Learning Statistics with JASP: A Tutorial for Psychology Students and Other Beginners 1 (Version ? ) 2 Danielle Navarro University of New South Wales [email protected] David Foxcroft Oxford Brookes University [email protected] Thomas J. Faulkenberry Tarleton State University [email protected] http://www.learnstatswithjasp.com Overview Learning Statistics with JASP covers the contents of an introductory statistics class, as typically taught to undergraduate psychology students. The book discusses how to get started in JASP as well as giving an introduction to data manipulation. From a statistical perspective, the book discusses descriptive statistics and graphing first, followed by chapters on probability theory, sampling and estimation, and null hypothesis testing. After introducing the theory, the book covers the analysis of contingency tables, correlation, t-tests, regression, ANOVA and factor analysis. Bayesian statistics is covered at the end of the book. Citation Navarro, D.J., Foxcroft, D.R., & Faulkenberry, T.J. (2019). Learning Statistics with JASP: A Tutorial for Psychology Students and Other Beginners. (Version ?1 ). 2 ii This book is published under a Creative Commons BY-SA license (CC BY-SA) version 4.0. This means that this book can be reused, remixed, retained, revised and redistributed (including commercially) as long as appropriate credit is given to the authors. If you remix, or modify the original version of this open textbook, you must redistribute all versions of this open textbook under the same license - CC BY-SA. https://creativecommons.org/licenses/by-sa/4.0/ iii The JASP-specific revisions to the original book by Navarro and Foxcroft were made possible by a generous grant to Tom Faulkenberry from the Tarleton State University Center for Instructional Innovation. iv Table of Contents Preface ix I Background1 1 Why do we learn statistics?3 1.1 On the psychology of statistics.............................3 1.2 The cautionary tale of Simpson’s paradox.......................6 1.3 Statistics in psychology.................................9 1.4 Statistics in everyday life................................ 11 1.5 There’s more to research methods than statistics................... 11 2 A brief introduction to research design 13 2.1 Introduction to psychological measurement...................... 13 2.2 Scales of measurement................................. 17 2.3 Assessing the reliability of a measurement....................... 22 2.4 The “role” of variables: predictors and outcomes................... 24 2.5 Experimental and non-experimental research...................... 25 2.6 Assessing the validity of a study............................ 27 2.7 Confounds, artefacts and other threats to validity................... 30 2.8 Summary......................................... 40 II Describing and displaying data with JASP 43 3 Getting started with JASP 45 3.1 Installing JASP..................................... 46 3.2 Analyses......................................... 47 3.3 Loading data in JASP.................................. 48 3.4 The spreadsheet..................................... 50 3.5 Changing data from one measurement scale to another................ 52 3.6 Quitting JASP..................................... 52 3.7 Summary......................................... 53 4 Descriptive statistics 55 4.1 Measures of central tendency.............................. 55 4.2 Measures of variability.................................. 66 4.3 Skew and kurtosis.................................... 73 4.4 Descriptive statistics separately for each group.................... 76 v 4.5 Standard scores..................................... 76 4.6 Summary......................................... 78 5 Drawing graphs 83 5.1 Histograms........................................ 84 5.2 Boxplots......................................... 86 5.3 Saving image files using JASP............................. 89 5.4 Summary......................................... 90 III Statistical theory 91 6 Introduction to probability 99 6.1 How are probability and statistics different?...................... 100 6.2 What does probability mean?.............................. 101 6.3 Basic probability theory................................. 106 6.4 The binomial distribution................................ 109 6.5 The normal distribution................................. 113 6.6 Other useful distributions................................ 118 6.7 Summary......................................... 122 7 Estimating unknown quantities from a sample 123 7.1 Samples, populations and sampling........................... 123 7.2 The law of large numbers................................ 131 7.3 Sampling distributions and the central limit theorem................. 133 7.4 Estimating population parameters........................... 139 7.5 Estimating a confidence interval............................. 147 7.6 Summary......................................... 152 8 Hypothesis testing 153 8.1 A menagerie of hypotheses............................... 154 8.2 Two types of errors................................... 157 8.3 Test statistics and sampling distributions....................... 159 8.4 Making decisions.................................... 161 8.5 The p value of a test.................................. 164 8.6 Reporting the results of a hypothesis test....................... 167 8.7 Running the hypothesis test in practice........................ 169 8.8 Effect size, sample size and power........................... 170 8.9 Some issues to consider................................. 177 8.10 Summary......................................... 179 vi IV Statistical tools 181 9 Categorical data analysis 183 9.1 The χ2 (chi-square) goodness-of-fit test........................ 183 9.2 The χ2 test of independence (or association)..................... 198 9.3 The continuity correction................................ 203 9.4 Effect size........................................ 203 9.5 Assumptions of the test(s)............................... 204 9.6 Summary......................................... 205 10 Comparing two means 207 10.1 The one-sample z-test.................................. 208 10.2 The one-sample t-test................................. 214 10.3 The independent samples t-test (Student test).................... 219 10.4 The independent samples t-test (Welch test)..................... 229 10.5 The paired-samples t-test............................... 232 10.6 One sided tests..................................... 237 10.7 Effect size........................................ 238 10.8 Checking the normality of a sample........................... 241 10.9 Testing non-normal data with Wilcoxon tests...................... 246 10.10 Summary......................................... 248 11 Correlation and linear regression 251 11.1 Correlations....................................... 251 11.2 Scatterplots....................................... 261 11.3 What is a linear regression model?........................... 262 11.4 Estimating a linear regression model.......................... 265 11.5 Multiple linear regression................................ 267 11.6 Quantifying the fit of the regression model...................... 270 11.7 Hypothesis tests for regression models......................... 273 11.8 Regarding regression coefficients............................ 277 11.9 Assumptions of regression............................... 279 11.10 Model checking..................................... 280 11.11 Model selection..................................... 288 11.12 Summary......................................... 290 12 Comparing several means (one-way ANOVA) 293 12.1 An illustrative data set................................. 293 12.2 How ANOVA works................................... 295 12.3 Running an ANOVA in JASP.............................. 305 12.4 Effect size........................................ 306 12.5 Multiple comparisons and post hoc tests........................ 307 12.6 Assumptions of one-way ANOVA............................ 311 vii 12.7 Removing the normality assumption.......................... 315 12.8 Repeated measures one-way ANOVA.......................... 319 12.9 The Friedman non-parametric repeated measures ANOVA test............ 324 12.10 On the relationship between ANOVA and the Student t-test............. 325 12.11 Summary......................................... 325 13 Factorial ANOVA 327 13.1 Factorial ANOVA 1: balanced designs, no interactions................. 327 13.2 Factorial ANOVA 2: balanced designs, interactions allowed.............. 339 13.3 Effect size........................................ 346 13.4 Assumption checking.................................. 349 13.5 Analysis of Covariance (ANCOVA)........................... 351 13.6 ANOVA as a linear model................................ 353 13.7 Different ways to specify contrasts........................... 361 13.8 Post hoc tests...................................... 365 13.9 The method of planned comparisons.......................... 368 13.10 Factorial ANOVA 3: unbalanced designs........................ 369 13.11 Summary......................................... 380 V Endings, alternatives and prospects 381 14 Bayesian statistics 383 14.1 Probabilistic reasoning by rational agents........................ 384 14.2 Bayesian hypothesis tests................................ 389 14.3 Why be a Bayesian?................................... 391 14.4 Bayesian t-tests..................................... 399 14.5