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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Book•
01 Jan 1982
TL;DR: In this article, Cox et al. present a survey of the history of statistical methods and their applications in the field of statistics, including the use of the Normal Curve and z scores.
Abstract: Preface I. DESCRIPTIVE STATISTICS 1. Introduction to Statistics Stumbling Blocks to Statistics A Brief Look at the History of Statistics Gertrude Cox (1900-1978) Benefits of a Course in Statistics General Fields of Statistics Summary Key Terms and Names Problems 2. Percentages, Graphs and Measures of Central Tendency Percentage Changes-Comparing Increases with Decreases Graphs Measures of Central Tendency Appropriate Use of the Mean the Median and the Mode Summary Key Terms Problems Computer Problems 3. Variability Measures of Variability Graphs and Variability Questionnaire Percentages Key Terms Computer Problems 4. The Normal Curve and z Scores The Normal Curve z Scores Carl Friedrich Gauss (1777-1855) Translating Raw Scores into z Scores z Score Translation in Practice Fun with your Calculator Summary Key Terms and Names Problems 5. z Scores Revisited: T Scores and Other Normal Curve Transformations Other Applications of the z Score The Percentile Table T Scores Normal Cure Equivalents Stanines Grade-Equivalent Scores: A Note of Caution The Importance of the z Score Summary Key Terms Problems 6. Probability The Definition of Probability Blaise Pascal (1623-1662) Probability and Percentage Areas of the Normal Curve Combining Probabilities for Independent Events A Reminder about Logic Summary Key Terms Problems II. INFERENTIAL STATISTICS 7. Statistics and Parameters Generalizing from the Few to the Many Key Concepts of Inferential Statistics Techniques of Sampling Sampling Distributions Infinite versus Finite Sampling Galton and the Concept of Error Back to z Some Words of Encouragement Summary Key Terms Problems 8. Parameter Estimates and Hypothesis Testing Estimating the Population Standard Deviation Estimating the Standard Error of the Mean Estimating the Population of the Mean: Interval Estimates and Hypothesis Testing The t Ratio The Type 1 Error Alpha Levels Effect Size Interval Estimates: No Hypothesis Test Needed Summary Key Terms Problems Computer Problems 9. The Fundamentals of Research Methodology Research Strategies Independent and Dependent Variables The Cause-and-Effect Trap Theory of Measurement Research: Experimental versus Post Facto The Experimental Method: The Case of Cause and Effect Creating Equivalent Groups: The True Experiment Designing the True Experiment The Hawthorne Effect Repeated-Measures Designs with Separate Control Groups Requirements for the True Experiment Post Facto-Research Combination Research Research Errors Experimental Errors Meta-Analysis Methodology as a Basis for More Sophisticated Techniques Summary Key Terms Problems 10. The Hypothesis of Difference Sampling Distribution of Differences Estimated Standard Error of Difference Two-Sample t Test for Independent Samples Significance William Sealy Gossett (1876-1937) Two-Tailed t Table Alpha Levels and Confidence Level The Minimum Difference Outliner One-Tail t Test Importance of Having at Least Two Samples Power Effect Size Summary Key Terms Problems Computer Problems 11. The Hypothesis of Association: Correlation Cause and Effect The Pearson r Interclass versus Intraclass Karl Pearon (1857-1936) Missing Data Correlation Matrix The Spearman r s' 293 An Important Difference between the Correlation Correlation Coefficient and t Test Summary Key Terms and Names Problems Computer Problems 12. Analysis of Variance Advantages of ANOVA The Bonferroni Test Ronald Aylmer, Fisher (1890-1962) Analyzing the Variance Applications of ANOVA The Factorial ANOVA Eta Square and d Graphing the Interaction Summary Key Terms and Names Problems Computer Problems 13. Nominal Data and the Chi Square Chi Square and Independent Samples Locating the Difference Chi Square Percentages Square and z Scores Chi Square and Dependent Samples Requirements for Using Chi Square Summary Key Terms Problems Computer Problems III. ADVANCED TOPICS IN INFERENTIAL STATISTICS 14. Regression Analysis Regression of Y on X Sir Francis Galton (1822-1911) Standard Error of Estimate Multiple R (Linear Regression with More Than Two Variables) Path Analysis The Multiple Rand Causation Partial Correlation Summary Key Terms and Names Computer Problems 15. Repeated-Measures and Matched-Subjects Designs With Interval Data Problem of Correlated or Dependent Samples Repeated Measures, Paired t Ratio Confidence Interval for Paired Differences Within-Subjects Effect Size Testing Correlated Experimental Data Summary Key Terms Problems Computer Problems 16. Nonparametrics Revisited: The Ordinal Case Mann-Whitney U Test for Two Ordinal Distributions with Independent Selection Kruskal-Wallis H Test for Three or More Ordinal Distributions with Independent Selection Wicoxon T Test for Two Ordinal Distributions with Correlated Selection Friedman ANOVA By Ranks for Three or More Ordinal Distributions with Correlated Selection Advantages and Disadvantages of Nonparametric Tests Summary Key Terms Problems 17. Tests and Measurements Norm and Criterion Referencing: Relative Versus Absolute Performance Measure The Problem of Bias Test Reliability Validityand Measurement Theory Test Validity Item Analysis Summary Key Terms Problems Computer Problems 18. Computers and Statistical Analysis Computer Literacy The Statistical Programs Ada Lovelace (nee Byron, 1815-1852) Logic Checkpoints Answers Recommended Reading 19. Research Simulations: Choosing the Correct Statistical Test Methodology: Research's Bottom Line Checklist Questions Critical Decision Points Research Simulations: From A to Z The Research Enterprise A Final Thought: The Burden of Proof Special Unit: The Binomial Case Appendix A Appendix B Glossary References Answers to Odd-Numbered Items (and Within-Chapter Exercises) Index Statistical Hall of Fame Biographies Gertrude Cox-Chapter 1 Carl Gauss-Chapter 4 Blaise Pascal-Chapter 6 William Gossett-Chapter 10 Karl Pearson-Chapter 11 Ronald Fisher-Chapter 12 Sir Francis Galton-Chapter 14 Ada Lovelace-Chapter 18
459 citations
Posted Content•
TL;DR: In this article, a brief overview of the class of models under study and central theoretical issues such as the curse of dimensionality, the bias-variance trade-off and rates of convergence are discussed.
