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.

Nonparametric Hypotheses and Rank Statistics for Unbalanced Factorial Designs

Abstract: Factorial designs are studied with independent observations, fixed number of levels, and possibly unequal number of observations per factor level combination. In this context, the nonparametric null hypotheses introduced by Akritas and Arnold are considered. New rank statistics are derived for testing the nonparametric hypotheses of no main effects, no interaction, and no factor effects in unbalanced crossed classifications. The formulation of all results includes tied observations. Extensions of these procedures to higher-way layouts are given, and the efficacies of the test statistics against nonparametric alternatives are derived. A modification of the test statistics and approximations to their finite-sample distributions are also given. The small-sample performance of the procedures for two factors is examined in a simulation study. As an illustration, a real dataset with ordinal data is analyzed.

The Chi-Square Test: Often Used and More Often Misinterpreted.

Abstract: The examination of cross-classified category data is common in evaluation and research, with Karl Pearson's family of chi-square tests representing one of the most utilized statistical analyses for answering questions about the association or difference between categorical variables. Unfortunately, these tests are also among the more commonly misinterpreted statistical tests in the field. The problem is not that researchers and evaluators misapply the results of chi-square tests, but rather they tend to over interpret or incorrectly interpret the results, leading to statements that may have limited or no statistical support based on the analyses preformed.This paper attempts to clarify any confusion about the uses and interpretations of the family of chi-square tests developed by Pearson, focusing primarily on the chi-square tests of independence and homogeneity of variance (identity of distributions). A brief survey of the recent evaluation literature is presented to illustrate the prevalence of the chi-...

Likelihood Ratio, Score, and Wald Tests in a Constrained Parameter Space

Abstract: Likelihood ratio, score, and Wald tests statistics are asymptotically equivalent. This statement is widely known to hold true under standard conditions. But what if the parameter space is constrained and the null hypothesis lies on the boundary of the parameter space, such as, for example, in variance component testing? Quite a bit is known in such situations too, but knowledge is scattered across the literature and considerably less well known among practitioners. Motivated from simple but generic examples, we show there is quite a market for asymptotic one-sided hypothesis tests, in the scalar as well as in the vector case. Reassuringly, the three standard tests can be used here as well and are asymptotically equivalent, but a somewhat more elaborate version of the score and Wald test statistics is needed. Null distributions take the form of mixtures of χ2 distributions. Statistical and numerical considerations lead us to formulate pragmatic guidelines as to when to prefer which of the three tests.

