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.
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TL;DR: In this paper, the authors describe the organization of data and describe individuals in distributions, and describe joint distributions of data, and test hypotheses about correlation and regression, and Pearson's chi-square.
Abstract: 1. The organization of data 2. Describing distributions 3. Describing individuals in distributions 4. Describing joint distributions of data 5. Introduction to probability 6. Discrete probability distributions 7. Continuous probability distributions 8. Sampling distributions and estimation 9. Hypothesis testing 10. Testing hypotheses about population means 11. Testing hypotheses about population variances 12. Testing hypotheses about several population means mu1, mu2,..., muj: analysis of variance 13. More complex analysis of variance 14. Testing hypotheses about correlation and regression 15. Testing hypotheses about entire distributions: Pearson's chi-square.
166 citations
TL;DR: In this paper, the authors conducted a simulation study to provide counterexamples to some commonly held generalizations about the benefits of nonparametric tests, and found that non-parametric methods are not always acceptable substitutes for parametric methods such as the t test and the F test when parametric assumptions are not satisfied.
Abstract: To provide counterexamples to some commonly held generalizations about the benefits of nonparametric tests, the author concurrently violated in a simulation study 2 assumptions of parametric statistical significance tests—normality and homogeneity of variance. For various combinations of nonnormal distribution shapes and degrees of variance heterogeneity, the Type I error probability of a non-parametric rank test, the Wilcoxon-Mann-Whitney test, was found to be biased to a far greater extent than that of its parametric counterpart, the Student t test. The Welch-Satterthwaite separate-variances version of the t test, together with a preliminary outlier detection and downweighting procedure, protected the statistical significance level more consistently than the nonparametric test did. Those findings reveal that nonparametric methods are not always acceptable substitutes for parametric methods such as the t test and the F test in research studies when parametric assumptions are not satisfied. They ...
166 citations
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TL;DR: RooStats as discussed by the authors is a set of C++ classes with coherent interfaces, so that can be used on arbitrary model and datasets in a common way, with emphasis on discoveries, confidence intervals, and combined measurements.
Abstract: RooStats is a project to create advanced statistical tools required for the analysis of LHC data, with emphasis on discoveries, confidence intervals, and combined measurements. The idea is to provide the major statistical techniques as a set of C++ classes with coherent interfaces, so that can be used on arbitrary model and datasets in a common way. The classes are built on top of the RooFit package, which provides functionality for easily creating probability models, for analysis combinations and for digital publications of the results. We will present in detail the design and the implementation of the different statistical methods of RooStats. We will describe the various classes for interval estimation and for hypothesis test depending on different statistical techniques such as those based on the likelihood function, or on frequentists or bayesian statistics. These methods can be applied in complex problems, including cases with multiple parameters of interest and various nuisance parameters.
166 citations
TL;DR: In this article, the form of the optimal design for choice experiments in which attributes need not have the same number of levels for testing main effects only, when there are k attributes, and all choice sets are of size m, was established.
166 citations
TL;DR: Preliminary statistical tests for outlying values and comparisons between calibration curves can be applied using basic functions found in standard spreadsheet software, and emphasise that the comparability of results arising from RT-QPCR needs further refinement and development at the data-handling phase.
Abstract: As real-time quantitative PCR (RT-QPCR) is increasingly being relied upon for the enforcement of legislation and regulations dependent upon the trace detection of DNA, focus has increased on the quality issues related to the technique. Recent work has focused on the identification of factors that contribute towards significant measurement uncertainty in the real-time quantitative PCR technique, through investigation of the experimental design and operating procedure. However, measurement uncertainty contributions made during the data analysis procedure have not been studied in detail. This paper presents two additional approaches for standardising data analysis through the novel application of statistical methods to RT-QPCR, in order to minimise potential uncertainty in results. Experimental data was generated in order to develop the two aspects of data handling and analysis that can contribute towards measurement uncertainty in results. This paper describes preliminary aspects in standardising data through the application of statistical techniques to the area of RT-QPCR. The first aspect concerns the statistical identification and subsequent handling of outlying values arising from RT-QPCR, and discusses the implementation of ISO guidelines in relation to acceptance or rejection of outlying values. The second aspect relates to the development of an objective statistical test for the comparison of calibration curves. The preliminary statistical tests for outlying values and comparisons between calibration curves can be applied using basic functions found in standard spreadsheet software. These two aspects emphasise that the comparability of results arising from RT-QPCR needs further refinement and development at the data-handling phase. The implementation of standardised approaches to data analysis should further help minimise variation due to subjective judgements. The aspects described in this paper will help contribute towards the development of a set of best practice guidelines regarding standardising handling and interpretation of data arising from RT-QPCR experiments.
165 citations