New Introduction to Statistics with SPSS for Social Science Gareth Norris Faiza Qureshi Dennis Howitt Duncan Cramer Aberystwyth University City University London University of Loughborough University of Loughborough PEARSON Harlow, England London York Boston San Francisco Toronto Sydney Auckland Singapore Hong Kong Tokyo Seoul Taipei New Delhi Cape Town Sao Paulo Mexico City Madrid Amsterdam Munich Paris Milan
Contents J Guided tour Introduction List of figures List of tables List of boxes List of calculation boxes Acknowledgements XVI xviii xxi xxiii xxviii xxix xxx Part 1 Descriptive statistics 1 Why you need statistics: types of data Overview 1.1 Introduction 1.2 Variables and measurement 1.3 Statistical significance 1.4 SPSS guide: an introduction 2 Describing variables: tables and diagrams Overview 2.1 Introduction 2.2 Choosing tables and diagrams 2.3 Errors to avoid 2.4 SPSS analysis 2.5 Pie diagram of category data 2.6 Bar chart of category data 2.7 Histograms 3 Describing variables numerically: averages, variation and spread Overview 3.1 Introduction: mean, median and mode 3 3 4 4 6 7 19 20 20 21 22 29 29 34 36 38 39 40 40 41
. viii CONTENTS V 3.2 Comparison of mean, median and mode 44 3.3 The spread of scores: variability 45 3.4 Probability 3.5 Confidence intervals 51 3.6 SPSS analysis /Cey po/nts 4 Shapes of distributions of scores 55 Ouerv/eiv 5 5 4.1 Introduction 56 4.2 Histograms and frequency curves 56 4.3 The normal curve 57 4.4 Distorted curves 58 4.5 Other frequency curves 60 4.6 SPSS analysis 5 Standard deviation, z-scores and standard error: the standard unit of measurement in statistics 67 Overview 67 5.1 Introduction 68 5.2 What is standard deviation? 68 5.3 When to use standard deviation 70 5.4 When not to use standard deviation 71 5.5 Data requirements for standard deviation 71 5.6 Problems in the use of standard deviation 72 5.7 SPSS analysis 5.8 Standard error: the standard deviation of the means of samples 76 5.9 When to use standard error 77 5.10 When not to use standard error 77 5.11 SPSS analysis for standard error 77 80 6 Relationships between two or more variables: diagrams and tables 81 Overview 81 6.1 Introduction 82 6.2 The principles of diagrammatic and tabular presentation 82 6.3 Type A: both variables numerical scores 83 6.4 Type B: both variables nominal categories 84 6.5 Type C: one variable nominal categories, the other numerical scores 86 6.6 SPSS analysis 49 51 54 63 66 72 88 98 J
another CONTENTS ix 7 Correlation coefficients: the Pearson correlation and Spearman's rho 99 Overview 99 7.1 Introduction 100 7.2 Principles of the correlation coefficient 100 7.3 Some rules to check out 106 7.4 Coefficient of determination 107 7.5 Data requirements for correlation coefficients 108 7.6 SPSS analysis 108 7.7 Spearman's rho - correlation coefficient 110 7.8 SPSS analysis for Spearman's rho 114 7.9 Scatter diagram using SPSS 115 7.10 Problems in the use of correlation coefficients 117 117 8 Regression and standard error 118 Overview 118 8.1 Introduction 119 8.2 Theoretical background and regression equations 121 8.3 When and when not to use simple regression 125 8.4 Data requirements for simple regression 125 8.5 Problems in the use of simple regression 125 8.6 SPSS analysis 126 8.7 Regression scatterplot 129 8.8 Standard error: how accurate are the predicted score and the regression equations? 132 133 V. Part 2 Inferential statistics 135 9 The analysis of a questionnaire/survey project 137 Overview 137 9.1 Introduction 138 9.2 The research project 138 9.3 The research hypothesis 139 9.4 Initial variable classification 140 9.5 Further coding of data 141 9.6 Data cleaning 142 9.7 Data analysis 142 9.8 SPSS analysis 144 144
