Statistics Explained

Description

Statistics Explained is an accessible introduction to statistical concepts and ideas. It makes few assumptions about the reader’s statistical knowledge, carefully explaining each step of the analysis and the logic behind it. The book: • provides a clear explanation of statistical analysis and the key statistical tests employed in analysing research data • gives accessible explanations of how and why statistical tests are used • includes a wide range of practical, easy-to-understand worked examples. Building on the international success of earlier editions, this fully updated revision includes developments in statistical analysis, with new sections explaining concepts such as bootstrapping and structural equation modelling. A new chapter - ‘Samples and Statistical Inference’ - explains how data can be analysed in detail to examine its suitability for certain statistical tests. The friendly and straightforward style of the text makes it accessible to all those new to statistics, as well as more experienced students requiring a concise guide. It is suitable for students and new researchers in disciplines including Psychology, Education, Sociology, Sports Science, Nursing, Communication, and Media and Business Studies. Presented in full colour and with an updated, reader-friendly layout, this new edition also comes with a companion website featuring supplementary resources for students. Unobtrusive cross-referencing makes it the ideal companion to Perry R. Hinton’s SPSS Explained, also published by Routledge. Perry R. Hinton has many years of experience in teaching statistics to students from a wide range of disciplines and his understanding of the problems students face forms the basis of this book. Cover Half Title Title Page Copyright Page Dedication Table of Contents List of figures Preface Chapter 1 Introduction Accompanying Website Chapter 2 Descriptive Statistics Measures of ‘Central Tendency’ Measures of ‘Spread’ Describing a Set of Data: In Conclusion Comparing Two Sets of Data with Descriptive Statistics Some Important Information about Numbers Chapter Recap Chapter 3 Standard Scores Comparing Scores from Different Distributions The Normal Distribution The Standard Normal Distribution Chapter Recap Chapter 4 Introduction to Hypothesis Testing Testing a Hypothesis One- and Two-Tailed Predictions Chapter Recap Chapter 5 Sampling Populations and Samples Selecting a Sample Sample Statistics and Population Parameters Chapter Recap Chapter 6 Hypothesis Testing with One Sample An Example When We Do Not Have the Known Population Standard Deviation Confidence Intervals Chapter Recap Chapter 7 Selecting Samples for Comparison Comparing Samples The Interpretation of Sample Differences Chapter Recap Chapter 8 Hypothesis Testing with Two Samples The Assumptions of the Two Sample t Test Paired Samples or Independent Samples The Paired Samples (Related) t Test The Independent t Test Chapter Recap Chapter 9 Significance, Error and Power Type I and Type II Errors Statistical Power The Power of a Test The Choice of α Level Effect Size Sample Size Chapter Recap Chapter 10 Samples and Statistical Inference Examining a Sample Normally Distributed Populations and Samples Skew Kurtosis Tests of Normality Outliers Sample Variation Parametric Tests and Measurement Bootstrapping Chapter Recap Chapter 11 Introduction to the Analysis of Variance Factors and Conditions The Limitations of the t Test Why Do Scores Vary in a Set of Data? The Process of Analysing Variability The F Distribution Chapter Recap Chapter 12 One Factor Independent Anova Analysing Variability in the Independent Anova Rejecting the Null Hypothesis Unequal Sample Sizes The Relationship of F to t Chapter Recap Chapter 13 Multiple Comparisons The Tukey Test (For All Pairwise Comparisons) The Scheffé Test (For Complex Comparisons) Chapter Recap Chapter 14 One Factor Repeated Measures Anova Deriving the F Value Multiple Comparisons Chapter Recap Chapter 15 The Interaction of Factors in the Analysis of Variance Interactions Dividing Up the Between Conditions Sums of Squares Simple Main Effects Chapter Recap Chapter 16 The Two Factor Anova The Two Factor Independent Anova The Two Factor Mixed Design Anova The Two Factor Repeated Measures Anova A Non-Significant Interaction Chapter Recap Chapter 17 Two Sample Nonparametric Analysis Ordinal Data Calculating Ranks The Mann–Whitney u Test (For Independent Samples) The Wilcoxon Signed-Ranks Test (For Paired Samples) Chapter Recap Chapter 18 One Factor Anova for Ranked Data Kruskal–Wallis Test (For Independent Measures) The Friedman Test (For Related Samples) Chapter Recap Chapter 19 Analysing Frequency Data: Chi-Square Nominal Data, Categories and Frequency Counts Introduction to X² Chi-Square (X²) As a ‘Goodness of Fit’ Test Chi-Square (X²) As a Test of Independence The Chi-Square Distribution The Assumptions of the X² Test Chapter Recap Chapter 20 Linear Correlation and Regression Introduction Pearson r Correlation Coefficient Linear Regression The Interpretation of Correlation and Regression Problems with Correlation and Regression The Standard Error of the Estimate The Spearman rs Correlation Coefficient Chapter Recap Chapter 21 Multiple Correlation and Regression Introduction to Multivariate Analysis Partial Correlation Multiple Correlation Multiple Regression The Significance of R² Chapter Recap Chapter 22 Complex Analyses Complex Analyses and the Analysis of Variation Reliability Factor Analysis Multivariate Analysis of Variance (Manova) Discriminant Function Analysis Structural Equation Modelling Chapter Recap Chapter 23 An Introduction to the General Linear Model Models An Example of a Linear Model Modelling Data The Model: The Regression Equation Selecting a Good Model Comparing Samples (The Analysis of Variance Once Again) Explaining Variations in the Data The General Linear Model Chapter Recap Chapter 24 Postscript Appendix: Acknowledgements and Statistical Tables A.1 The standard normal distribution tables A.2 Critical values of the t distribution A.3 Critical values of the F distribution A.4 Critical values of the Studentized range statistic, q A.5 Critical values of the Mann–Whitney U statistic A.6 Critical values of the Wilcoxon T statistic A.7 Critical values of the chi-square (X²) distribution A.8 Table of probabilities for X²r when k and n are small A.9 Critical values of the Pearson r correlation coefficient A.10 Critical values of the Spearman rs ranked correlation coefficient A.11 Excel commands for the D’Agostino–Pearson omnibus K² test Glossary References Index Choosing a statistical test