Prescriptions for Working Statisticians

ISBN-13: 9781461283546 / Angielski / Miękka / 2012 / 295 str.

Albert Madansky

Opis

The first course in statistics, no matter how "good" or "long" it is, typically covers inferential procedures which are valid only if a number of preconditions are satisfied by the data. For example, students are taught about regression procedures valid only if the true residuals are independent, homoscedastic, and normally distributed. But they do not learn how to check for indepen dence, homoscedasticity, or normality, and certainly do not learn how to adjust their data and/or model so that these assumptions are met. To help this student out I designed a second course, containing a collec tion of statistical diagnostics and prescriptions necessary for the applied statistician so that he can deal with the realities of inference from data, and not merely with the kind of classroom problems where all the data satisfy the assumptions associated with the technique to be taught. At the same time I realized that I was writing a book for a wider audience, namely all those away from the classroom whose formal statistics education ended with such a course and who apply statistical techniques to data."

Spis treści

0 A Thoughtful Student’s Retrospective on Statistics 101.- 0. Introduction.- 1. The Introductory Model.- 2. The Regression Model.- References.- 1 Testing for Normality.- 0. Introduction.- 1. Normal Plots.- 2. Regression Procedures.- (a) Shapiro—Wilk Statistic.- (b) Filliben Statistic.- (c) D’Agostino Statistic.- 3. Studentized Range.- 4. Moment Checking.- 5. Standard Tests of Goodness-of-Fit.- (a) Chi-Square Test.- (b) Kolmogorov Test.- (c) Durbin Test.- 6. Evaluation.- Appendix I.- References.- 2 Testing for Homoscedasticity.- 0. Introduction.- 1. Comparing Variances of Two Normal Distributions.- 2. Testing Homoscedasticity of Many Populations.- (a) Bartlett Test.- (b) Normal Score Procedure (Fligner—Killeen).- (c) Use of Analysis of Variance (Levene).- (d) Evaluation.- 3. Regression Residuals.- (a) Standard Estimates.- (b) Homoscedastic Estimated Residuals.- (i) BLUS.- (ii) Recursive Residuals.- 4. Testing Homoscedasticity of Regression Residuals.- (a) Goldfeld—Quandt Procedure.- (b) Lagrange Multiplier Test.- (c) White Procedure.- (d) Robust Procedures.- (e) Nonparametric Tests.- (f) Adapting Tests of Homogeneity of Variances.- (g) Evaluation.- Appendix I.- References.- 3 Testing for Independence of Observations.- 0. Introduction.- 1. Parametric Procedures.- (a) Independence of Observations.- (b) Autocorrelation.- (c) Independence of Regression Residuals.- (d) Box—Pierce Statistic.- 2. Nonparametric Procedures.- (a) Runs Above and Below the Median.- (b) Runs Up-and-Down.- (c) Rank von Neumann Ratio.- References.- 4 Identification of Outliers.- 0. Introduction.- 1. Normal Distribution.- (a) One Outlier.- (b) Multiple Outlier Indication.- (c) Multiple Outlier Detection—Known Number.- (d) Multiple Outlier Detection—Unknown Number.- 2. Nonparametric Procedures.- 3. Outliers in Regression.- References.- 5 Transformations.- 0. Introduction.- 1. Deflating Heteroscedastic Regressions.- 2. Variance Stabilizing Transformations.- 3. Power Transformations (Box—Cox).- (a) Maximum Likelihood.- (b) Hinkley Estimation Procedure.- (c) Graphic Procedure.- 4. Letter-Values and Boxplots.- 5. Power Transformations of Regression Independent Variables.- Appendix I.- References.- 6 Independent Variable Selection in Multiple Regression.- 0. Introduction.- 1. Criteria for Goodness of Regression Model.- 2. Stepwise Procedures.- (a) Order of Selection of Variables.- (b) Theoretical Description.- (c) Cutoff Rules.- (d) Example.- 3. Multicollinearity.- (a) Description of the Phenomenon.- (b) Diagnostics.- (c) Ridge Regression.- References.- 7 Categorical Variables in Regression.- 0. Introduction.- 1. Two Sample Tests.- (a) Parametric Procedures.- (b) Nonparametric Procedures.- 2. Analysis of Variance via Regression (Model I).- (a) One-Way Anova.- (b) Unbalanced Two-Way Anova with Only Main Effects.- (c) Unbalanced Two-Way Anova with Interaction.- (d) Median Polish.- 3. Components of Variance (Model II).- 4. Dichotomous Dependent Variables.- References.- 8 Analysis of Cross-Classified Data.- 0. Introduction.- 1. Independence in the r1 × r2 Table.- (a) General.- (b) 2 × 2 Tables.- 2. Log-Linear Models in the r1 × r2 Table.- 3. The Three-Dimensional Table.- 4. Analysis of Cross-Classifications with Ordered Categories.- 5. Latent Class Model.- Appendix I.- Appendix II.- References.- Index of Reference Tables.