Statistical hypothesis testing

About: Statistical hypothesis testing is a research topic. Over the lifetime, 19580 publications have been published within this topic receiving 1037815 citations. The topic is also known as: statistical hypothesis testing & confirmatory data analysis.

Statistical analysis of multi-eye data in ophthalmic research.

Abstract: An apparently common error in statistical analysis of ophthalmic data is to perform statistical tests that do not account for the correlation generally present between observations made for the right and left eyes of a subject. This error has as a consequence an overstatement of the precision of the study, resulting in incorrect P values which indicate a greater measure of statistical significance than the data warrant. As measures to reduce the occurrence of this serious error in statistical analyses, the authors recommend increased emphasis on educational programs for investigators, stimulation of nontechnical articles reviewing statistical methods, and a sharper focus upon statistical analysis in the peer review process.

Two-Sample Covariance Matrix Testing and Support Recovery in High-Dimensional and Sparse Settings

Abstract: In the high-dimensional setting, this article considers three interrelated problems: (a) testing the equality of two covariance matrices and ; (b) recovering the support of ; and (c) testing the equality of and row by row. We propose a new test for testing the hypothesis H 0: and investigate its theoretical and numerical properties. The limiting null distribution of the test statistic is derived and the power of the test is studied. The test is shown to enjoy certain optimality and to be especially powerful against sparse alternatives. The simulation results show that the test significantly outperforms the existing methods both in terms of size and power. Analysis of a prostate cancer dataset is carried out to demonstrate the application of the testing procedures. When the null hypothesis of equal covariance matrices is rejected, it is often of significant interest to further investigate how they differ from each other. Motivated by applications in genomics, we also consider recovering the support of and ...

Intensity-based hierarchical Bayes method improves testing for differentially expressed genes in microarray experiments

Abstract: The small sample sizes often used for microarray experiments result in poor estimates of variance if each gene is considered independently. Yet accurately estimating variability of gene expression measurements in microarray experiments is essential for correctly identifying differentially expressed genes. Several recently developed methods for testing differential expression of genes utilize hierarchical Bayesian models to "pool" information from multiple genes. We have developed a statistical testing procedure that further improves upon current methods by incorporating the well-documented relationship between the absolute gene expression level and the variance of gene expression measurements into the general empirical Bayes framework. We present a novel Bayesian moderated-T, which we show to perform favorably in simulations, with two real, dual-channel microarray experiments and in two controlled single-channel experiments. In simulations, the new method achieved greater power while correctly estimating the true proportion of false positives, and in the analysis of two publicly-available "spike-in" experiments, the new method performed favorably compared to all tested alternatives. We also applied our method to two experimental datasets and discuss the additional biological insights as revealed by our method in contrast to the others. The R-source code for implementing our algorithm is freely available at http://eh3.uc.edu/ibmt . We use a Bayesian hierarchical normal model to define a novel Intensity-Based Moderated T-statistic (IBMT). The method is completely data-dependent using empirical Bayes philosophy to estimate hyperparameters, and thus does not require specification of any free parameters. IBMT has the strength of balancing two important factors in the analysis of microarray data: the degree of independence of variances relative to the degree of identity (i.e. t-tests vs. equal variance assumption), and the relationship between variance and signal intensity. When this variance-intensity relationship is weak or does not exist, IBMT reduces to a previously described moderated t-statistic. Furthermore, our method may be directly applied to any array platform and experimental design. Together, these properties show IBMT to be a valuable option in the analysis of virtually any microarray experiment.