remaining ones are continuous. Among many models that can be used in this case the most useful are the location model and the kernel model. The problem arises when the observed data contain missing values i.e. on some individuals some of the variables have not been observed with no particular pattern of missingness. An application of the EM algorithm will allow us to estimate the parameters of the location model from incomplete data. The method is described in Section 2. In Section 3 some suggestions how to deal with incompleteness when the kernel model is used are made. Finally, Section 4 contains an example.