Comparing mean ranks for repeated measures data

Rank tests are considered that compare t treatments in repeated measures designs. A statistic is given that contains as special cases several that have been proposed for this problem, including one that corresponds to the randomized block ANOVA statistic applied to the rank transformed data. Another statistic is proposed, having a null distribution holding under more general conditions, that is the rank transform of the Hotelling statistic for repeated measures. A statistic of this type is also given for data that are ordered categorical rather than fully rankedo Unlike the Friedman statistic, the statistics discussed in this article utilize a single ranking of the entire sample. Power calculations for an underlying normal distribution indicate that the rank transformed ANOVA test can be substantially more powerful than the Friedman test.     

Partial Round-Robin Comparisons with Perfect Rankings

In teaching the development of uniformly most powerful unbiased (UMPU) tests, one rarely discusses the performance of alternative biased tests. It is shown, through the comparison of two independent Bernoulli proportions, that a biased test (the Z test) can be more powerful than the UMPU test (Fisher's exact test—randomized) in a large region of the alternative parameter space. A more general example is also given.     

Comparing several experimental groups with a control in the multivariate case

This paper presents a multivariate extension of Dunnett's test for comparing simultaneously k treatment group means with a single control group mean. A test based on Hotelling T²statistics is presented and approximate critical values are evaluated for the case of equal numbers of observations in each group, for the .05 and .01 levels of significance, for 1 to 5 variates, for 1 to 10 treatment groups, and for varying degrees of freedom. The accuracy of the procedure for generating approximate critical values is assessed via simulation studies conducted for selected cases and an example is presented using real data.     

Rotation test with pairwise distance measures of sample vectors in a GLM

One way to cope with high-dimensional data even in small samples is the use of pairwise distance measures—such as the Euclidean distance—between the sample vectors. This is usually done with permutation tests. Here we propose the application of exact parametric rotation tests which are no longer restricted by the finite number of possible permutations of a sample. The method is presented in the framework of the general linear model.     

BARTLETT CORRECTED LIKELIHOOD RATIO TESTS IN LOCATION-SCALE NONLINEAR MODELS

The paper derives Bartlett corrections for improving the chisquare approximation to the likelihood ratio statistics in a class of location-scale family of distributions, which encompasses the elliptical family of distributions and also asymmetric distributions such as the extreme value distributions. We present, in matrix notation, a Bartlett corrected likelihood ratio statistic for testing that a subset of the nonlinear regression coefficients in this class of models equals a given vector of constants. The formulae derived are simple enough to be used analytically to obtain several Bartlett corrections in a variety of important models. We show that these formulae generalize a number of previously published results. We also present simulation results comparing the sizes and powers of the usual likelihood ratio tests and their Bartlett corrected versions when the scale parameter is considered known and when this parameter is uncorrectly specified.     

A robust procedure for testing an assumed value of the population correlation coefficient

For testing that the population correlations coefficientp Q, Tiku and Balakrishnan1986) developed a robust test. This test is extended here to situcitions where one wants to test that p p , p being a specified non-zero value of p. o o     

城市居民旅游环境影响与社会文化影响感知问卷量表的开发

城市居民旅游感知研究,对了解和掌握当地居民对旅游发展的态度与行为意义重大,是旅游地可持续发展的必然要求。作者针对国内城市居民旅游感知进行量表开发,先查阅了大量的国内外相关学术文献,接着进行了深入的文献研究,在此基础上设计了调查问卷初稿,问卷初稿包括居民旅游经济影响感知、旅游环境影响感知、旅游社会文化影响感知、旅游发展态度和满意的总体感知、居民参与旅游发展经营管理水平感知等五个维度,每个维度包括正面影响、负面影响两个构面。随后对初试问卷进行小样本调查,根据小样本调查的数据,使用统计分析软件SPSS16.0进行数据分析,对问卷量表进行信度和效度检验,对问卷测量题项进行净化,剔除相关度较低的测量项目,最终形成正式问卷。分析结果证明,量表具有很高的信度和效度。因篇幅所限,文章只对旅游环境影响感知、旅游社会文化影响感知二个维度的净化过程进行论述。     

A class of distribution-free tests for two-way layout

In this article a class of distribution-free tests for the hypothesis of no row (treatment) effect in a two-way layout design, with several observations per cell, is proposed. The tests are based on U-statistics, constructed by considering minima of all possible subsamples of same size from each cell.The proposed class of tests is compared with the parametric test, Mack and Skillings test and Yate's test for two-way layout, in terms of Pitman ARE sense. It is seen that for the case of equal number of observations per cell, the proposed tests have better efficiency for exponential and uniform error distributions.     

The power functions of the likelihood ratio tests for a simply ordered trend in normal means

Likelihood ratio tests for the homogeneity of k normal means with the alternative restricted by an increasing trend are considered as well as the likelihood ratio tests of the null hypothesis that the means satisfy the trend. While the work is primarily a survey of results concerning the power functions of these tests, the extensions of some results to the case of not necessarily equal sample sizes are presented. For the case of known or unknown population variances, exact expressions are given for the power functions for k=3,4, and approximations are discussed for larger k. The topics of consistency, bias and monotonicity of the power functions are included. Also, Bartholomew's conjectures concerning minimal and maximal powers are investigated, with results of a new numerical study given.