Abstract: This introduction to nonparametric regression emphasizes techniques that might be most accessible and useful to the applied economist. The paper begins with a brief overview of the class of models under study and central theoretical issues such as the curse of dimensionality, the bias-variance trade-off and rates of convergence. The paper then focuses on kernel and nonparametric least squares estimation of the nonparametric regression model, and optimal differencing estimation of the partial linear model. Constrained estimation and hypothesis testing is also discussed. Empirical examples include returns to scale in electricity distribution and hedonic pricing of housing attributes.
458 citations
TL;DR: This study demonstrates how applying signal classification to Gaussian random signals can yield decoding accuracies of up to 70% or higher in two-class decoding with small sample sets, taking sample size into account.
452 citations
Book•
01 Jan 2003
TL;DR: In this article, a stepwise multiple testing procedure that asymptotically controls the familywise error rate is proposed, which implicitly captures the joint dependence structure of the test statistics, which results in increased ability to detect false hypotheses.
Abstract: In econometric applications, often several hypothesis tests are carried out at once. The problem then becomes how to decide which hypotheses to reject, accounting for the multitude of tests. This paper suggests a stepwise multiple testing procedure that asymptotically controls the familywise error rate. Compared to related single-step methods, the procedure is more powerful and often will reject more false hypotheses. In addition, we advocate the use of studentization when feasible. Unlike some stepwise methods, the method implicitly captures the joint dependence structure of the test statistics, which results in increased ability to detect false hypotheses. The methodology is presented in the context of comparing several strategies to a common benchmark. However, our ideas can easily be extended to other contexts where multiple tests occur. Some simulation studies show the improvements of our methods over previous proposals. We also provide an application to a set of real data.
452 citations
TL;DR: A generalization of the K statistic of Blomberg et al. that is useful for quantifying and evaluating phylogenetic signal in highly dimensional multivariate data is described and the utility of the new approach is illustrated by evaluating the strength of phylogenetics signal for head shape in a lineage of Plethodon salamanders.
Abstract: Phylogenetic signal is the tendency for closely related species to display similar trait values due to their common ancestry. Several methods have been developed for quantifying phylogenetic signal in univariate traits and for sets of traits treated simultaneously, and the statistical properties of these approaches have been extensively studied. However, methods for assessing phylogenetic signal in high-dimensional multivariate traits like shape are less well developed, and their statistical performance is not well characterized. In this article, I describe a generalization of the K statistic of Blomberg et al. that is useful for quantifying and evaluating phylogenetic signal in highly dimensional multivariate data. The method (Kmult) is found from the equivalency between statistical methods based on covariance matrices and those based on distance matrices. Using computer simulations based on Brownian motion, I demonstrate that the expected value of Kmult remains at 1.0 as trait variation among species is increased or decreased, and as the number of trait dimensions is increased. By contrast, estimates of phylogenetic signal found with a squared-change parsimony procedure for multivariate data change with increasing trait variation among species and with increasing numbers of trait dimensions, confounding biological interpretations. I also evaluate the statistical performance of hypothesis testing procedures based on Kmult and find that the method displays appropriate Type I error and high statistical power for detecting phylogenetic signal in high- dimensional data. Statistical properties of Kmult were consistent for simulations using bifurcating and random phylogenies, for simulations using different numbers of species, for simulations that varied the number of trait dimensions, and for different underlying models of trait covariance structure. Overall these findings demonstrate that Kmult provides a useful means of evaluating phylogenetic signal in high-dimensional multivariate traits. Finally, I illustrate the utility of the new approach by evaluating the strength of phylogenetic signal for head shape in a lineage of Plethodon salamanders. (Geometric morphometrics; macroevolution; morphological evolution; phylogenetic comparative method.)
452 citations