Search results for "Null distribution"

Testing for homogeneity in meta-analysis I. The one-parameter case: standardized mean difference.

2010

Meta-analysis seeks to combine the results of several experiments in order to improve the accuracy of decisions. It is common to use a test for homogeneity to determine if the results of the several experiments are sufficiently similar to warrant their combination into an overall result. Cochran's Q statistic is frequently used for this homogeneity test. It is often assumed that Q follows a chi-square distribution under the null hypothesis of homogeneity, but it has long been known that this asymptotic distribution for Q is not accurate for moderate sample sizes. Here, we present an expansion for the mean of Q under the null hypothesis that is valid when the effect and the weight for each s…

Commentary: Psychological Science's Aversion to the Null

2017

Inference based on the affine invariant multivariate Mann–Whitney–Wilcoxon statistic

2003

A new affine invariant multivariate analogue of the two-sample Mann–Whitney–Wilcoxon test based on the Oja criterion function is introduced. The associated affine equivariant estimate of shift, the multivariate Hodges-Lehmann estimate, is also considered. Asymptotic theory is developed to provide approximations for null distribution as well as for a sequence of contiguous alternatives to consider limiting efficiencies of the test and estimate. The theory is illustrated by an example. Hettmansperger et al. [9] considered alternative slightly different affine invariant extensions also based on the Oja criterion. The methods proposed in this paper are computationally more intensive, but surpri…

On the use of asymptotic expansion in computing the null distribution of page's L-statistic

1989

Suppose that each out of n randomized complete blocks is obtained by observing a jointly continuous random variable taking values in Rk. Page's L-statistic is given then as a sum of i.i.d. lattice variables with finite moments of any order. Applying a well-known theorem on asymptotic expansions for the distribution function of such a sum yields higher order approximations to the significance probability of any observed value of L. The formula obtained by discarding terms smaller than o(n –1) is still very simple to use. Yet, due to it's strong analytical basis, it can be expected to provide substantial improvement on the traditional normal approximation. The results of extensive numerical i…

Assessment of the statistical significance of classifications in infrared spectroscopy based diagnostic models.

2014

Fourier transform infrared (IR) spectroscopy in combination with multivariate data analysis is a versatile tool that can be applied to disease diagnosis. However, a rigorous validation of the obtained models is necessary in order to obtain robust results. This work evaluates the advantages of the use of permutation testing for determining the statistical significance of the misclassification errors obtained from IR based diagnostic models through cross validation (CV). The model performance, estimated by CV, is compared to a distribution of CV-performance values obtained using randomly permuted class labels. The distribution of ‘random CV-values’ is considered as a null distribution and use…