SUMMARY AND ANALYSIS OF EXTENSION PROGRAM EVALUATION IN R SALVATORE S. MANGIAFICO Rutgers Cooperative Extension New Brunswick, NJ VERSION 1.18.8 i ©2016 by Salvatore S. Mangiafico. Non-commercial reproduction of this content, with attribution, is permitted. For-profit reproduction without permission is prohibited. If you use the code or information in this site in a published work, please cite it as a source. Also, if you are an instructor and use this book in your course, please let me know. [email protected] Mangiafico, S.S. 2016. Summary and Analysis of Extension Program Evaluation in R, version 1.18.8. rcompanion.org/documents/RHandbookProgramEvaluation.pdf . Web version: rcompanion.org/handbook/ ii List of Chapters List of Chapters List of Chapters .......................................................................................................................... iii Table of Contents ...................................................................................................................... vi Introduction ............................................................................................................................... 1 Purpose of This Book.......................................................................................................................... 1 Author of this Book and Version Notes ............................................................................................... 2 Using R .............................................................................................................................................. 3 Statistics Textbooks and Other Resources ......................................................................................... 14 Statistics for Educational Program Evaluation ........................................................................... 17 Why Statistics? ................................................................................................................................ 17 Evaluation Tools and Surveys ........................................................................................................... 18 Variables, Descriptive Statistics, and Plots ................................................................................ 24 Types of Variables ............................................................................................................................ 24 Descriptive Statistics ........................................................................................................................ 30 Confidence Intervals ........................................................................................................................ 62 Basic Plots ....................................................................................................................................... 73 Understanding Statistics and Hypothesis Testing .................................................................... 113 Hypothesis Testing and p-values ......................................................................................................113 Reporting Results of Data and Analyses ...........................................................................................134 Choosing a Statistical Test ...............................................................................................................138 Independent and Paired Values .......................................................................................................146 Likert Data ............................................................................................................................. 152 Introduction to Likert Data ..............................................................................................................152 Descriptive Statistics for Likert Data ................................................................................................162 Descriptive Statistics with the likert Package ................................................................................... 184 Confidence Intervals for Medians ....................................................................................................189 Converting Numeric Data to Categories ...........................................................................................197 Traditional Nonparametric Tests............................................................................................. 208 Introduction to Traditional Nonparametric Tests ............................................................................. 208 One-sample Wilcoxon Signed-rank Test ...........................................................................................212 Sign Test for One-sample Data ........................................................................................................218 iii Two-sample Mann–Whitney U Test ................................................................................................. 221 Mood’s Median Test for Two-sample Data ......................................................................................234 Two-sample Paired Signed-rank Test ...............................................................................................237 Sign Test for Two-sample Paired Data ..............................................................................................245 Kruskal–Wallis Test .........................................................................................................................248 Mood’s Median Test .......................................................................................................................261 Friedman Test ................................................................................................................................. 267 Quade Test .....................................................................................................................................279 Scheirer–Ray–Hare Test ..................................................................................................................286 Aligned Ranks Transformation ANOVA ............................................................................................291 Nonparametric Regression and Local Regression ............................................................................. 304 Nonparametric Regression for Time Series ......................................................................................313 Permutation Tests .................................................................................................................. 320 Introduction to Permutation Tests ...................................................................................................320 One-way Permutation Test of Independence for Ordinal Data .......................................................... 324 One-way Permutation Test of Symmetry for Paired Ordinal Data ..................................................... 333 Permutation Tests for Medians and Percentiles ............................................................................... 343 Tests for Ordinal Data in Tables .............................................................................................. 349 Association Tests for Ordinal Tables ................................................................................................349 Measures of Association for Ordinal Tables ..................................................................................... 359 Concepts for Linear Models ..................................................................................................... 368 Introduction to Linear Models .........................................................................................................368 Using Random Effects in Models......................................................................................................371 What are Estimated Marginal Means? .............................................................................................376 Estimated Marginal Means for Multiple Comparisons ...................................................................... 379 Factorial ANOVA: Main Effects, Interaction Effects, and Interaction Plots ......................................... 387 p-values and R-square Values for Models ........................................................................................399 Accuracy and Errors for Models .......................................................................................................410 Ordinal Tests with Cumulative Link Models ............................................................................. 416 Introduction to Cumulative Link Models (CLM) for Ordinal Data ....................................................... 416 Two-sample Ordinal Test with CLM ................................................................................................. 418 Two-sample Paired Ordinal Test with CLMM ................................................................................... 422 One-way Ordinal Regression with CLM ............................................................................................427 iv One-way Repeated Ordinal Regression with CLMM ......................................................................... 433 Two-way Ordinal Regression with CLM ............................................................................................442 Two-way Repeated Ordinal Regression