Statistics for the Behavioural Sciences

Riccardo Russo is a Professor of Psychology at the University of Essex, UK, and the University of Pavia, Italy. His research interests vary in applied and theoretical areas of cognitive psychology and cognitive neuroscience.

Praise from the Previous Edition:"This is an outstanding introductory text that will appeal to instructors for its attention to detail, and to students for its clarity." - Thom Baguley, Loughborough University"This book explains how students can understand the basic concepts of statistical inference. I enjoyed reading it and would definitely recommend it to my students." - Naz Derakshan, University of Leeds"I like this book a lot and would recommend it to my undergraduate students." - David Clark-Carter, Staffordshire University

• Preface edition 1 Acknowledgements edition IPreface edition II Acknowledgements edition II 0. Mathematics and Algebra: A Rapid-Mini Review0.1. Operators and symbols0.2. Orders of operations 0.3. Dealing with fractions0.4. Variables, constants and equations0.5. Graphs and equations0.6. How to solve an equation with one unknown1. Introduction and basic concepts 1.1. Why is statistics useful in the behavioural sciences? 1.2. Simple example of statistical teseting1.3. Descriptive and inferential statistics 1.4. Descriptive and inferential statistics 1.5 What is an experiment?1.6 Correlational studies1.7 Irrelevant variables2. Descriptive statistics 2.1. Organising raw data 2.2. Frequency distributions and histograms 2.3. Grouped data 2.4. Stem-and-leaf diagrams 2.5. Summarising data 2.6. Measures of central tendency: Mode, median, and mean 2.7. Advantages and disadvantages of mode, median, and mean 2.8. A useful digression on the Σ notation 2.9. Measures of dispersion (or variability)2.10. Further on the mean, variance, and standard deviation of frequency distributions2.11. How to calculate the combined mean and the combined variance of several samples (Web only content)2.12. Properties of estimators 2.13. Mean and variance of linearly transformed data2.14 Using JASP for data analysis: Descriptive statistics3. Introduction to probability 3.1. Why are some notions of probability useful? 3.2. Some preliminary definitions and the concept of probability 3.3. Venn diagrams and probability 3.4. The addition rule and the multiplication rule of probability 3.5. Probability trees 3.6. Conditional probability 3.7. Independence and conditional probability 3.8. Bayes’s Theorem4. Introduction to inferential statistics4.1. Inferential statistics and probability4.2. The Classical/Frequentist approach to inferential statistics4.3. How the inferential statistic process operates in frequentist statistics4.4. Reducing the risk of false positives4.5. The risk of making false negative errors4.6. Estimating the magnitude of the size of the parameter associated to the theory4.7. Confidence intervals and inferential statistics.4.8. The Bayesian approach to inferential statistics4.9. Odds, probabilities and how to update probabilities4.10. Chickenpox or Smallpox? This is the dilemma. Bayesian inference in practice.4.11. The Bayes Factor: The Bayesian equivalent of significance testing4.12. The Bayes Factor in practice4.13. Computing the BF and interpreting its function in statistical inference4.14. Estimating the magnitude of the size of the parameter associated to the theory: Credible intervals4.15. Frequentist and Bayesian approaches to statistical inference: A rough comparison5. Probability distributions and the binomial distribution 5.1. Introduction 5.2. Probability distributions 5.3. Calculating the mean (μ) of a probability distribution 5.4. Calculating the variance (σ2) and the standard deviation (σ) of a probability distribution5.5. Orderings (or permutations) 5.6. Combinations 5.7. The binomial distribution 5.8. Mean and variance of the binomial distribution 5.9. How to use the binomial distribution in testing hypotheses: The Frequentist approach 5.10. The sign test 5.11. Further on the binomial distribution and its use in hypothesis testing (Web only content)5.12. Using JASP to conduct the binomial test (Frequentist approach) 5.13. The Bayesian binomial test5.14. Using JASP to conduct the binomial test (Bayesian approach) 5.15. The selection of the prior 6. Continuous random variables and the normal distribution 6.1. Introduction 6.2. Continuous random variables and their distribution 6.3. The normal distribution 6.4. The standard normal distribution 6.5. Hypothesis testing and the normal distribution: The Frequentist approach 6.6. Type I and Type II errors 6.7. One-tailed and two-tailed statistical tests 6.8. Hypothesis testing and the normal distribution: The Bayesian approach6.9. Using the normal distribution as an approximation of the binomial distribution (Web only content)7. Sampling distribution of the mean, its use in hypothesis testing and the one-sample t-test (Frequentist approach)7.1. Introduction 7.2. The sampling distribution of the mean and the Central Limit Theorem 7.3. Testing hypotheses about means when σ is known 7.4. Testing hypotheses about means when σ is unknown: The Student’s t-distribution and the one-sample t-test7.5. Two-sided confidence intervals for a population mean: Estimating the size of the population mean.7.6. A fundamental conceptual equation in frequentist data analysis: Magnitude of a significance test = Size of the effect × Size of the study7.7. Statistical power analysis: A brief introduction and its application to the