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.

Testing for Linearity

Abstract: The problem of testing for linearity and the number of regimes in the context of self-exciting threshold autoregressive (SETAR) models is reviewed. We describe least-squares methods of estimation and inference. The primary complication is that the testing problem is non-standard, due to the presence of parameters which are only defined under the alternative, so the asymptotic distribution of the test statistics is non-standard. Simulation methods to calculate asymptotic and bootstrap distributions are presented. As the sampling distributions are quite sensitive to conditional heteroskedasticity in the error, careful modeling of the conditional variance is necessary for accurate inference on the conditional mean. We illustrate these methods with two applications--annual sunspot means and monthly U.S. industrial production. We find that annual sunspots and monthly industrial production are SETAR(2) processes. Copyright 1999 by Blackwell Publishers Ltd

Testing When a Parameter is on the Boundary of the Maintained Hypothesis

Abstract: This paper considers testing problems where several of the standard regularity conditions fail to hold. We consider the case where (i) parameter vectors in the null hypothesis may lie on the boundary of the maintained hypothesis and (ii) there may be a nuisance parameter that appears under the alternative hypothesis, but not under the null. The paper establishes the asymptotic null and local alternative distributions of quasi-likelihood ratio, rescaled quasi-likelihood ratio, Wald, and score tests in this case. The results apply to tests based on a wide variety of extremum estimators and apply to a wide variety of models. Examples treated in the paper are: (i) tests of the null hypothesis of no conditional heteroskedasticity in a GARCH(1, 1) regression model and (ii) tests of the null hypothesis that some random coefficients have variances equal to zero in a random coefficients regression model with (possibly) correlated random coefficients.

Foundations of behavioral statistics: An insight-based approach.

Abstract: Part I Introductory Terms and Concepts. Definitions of Some Basic Terms. Levels of Scale. Some Experimental Design Considerations. Some Key Concepts. Reflection Problems. Part II Location. Reasonable Expectations for Statistics. Location Concepts. Three Classical Location Descriptive Statistics. Four Criteria for Evaluating Statistics. Two Robust Location Statistics. Some Key Concepts. Reflection Problems. Part III Dispersion.Quality of Location Descriptive Statistics. Important in Its Own Right. Measures of Score Spread. Variance. Situation-Specific Maximum Dispersion. Robust Dispersion Descriptive Statistics. Standardized Score World. Some Key Concepts. Reflection Problems. Part IV Shape. Two Shape Descriptive Statistics. Normal Distributions. Two Additional Univariate Graphics. Some Key Concepts. Reflection Problems. Part V Bivariate Relationships. Pearson's r. Three Features of r. Three Interpretation Contextual Factors. Psychometrics of the Pearson r. Spearman's rho. Two Other r -Equivalent Correlation Coefficients. Bivariate Normality. Some Key Concepts. Reflection Problems. Part VI Statistical Significance. Sampling Distributions. Hypothesis Testing. Properties of Sampling Distributions. Standard Error/Sampling Error. Test Statistics. Statistical Precision and Power. pCALCULATED. Some Key Concepts. Reflection Problems. Part VII Practical Significance. Effect Sizes. Confidence Intervals. Confidence Intervals for Effect Sizes. Some Key Concepts. Reflection Problems. Part VIII Multiple Regression Analysis: Basic GLM Concepts. Purposes of Regression. Simple Linear Prediction. Case #1: Perfectly Uncorrelated Predictors. Case #2: Correlated Predictors, No Suppressor. Effects. Case #3: Correlated Predictors, Suppressor. Effects Present. b Weights versus Structure Coefficients. A Final Comment on Collinearity. Some Key Concepts. Reflection Problems. Part IX A GLM Interpretation Rubric. Do I Have Anything?Where Does My Something Originate? Stepwise Methods. Invoking Some Alternative Models. Some Key Concepts. Reflection Problems. Part X One-way Analysis of Variance (ANOVA). Experimentwise Type I Error. ANOVA Terminology. The Logic of Analysis of Variance. Practical and Statistical Significance. The "Homogeneity of Variance" Assumption. Post Hoc Tests. Some Key Concepts. Reflection Problems. Part XI Multiway and Alternative ANOVA Models. Multiway Models. Factorial versus Nonfactorial Analyses. Fixed-, Random-, and Mixed-Effects Models. Brief Comment on ANCOVA. Some Key Concepts. Reflection Problems. Part XII The General Linear Model (GLM): ANOVA via Regression. Planned Contrasts. Trend/Polynomial Planned Contrasts. Repeated Measures ANOVA via Regression. GLM Lessons. Some Key Concepts. Reflection Problems. Part XIII Some Logistic Models: Model Fitting in a Logistic Context. Logistic Regression. Loglinear Analysis. Some Key Concepts. Reflection Problems. Appendix: Scores (n = 100) with Near Normal Distributions.