An empirical comparison of several methods for testing the equality of dependent proportions

Three methods for testing the equality of nonindependent proportions were compared with, the use of Monte Carlo techniques. The three methods included Cochran's test, an ANOVA F test, and Hotelling's T² test. With respect to empirical significance levels, the ANOVA F test is recommended as the preferred method of analysis.

Oftentimes an experimenter is interested in testing the equality of several proportions. When the proportions are independent Kemp and Butcher (1972) and Butcher and Kemp (1974) compared several methods for analysing large sample binomial data for the case of a 3 x 3 factorial design without replication. In addition, Levy and Narula (1977) compared many of the same methods for analyzing binomial data; however, Levy and Narula investigated the relative utility of the methods for small sample sizes.     

The win ratio: Impact of censoring and follow‐up time and use with nonproportional hazards

The win ratio has been studied methodologically and applied in data analysis and in designing clinical trials. Researchers have pointed out that the results depend on follow‐up time and censoring time, which are sometimes used interchangeably. In this article, we distinguish between follow‐up time and censoring time, show theoretically the impact of censoring on the win ratio, and illustrate the impact of follow‐up time. We then point out that, if the treatment has long‐term benefit from a more important but less frequent endpoint (eg, death), the win ratio can show that benefit by following patients longer, avoiding masking by more frequent but less important outcomes, which occurs in conventional time‐to‐first‐event analyses. For the situation of nonproportional hazards, we demonstrate that the win ratio can be a good alternative to methods such as landmark survival rate, restricted mean survival time, and weighted log‐rank tests.     

Simultaneous prediction intervals for all patrwise differences among several future sample means

Hahn (1977) suggested a procedure for constructing prediction intervals for the difference between the means of two future samples from normal populations having equal variance, based on past samples selected from both populations. In this paper, we extend Hahn's work by constructing simultaneous prediction intervals for all pairwise differences among the means of k ≥ 2 future samples from normal populations with equal variances, using past samples taken from each of the k populations. For K = 2, this generalization reduces to Hahn's special case. These prediction intervals may be used when one has sampled the performance of several products and wishes to simultaneously as- sess the differences in future sample mean performance of these products with a predetermined overall coverage probability. The use of the new procedure is demonstrated with a numerical example.     

Tables of percentage points of the k-variate normal distribution for large values of k

This paper gives tabulations of the upper α percentage points of the maximum absolute value of the k-variate normal distribution with common correlation ρ for values of k as high as 500. The tables are useful for performing multiple comparison procedures in experiments with large numbers of treatments.     

On rules based on sample medians for selection of the largest location parameter

The problem of selection of a subset containing the largest of several location parameters is considered, and a Gupta-type selection rule based on sample medians is investigated for normal and double exponential populations. Numerical comparisons between rules based on medians and means of small samples are made for normal and contaminated normal populations, assuming the popula-tion means to be equally spaced. It appears that the rule based on sample means loses its superiority over the rule based on sample medians in case the samples are heavily contaminated. The asymptotic relative efficiency (ARE) of the medians procedure relative to the means procedure is also computed, assuming the normal means to be in a slippage configuration. The means proce-dure is found to be superior to the median procedure in the sense of ARE. As in the small sample case, the situation is reversed if the normal populations are highly contaminate.     

On the heterogeneity of proportions

The comparison amongmproportions can be viewed as the clustering of the means of Bernoulli trials. By introducing a distribution which is supported on the means of Bernoulli trials, we suggest a moment method approach to determine the center of the clusters. We also suggest using model selection criteria rather than the usual testing hypothesis approach to determine the grouping of the means. The discrepancy function for all possible models are compared based on the bootstrap results.     

A mixture approximation to the distribution of a weighted sum of chi-squared variables

The problem of Computing the Values of the distribution functions of linear combinations of chi-squared random variables and their percentile points was previously studied by Grad and Solomon (1955), Imhof (1961). Jensen and Solomon (1972). Solomon and Stephens (1977) and others. All the methods available in the literature either demand lengthy computations or are insufficiently accurate. In the present paper a new method is proposed which reduces the amount of needed computations and yet yields sufficiently accurate results.     

C194. A nearly flat prior,some unsolved problexs,anb soxe comments about improper priors

Two different approaches to obtaining finite-sample corrections to score tests are the analytical and the computational approaches. The former is based either on a Bartletttype correction to the test statistic or on the inversion of an Edgeworth expansion to its null distribution. The latter, on the other hand, is usually based on a bootstrapping resampling scheme. This paper provides a numerical comparison of the size and power properties of these two approaches both under correct model specification and under model misspecification.     

Designs for first-order interactions in paired comparison experiments with two-level factors

For paired comparison experiments involving options described by a common set of two-level factors a new method for generating exact designs is presented. These designs allow the efficient estimation of main effects and first-order interactions and perform better than alternative designs available in the literature.     

Balanced Treatment incomplete block (BTIB) designs for comparing treatments with a control: minimal complete sets of generator designs for k = 3, p = 3(1)10

Bechhofer and Tamhane (1981) proposed a new class of incomplete block designs called BTIB designs for comparing p ≥ 2 test treatments with a control treatment in blocks of equal size k < p + 1. All BTIB designs for given (p,k) can be constructed by forming unions of replications of a set of elementary BTIB designs called generator designs for that (p,k). In general, there are many generator designs for given (p,k) but only a small subset (called the minimal complete set) of these suffices to obtain all admissible BTIB designs (except possibly any equivalent ones). Determination of the minimal complete set of generator designs for given (p,k) was stated as an open problem in Bechhofer and Tamhane (1981). In this paper we solve this problem for k = 3. More specifically, we give the minimal complete sets of generator designs for k = 3, p = 3(1)10; the relevant proofs are given only for the cases p = 3(1)6. Some additional combinatorial results concerning BTIB designs are also given.