Statistics for Microarrays : Design, Analysis and Inference

Abstract: Preface.1 Preliminaries.1.1 Using the R Computing Environment.1.1.1 Installing smida.1.1.2 Loading smida.1.2 Data Sets from Biological Experiments.1.2.1 Arabidopsis experiment: Anna Amtmann.1.2.2 Skin cancer experiment: Nighean Barr.1.2.3 Breast cancer experiment: John Bartlett.1.2.4 Mammary gland experiment: Gusterson group.1.2.5 Tuberculosis experiment: B G@S group.I Getting Good Data.2 Set-up of a Microarray Experiment.2.1 Nucleic Acids: DNA and RNA.2.2 Simple cDNA Spotted Microarray Experiment.2.2.1 Growing experimental material.2.2.2 Obtaining RNA.2.2.3 Adding spiking RNA and poly-T primer.2.2.4 Preparing the enzyme environment.2.2.5 Obtaining labelled cDNA.2.2.6 Preparing cDNA mixture for hybridization.2.2.7 Slide hybridization.3 Statistical Design of Microarrays.3.1 Sources of Variation.3.2 Replication.3.2.1 Biological and technical replication.3.2.2 How many replicates?3.2.3 Pooling samples.3.3 Design Principles.3.3.1 Blocking, crossing and randomization.3.3.2 Design and normalization.3.4 Single-channelMicroarray Design.3.4.1 Design issues.3.4.2 Design layout.3.4.3 Dealing with technical replicates.3.5 Two-channelMicroarray Designs.3.5.1 Optimal design of dual-channel arrays.3.5.2 Several practical two-channel designs.4 Normalization.4.1 Image Analysis.4.1.1 Filtering.4.1.2 Gridding.4.1.3 Segmentation.4.1.4 Quantification.4.2 Introduction to Normalization.4.2.1 Scale of gene expression data.4.2.2 Using control spots for normalization.4.2.3 Missing data.4.3 Normalization for Dual-channel Arrays.4.3.1 Order for the normalizations.4.3.2 Spatial correction.4.3.3 Background correction.4.3.4 Dye effect normalization.4.3.5 Normalization within and across conditions.4.4 Normalization of Single-channel Arrays.4.4.1 Affymetrix data structure.4.4.2 Normalization of Affymetrix data.5 Quality Assessment.5.1 Using MIAME in Quality Assessment.5.1.1 Components of MIAME.5.2 Comparing Multivariate Data.5.2.1 Measurement scale.5.2.2 Dissimilarity and distance measures.5.2.3 Representing multivariate data.5.3 Detecting Data Problems.5.3.1 Clerical errors.5.3.2 Normalization problems.5.3.3 Hybridization problems.5.3.4 Array mishandling.5.4 Consequences of Quality Assessment Checks.6 Microarray Myths: Data.6.1 Design.6.1.1 Single-versus dual-channel designs?6.1.2 Dye-swap experiments.6.2 Normalization.6.2.1 Myth: 'microarray data is Gaussian'.6.2.2 Myth: 'microarray data is not Gaussian'.6.2.3 Confounding spatial and dye effect.6.2.4 Myth: 'non-negative background subtraction'.II Getting Good Answers.7 Microarray Discoveries.7.1 Discovering Sample Classes.7.1.1 Why cluster samples?7.1.2 Sample dissimilarity measures.7.1.3 Clustering methods for samples.7.2 Exploratory Supervised Learning.7.2.1 Labelled dendrograms.7.2.2 Labelled PAM-type clusterings.7.3 Discovering Gene Clusters.7.3.1 Similarity measures for expression profiles.7.3.2 Gene clustering methods.8 Differential Expression.8.1 Introduction.8.1.1 Classical versus Bayesian hypothesis testing.8.1.2 Multiple testing 'problem'.8.2 Classical Hypothesis Testing.8.2.1 What is a hypothesis test?8.2.2 Hypothesis tests for two conditions.8.2.3 Decision rules.8.2.4 Results from skin cancer experiment.8.3 Bayesian Hypothesis Testing.8.3.1 A general testing procedure.8.3.2 Bayesian t-test.9 Predicting Outcomes with Gene Expression Profiles.9.1 Introduction.9.1.1 Probabilistic classification theory.9.1.2 Modelling and predicting continuous variables.9.2 Curse of Dimensionality: Gene Filtering.9.2.1 Use only significantly expressed genes.9.2.2 PCA and gene clustering.9.2.3 Penalized methods.9.2.4 Biological selection.9.3 Predicting ClassMemberships.9.3.1 Variance-bias trade-off in prediction.9.3.2 Linear discriminant analysis.9.3.3 k-nearest neighbour classification.9.4 Predicting Continuous Responses.9.4.1 Penalized regression: LASSO.9.4.2 k-nearest neighbour regression.10 Microarray Myths: Inference.10.1 Differential Expression.10.1.1 Myth: 'Bonferroni is too conservative'.10.1.2 FPR and collective multiple testing.10.1.3 Misinterpreting FDR.10.2 Prediction and Learning.10.2.1 Cross-validation.Bibliography.Index.

A unified approach to model selection using the likelihood ratio test

Abstract: Summary 1. Ecological count data typically exhibit complexities such as overdispersion and zero-inflation, and are often weakly associated with a relatively large number of correlated covariates. The use of an appropriate statistical model for inference is therefore essential. A common selection criteria for choosing between nested models is the likelihood ratio test (LRT). Widely used alternatives to the LRT are based on information-theoretic metrics such as the Akaike Information Criterion. 2. It is widely believed that the LRT can only be used to compare the performance of nested models – i.e. in situations where one model is a special case of another. There are many situations in which it is important to compare non-nested models, so, if true, this would be a substantial drawback of using LRTs for model comparison. In reality, however, it is actually possible to use the LRT for comparing both nested and non-nested models. This fact is well-established in the statistical literature, but not widely used in ecological studies. 3. The main obstacle to the use of the LRT with non-nested models has, until relatively recently, been the fact that it is difficult to explicitly write down a formula for the distribution of the LRT statistic under the null hypothesis that one of the models is true. With modern computing power it is possible to overcome this difficulty by using a simulation-based approach. 4. To demonstrate the practical application of the LRT to both nested and non-nested model comparisons, a case study involving data on questing tick (Ixodes ricinus) abundance is presented. These data contain complexities typical in ecological analyses, such as zero-inflation and overdispersion, for which comparison between models of differing structure – e.g. non-nested models – is of particular importance. 5. Choosing between competing statistical models is an essential part of any applied ecological analysis. The LRT is a standard statistical test for comparing nested models. By use of simulation the LRT can also be used in an analogous fashion to compare non-nested models, thereby providing a unified approach for model comparison within the null hypothesis testing paradigm. A simple practical guide is provided in how to apply this approach to the key models required in the analyses of count data.