one-sample t-test7.8. Power calculations for the one-sample t-test7.9. Using JASP to conduct the one sample t-test (Frequentist approach)8. Comparing a pair of means: the matched- and the independent-samples t-test (Frequentist approach) 8.1. Introduction8.2. The matched-samples t-test 8.3. Confidence intervals for a population mean 8.4. Counterbalancing 8.5. The sampling distribution of the difference between pairs of means and the independent-samples t-test8.6 The independent-samples t-test8.7. An application of the independent-samples t-test8.8. Confidence intervals for the difference between two population means 8.9. The robustness of the independent-samples t-test8.10. An example of the violation of the assumption of homogeneity of variances (Web only content) 8.11. Ceiling and floor effects8.12. Matched-samples or independent-samples t-test: Which of these two tests should be used? 8.13. A fundamental conceptual equation in data analysis: Magnitude of a significance test = Size of the effect × Size of the study8.14. Power analysis for the independent-samples and the paired-samples t-test8.15. Using JASP to conduct the paired and the independent sample t-test (Frequentist approach) 9. The Bayesian approach to the t-test9.1. Introduction9.2. An illustration of how to calculate the Bayes Factor for the one-sample t-test case9.3. Credible intervals (i.e. the Bayesian version of Frequentist confidence intervals)9.4. Using JASP to perform the one-sample t-test and the selection of the distribution to model your prior9.5. JASP in practice: The Bayesian one-sample t-test9.6. JASP in practice: The Bayesian paired-samples t-test9.7. JASP in practice: The Bayesian independent-samples t-test9.8. Bayesian t-test using Dienes’ calculator10. Correlation10.1. Introduction 10.2. Linear relationships between two continuous variables 10.3. More on linear relationships between two variables 10.4. The covariance between two variables 10.5. The Pearson product-moment correlation coefficient r10.6. Hypothesis testing on the Pearson correlation coefficient r 10.7. Confidence intervals for the Pearson correlation coefficient 10.8. Testing the significance of the difference between two independent Pearson correlation coefficients r10.9. Testing the significance of the difference between two nonindependent Pearson correlation coefficients r 10.10. Partial correlation 10.11. Factors affecting the Pearson correlation coefficient r 10.12. The point biserial correlation rpb 10.13. The Spearman Rank correlation coefficient 10.14. Kendall’s coefficient of concordance W 10.15. Power calculation for correlation coefficients10.16. Power calculation for the difference between two independent Pearson correlation coefficients r 10.17. Using JASP to perform correlation analyses (Frequentist approach)10.19. Using JASP to perform correlation analyses (Bayesian approach)11. Regression 11.1. Introduction 11.2. The regression line 11.3. Linear regression and correlation 11.4. Hypothesis testing on the slope b 11.5. Confidence intervals for the population regression slope β 11.6. Further on the relationship between linear regression and Pearson’s r: r2 as a measure of effect size11.7. Further on the error of prediction 11.8. Why the term regression?11.9. Using JASP to conduct a Linear regression analysis (Frequentist approach)11.10. Using JASP to conduct a Linear regression analysis (Bayesian approach)12. The chi-square distribution and the analysis of categorical data 12.1. Introduction 12.2. The chi-square (χ2) distribution 12.3. The Pearson’s chi-square test 12.4. The Pearson’s χ2 goodness of fit test12.5. Pearson’s χ2 test used in assessing how well the distribution of a set of data fits a prescribed distribution (Web only content)12.6. Further on the goodness of fit test (Web only content)12.7. Assumptions underlying the use of Pearson's χ2 test12.8. Compacting a set of data for the goodness of fit test 12.9. Pearson’s χ2 test and the analysis of 2 × 2 contingency tables 12.10. Further on the degrees of freedom and the calculation of the expected frequencies for any contingency table12.11. The analysis of R × C contingency tables 12.12. One- and two-tailed tests12.13. How to measure the strength of the association between variables in a contingency table 12.14. A fundamental conceptual equation in data analysis: Magnitude of a significance test = Size of the effect × Size of the study12.15. The odds ratio and the analysis of 2 × 2 contingency tables12.16. An important note on the inclusion of non-occurrences in contingency tables12.17. The analysis of contingency tables using JASP (Frequentist approach)12.17. The analysis of contingency tables using JASP (Bayesian approach)13. Statistical tests on proportions (Web only content)13.1. Introduction 13.2. Statistical tests on the proportion of successes in a sample 13.3. Confidence intervals for population proportions 13.4. Statistical tests on the difference between the proportions of successes from two independent samples13.5. Confidence intervals for the difference between two independent population proportions 13.6. Power calculation for a single proportion13.7. Power calculation for the difference between two independent proportions 13.8. Statistical tests on the difference between nonindependent proportions of successes (McNemar test)14. Nonparametric statistical tests (Web only content)14.1. Introduction 14.2. The Wilcoxon matched-pairs signed-ranks test 14.3. The Wilcoxon rank-sum test Appendix References Index