CONTENTS 10 The related f-test: comparing two samples of correlated/ related scores 145 Overview 145 10.1 Introduction 146 10.2 Dependent and independent variables 147 10.3 Theoretical considerations 148 10.4 SPSS analysis 153 10.5 A cautionary note 156 157 11 The unrelated f-test: comparing two samples of unrelated/ uncorrelated scores 158 Overview 158 11.1 Introduction 159 11.2 Theoretical considerations 160 11.3 Standard deviation and standard error 164 11.4 A cautionary note 170 11.5 Data requirements for the unrelated f-test 170 11.6 When not to use the unrelated f-test 170 11.7 Problems in the use of the unrelated f-test 171 11.8 SPSS analysis 171 175 12 Chi-square: differences between samples of frequency data 176 Overview 176 12.1 Introduction 177 12.2 Theoretical considerations 178 12.3 When to use chi-square 183 12.4 When not to use chi-square 183 12.5 Data requirements for chi-square 183 12.6 Problems in the use of chi-square 184 12.7 SPSS analysis 184 12.8 The Fisher exact probability test 189 12.9 SPSS analysis for the Fisher exact test 192 12.10 Partitioning chi-square 193 12.11 Important warnings 195 12.12 Alternatives to chi-square 195 12.13 Chi-square and known populations 196 196 Recommended further reading 196
CONTENTS xi Part 3 Introduction to analysis of variance 197; 13 Analysis of variance (ANOVA): introduction to one-way unrelated or uncorretated ANOVA 199 Overview 199 13.1 Introduction 200 13.2 Theoretical considerations 200 13.3 Degrees of freedom 204 13.4 When to use one-way ANOVA 204 13.5 When not to use one-way ANOVA 205 13.6 Data requirements for one-way ANOVA 205 13.7 Problems in the use of one-way ANOVA 205 13.8 SPSS analysis 205 13.9 Computer analysis for one-way unrelated ANOVA 208 211 14 Two-way analysis of variance for unrelated/uncorrelated scores: two studies for the price of one? 212 Overview 212 14.1 Introduction 213 14.2 Theoretical considerations 214 14.3 Steps in the analysis 215 14.4 When to use two-way ANOVA 220 14.5 When not to use two-way ANOVA 220 14.6 Data requirements for two-way ANOVA 220 14.7 Problems in the use of two-way ANOVA 220 14.8 SPSS analysis 221 14.9 Computer analysis for two-way unrelated ANOVA 227 14.10 Three or more independent variables 233 14.11 Multiple-comparisons testing in ANOVA 234 239 15 Analysis of covariance (ANCOVA): controlling for additional variables 240 Overview 240 15.1 Introduction 241 15.2 Example of the analysis of covariance 241 15.3 When to use ANCOVA 250 15.4 When not to use ANCOVA 250 15.5 Data requirements for ANCOVA 250
CONTENTS 15.6 SPSS analysis 250 257 Recommended further reading 257 16 Multivariate analysis of variance (MANOVA) 258 Overview 258 16.1 Introduction 259 16.2 Questions for MANOVA 260 16.3 MANOVA's two stages 261 16.4 Doing MANOVA 262 16.5 When to use MANOVA 266 16.6 When not to use MANOVA 267 16.7 Data requirements for MANOVA 267 16.8 Problems in the use of MANOVA 268 16.9 SPSS analysis 268 273 Recommended further reading 273 Part 4 More advanced statistics and techniques 275 J 17 Partial correlation: spurious correlation, third or confounding variables (control variables), suppressor variables 277 Overview 277 17.1 Introduction 278 17.2 Theoretical considerations 278 17.3 The calculation 280 17.4 Multiple control variables 282 17.5 Suppressor variables 282 17.6 An example from the research literature 282 17.7 When to use partial correlation 284 17.8 When not to use partial correlation 284 17.9 Data requirements for partial correlation 284 17.10 Problems in the use of partial correlation 284 17.11 SPSS analysis 284 287 18 Factor analysis: simplifying complex data 288 Overview 288 18.1 Introduction 289 18.2 Data issues in factor analysis 290
