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.

An Introduction to Probability and Statistics

Abstract: Probability Random Variables and Their Probability Distributions Moments and Generating Functions Multiple Random Variables Some Special Distributions Limit Theorems Sample Moments and Their Distributions Parametric Point Estimation Neyman-Pearson Theory of Testing of Hypotheses Some Further Results on Hypotheses Testing Confidence Estimation The General Linear Hypothesis Nonparametric Statistical Inference.

Evaluating and Modifying Covariance Structure Models: A Review and Recommendation

Abstract: The purpose of this article is to present a strategy for the evaluation and modification of covariance structure models. The approach makes use of recent developments in estimation under non-standard conditions and unified asymptotic theory related to hypothesis testing. Factors affecting the evaluation and modification of these models are reviewed in terms of nonnormality, missing data, specification error, and sensitivity to large sample size. Alternative model evaluation and specification error search strategies are also reviewed. The approach to covariance structure modeling advocated in this article utilizes the LISREL modification index for assessing statistical power, and the expected parameter change statistic for guiding specification error searches. It is argued that the common approach of utilizing alternative fit indices does not allow the investigator to rule out plausible explanations for model misfit. The approach advocated in this article allows one to determine the extent of sample size sensitivity and the effects of specification error by relying on existing statistical theory underlying covariance structure models.

Recent Trends in the Use of Statistical Tests for Comparing Swarm and Evolutionary Computing Algorithms: Practical Guidelines and a Critical Review

Abstract: A key aspect of the design of evolutionary and swarm intelligence algorithms is studying their performance. Statistical comparisons are also a crucial part which allows for reliable conclusions to be drawn. In the present paper we gather and examine the approaches taken from different perspectives to summarise the assumptions made by these statistical tests, the conclusions reached and the steps followed to perform them correctly. In this paper, we conduct a survey on the current trends of the proposals of statistical analyses for the comparison of algorithms of computational intelligence and include a description of the statistical background of these tests. We illustrate the use of the most common tests in the context of the Competition on single-objective real parameter optimisation of the IEEE Congress on Evolutionary Computation (CEC) 2017 and describe the main advantages and drawbacks of the use of each kind of test and put forward some recommendations concerning their use.

Statistics and Truth in Phylogenomics

Abstract: Phylogenomics refers to the inference of historical relationships among species using genome-scale sequence data and to the use of phylogenetic analysis to infer protein function in multigene families. With rapidly decreasing sequencing costs, phylogenomics is becoming synonymous with evolutionary analysis of genome-scale and taxonomically densely sampled data sets. In phylogenetic inference applications, this translates into very large data sets that yield evolutionary and functional inferences with extremely small variances and high statistical confidence (P value). However, reports of highly significant P values are increasing even for contrasting phylogenetic hypotheses depending on the evolutionary model and inference method used, making it difficult to establish true relationships. We argue that the assessment of the robustness of results to biological factors, that may systematically mislead (bias) the outcomes of statistical estimation, will be a key to avoiding incorrect phylogenomic inferences. In fact, there is a need for increased emphasis on the magnitude of differences (effect sizes) in addition to the P values of the statistical test of the null hypothesis. On the other hand, the amount of sequence data available will likely always remain inadequate for some phylogenomic applications, for example, those involving episodic positive selection at individual codon positions and in specific lineages. Again, a focus on effect size and biological relevance, rather than the P value, may be warranted. Here, we present a theoretical overview and discuss practical aspects of the interplay between effect sizes, bias, and P values as it relates to the statistical inference of evolutionary truth in phylogenomics.

Maximum likelihood trees from dna sequences: a peculiar statistical estimation problem

Abstract: The parameter space of the phylogenetic tree estimation problem consists of three com? ponents, T, t, and 8. The tree topology T is a discrete entity that is not a proper statistical parameter but that can nevertheless be estimated using the maximum likelihood criterion. Its role is to specify the branch length parameters and the form of the likelihood function(s). Branch lengths t are conditional on T and are meaningful only for specific values of T. Parameters 8 in the model of nucleotide substitution are common to all the tree topologies and represent such values as the transition/trans version rate ratio. T and t thus represent the tree, and 8 represents the model. With typical DNA sequence data, differences in T have only a small effect on the likelihood, but changing 8 will influence the likelihood greatly. Estimates of 8 are also found to be insensitive to T, making it possible to obtain reliable estimates of 8 and to perform tests concerning the model (8) even if knowledge of the evolutionary relationship (T) is not available. In contrast, tests con? cerning t, such as testing the existence of a molecular clock, appear to be more difficult to perform when the true topology is unknown. In this paper, we explore the peculiarity of the parameter space of the tree estimation problem and suggest methods for overcoming some difficulties in? volved with tests concerning the model. We also address difficulties concerning hypothesis testing on T, i.e., evaluation of the reliability of the estimated tree topology. We note that estimation of and particularly tests concerning T depend critically on the assumed model. (Maximum likeli? hood; models; parameter space; consistency; sampling errors; hypothesis testing; nucleotide sub? stitution; phylogeny estimation; molecular systematics; molecular clock.)