scispace - formally typeset
Search or ask a question
Topic

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.


Papers
More filters
Journal ArticleDOI
TL;DR: It is shown that nonparametric statistical tests provide convincing and elegant solutions for both problems and allow to incorporate biophysically motivated constraints in the test statistic, which may drastically increase the sensitivity of the test.

269 citations

Journal ArticleDOI
TL;DR: In this paper, alternative testing criteria in the linear multivariate regression model, and the possibility of conflict among them, are surveyed and a strong result is that a systematic numerical inequality relationship exists; specifically, Wald, LRa LM, and likelihood ratio (LR).
Abstract: This paper surveys alternative testing criteria in the linear multivariate regression model, and investigates the possibility of conflict among them. We consider the asymptotic Wald, likelihood ratio (LR), and Lagrange multiplier (LM) tests. These three test statistics have identical limiting chi-square distributions; thus their critical regions coincide. A strong result we obtain is that a systematic numerical inequality relationship exists; specifically, Wald , LRa LM. Since the equality relationship holds only if the null hypothesis is exactly true in the sample, in practice there will always exist a significance level for which the asymptotic Wald, LR, and LM tests will yield conflicting inference. However, when the null hypothesis is true, the dispersion among the teststatistics will tend to decrease as the sample size increases. We illustrate relationships among the alternative testing criteria with an empirical example based on the three reduced form equations of Klein's Model I of the United States economy, 1921-1941.

269 citations

Journal ArticleDOI
TL;DR: Two programs, CHIRXC and CHIHW, which estimate the significance of x statistics using pseudo-probability tests, permit analysis of sparse table data without pooling rare categories and prevents loss of information.
Abstract: where o, and e, are observed and expected (under the null hypothesis) numbers of the fth category (see any textbook on biometry or population genetics, e.g., Ayala and Kiger 1984; Sokal and Rohlf 1981). An unfortunate requirement of the test is that the expected numbers (e,) should not be small. Different authors give different recommendations; common opinion is that e, should not be less than 4 (see cited books). Introduction into population genetics of molecular techniques revealed a great wealth of genetic variation—allozymic, DNA restriction fragment length polymorphisms, etc.—in both plants and animals. Hence, samples of practical size (say, hundreds of individuals) will very often contain rare phenotypic or allelic categories. To obtain reliable x estimates one should then pool these rare categories, otherwise the calculated x will be inflated. Unfortunately, this causes loss of information, which is undesirable. An alternative is to use Fisher's exact probability test, but in the case of many categories and considerable total sample size, this is impractical. Roff and Bentzen (1989) suggested another practical alternative (without any pooling of data) for testing heterogeneity in R x C contingency tables containing rare categories. They used a Monte Carlo procedure, which was termed by Hernandez and Weir (1989) a pseudo-probability test, to test Hardy-Weinberg equilibrium. The procedure consists of (1) generating a sample of all possible data sets having the same marginal totals as the original data set and (2) computing x for each derived data set and counting all the sets for which x is larger than that of the original sample. The ratio of the obtained number to the overall number of generated data sets is the estimate of probability of the null hypothesis. We present here two programs, CHIRXC and CHIHW, which estimate the significance of x statistics using pseudo-probability tests. Thus, our programs permit analysis of sparse table data without pooling rare categories. This saves time and prevents loss of information. The CHIRXC analyzes R x C contingency tables. For the 2 x 2 case, it can perform Fisher's exact probability test as well. The CHIHW estimates conformity of genotypic proportions in a sample to Hardy-Weinberg expectations. It also computes an index of heterozygote deficiency or excess [D = (Ho He)/He] (Koehn et al. 1973) and estimates its significance through the pseudoprobability test. The programs are written in C (Turbo C, ver. 2, Copyright Borland International 1988). They will run on an IBM PC and compatibles. Sample sizes and dimensionality of R x C tables under analysis are limited only by the available computer memory. The approach of Roff and Bentzen (1989) was used in the MONTE program in REAP (McElroy et al. 1991). Our algorithm of randomization is different from theirs and much faster (Pudovkin Al and Zaykin DV, unpublished). The programs are available from the authors. To receive a copy, send a nonformatted 5.25-in diskette, and we will supply the disk with the programs (executables and listings), README files with user instructions, and input file formats.

269 citations

Journal ArticleDOI
TL;DR: In this paper, the problem of multiple testing under dependence in a compound decision theoretic framework is considered, where the observed data are assumed to be generated from an underlying two-state hidden Markov model.
Abstract: Summary. The paper considers the problem of multiple testing under dependence in a compound decision theoretic framework. The observed data are assumed to be generated from an underlying two-state hidden Markov model. We propose oracle and asymptotically optimal datadriven procedures that aim to minimize the false non-discovery rate FNR subject to a constraint on the false discovery rate FDR. It is shown that the performance of a multiple-testing procedure can be substantially improved by adaptively exploiting the dependence structure among hypotheses, and hence conventional FDR procedures that ignore this structural information are inefficient. Both theoretical properties and numerical performances of the procedures proposed are investigated. It is shown that the procedures proposed control FDR at the desired level, enjoy certain optimality properties and are especially powerful in identifying clustered non-null cases. The new procedure is applied to an influenza-like illness surveillance study for detecting the timing of epidemic periods.

268 citations

Journal Article
TL;DR: Tests and evaluations of seven speed-DENSITY models found the relationship between Edie and Underwood improved on innovative ground conditions, but failed to find any conclusive results.
Abstract: THE OBJECTIVE OF THIS STUDY WAS TO TEST AND EVALUATE SEVEN DIFFERENT SPEED-DENSITY MODELS: THE GREENSHIELD, GREENBERG, UNDERWOOD, EDIE, 2-REGIME LINEAR, 3-REGIME LINEAR, AND BELL CURVE MODELS. DATA WERE COLLECTED ON THE EISENHOWER EXPRESSWAY DURING NORMAL TRAFFIC AND WEATHER CONDITIONS. AFTER FAILING TO ACHIEVE ANY CONCLUSIVE RESULTS FROM THE STATISTICAL TESTS, THE AUTHORS RECOMMENDED THE RELATIONSHIP ADVANCED BY EDIE ON INTUITIVE GROUNDS. /FHWA/

268 citations


Network Information
Related Topics (5)
Estimator
97.3K papers, 2.6M citations
88% related
Linear model
19K papers, 1M citations
88% related
Inference
36.8K papers, 1.3M citations
87% related
Regression analysis
31K papers, 1.7M citations
86% related
Sampling (statistics)
65.3K papers, 1.2M citations
83% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023267
2022696
2021959
2020998
20191,033
2018943