CONTENTS xiii / 18.3 Concepts in factor analysis 291 18.4 Decisions, decisions, decisions 293 18.5 When to use factor analysis 298 18.6 When not to use factor analysis 298 18.7 Data requirements for factor analysis 299 18.8 Problems in the use of factor analysis 299 18.9 SPSS analysis 299 306 Recommended further reading 307 19 Multiple regression and multiple correlation 308 Overview 308 19.1 Introduction 309 19.2 Theoretical considerations 309 19.3 Stepwise multiple regression example 314 19.4 Reporting the results 317 19.5 What is stepwise multiple regression? 317 19.6 When to use stepwise multiple regression 318 19.7 When not to use stepwise multiple regression 318 19.8 Data requirements for stepwise multiple regression 319 19.9 Problems in the use of stepwise multiple regression 319 19.10 SPSS analysis 319 19.11 What is hierarchical multiple regression? 324 19.12 When to use hierarchical multiple regression 325 19.13 When not to use hierarchical multiple regression 325 19.14 Data requirements for hierarchical multiple regression 325 19.15 Problems in the use of hierarchical multiple regression 326 19.16 SPSS analysis 326 330 Recommended further reading 331 20 Multinomial logistic regression: distinguishing between several different categories or groups 332 Overview 332 20.1 Introduction 333 20.2 Dummy variables 335 20.3 What can multinomial logistic regression do? 335 20.4 Worked example 337 20.5 Accuracy of the prediction 338 20.6 How good are the predictors? 339 20.7 The prediction 342 20.8 What have we found? 344 V
Xiv CONTENTS 20.9 Reporting the results 345 20.10 When to use multinomial logistic regression 345 20.11 When not to use multinomial logistic regression 345 20.12 Data requirements for multinomial logistic regression 346 20.13 Problems in the use of multinomial logistic regression 346 20.14 SPSS analysis 346 356 21 Binomial logistic regression 357 Overview 357 21.1 Introduction 358 21.2 Simple logistic regression 358 21.3 Typical example 362 21.4 Applying the logistic regression procedure 365 21.5 The regression formula 368 21.6 Reporting the results 370 21.7 When to use binomial logistic regression 370 21.8 When not to use binomial logistic regression 370 21.9 Data requirements for binomial logistic regression 370 21.10 Problems in the use of binomial logistic regression 371 21.11 SPSS analysis 371 377 22 Log-linear methods: the analysis of complex contingency tables 378 Overview 378 22.1 Introduction 379 22.2 A two-variable example 381 22.3 A three-variable example 388 22.4 Reporting the results 398 22.5 When to use log-linear analysis 399 22.6 When not to use log-linear analysis 399 22.7 Data requirements for log-linear analysis 400 22.8 Problems in the use of log-linear analysis 400 22.9 SPSS analysis 400 405 Recommended further reading 405 V Appendices 407 A Testing for excessively skewed distributions 409 A.l Skewness 409 A.2 Standard error of skewness 410 J
CONTENTS XV B Extended table of significance for the Pearson correlation coefficient 412 C Table of significance for the Spearman correlation coefficient 416 D Extended table of significance for the f-test 420 E Table of significance for chi-square 424 F Extended table of significance for the sign test 425 G Table of significance for the Wilcoxon matched pairs test 429 H Tables of significance for the Mann-Whitney L/-test 433 I Tables of significant values for the F-distribution 436 J Table of significant values of f when making multiple f-tests 439 K Some other statistics in SPSS Statistics 443 Glossary 445 References 453 Index 454 V. J