DISCOVERING STATISTICS USING SPSS T H I R D E D I T I O N

Transcription

1 DISCOVERING STATISTICS USING SPSS T H I R D E D I T I O N (and sex and drugs and rock 'n' ro ANDY FIELD DSAGE Los Angeles London New Delhi Singapore Washington DC

2 CONTENTS Preface How to use this book Acknowledgements Dedication Symbols used in this book Some maths revision XIX xxiv xxviii xxx xxxi xxxiii Why is my evil lecturer forcing me to learn statistics? 1.1. What will this chapter tell me? 1.2. What the hell am I doing here? I don't belong here The research process 1.3. Initial observation: finding something that needs explaining 1.4. Generating theories and testing them 1.5. Data collection 1: what to measure Variables Measurement error Validity and reliability 1.6. Data collection 2: how to measure Correlational research methods Experimental research methods Randomization 1.7. Analysing data Frequency distributions The centre of a distribution The dispersion in a distribution Using a frequency distribution to go beyond the data Fitting statistical models to the data What have I discovered about statistics? Key terms that I've discovered Smart Alex's stats quiz Further reading Interesting real research

3 VI DISCOVERING STATISTICS USING SPSS 2 Everything you ever wanted to know about statistics (well, sort of) What will this chapter tell me? Building statistical models Populations and samples Simple statistical models The mean: a very simple statistical model Assessing the fit of the mean: sums of squares, variance and standard deviations Expressing the mean as a model Going beyond the data The standard error Confidence intervals Using statistical models to test research questions Test statistics One-and two-tailed tests Type I and Type II errors Effect sizes Statistical power 58 What have I discovered about statistics? 59 Key terms that I've discovered 59 Smart Alex's stats quiz 59 Further reading 60 Interesting real research 60 3 The SPSS environment What will this chapter tell me? Versions of SPSS Getting started The data editor Entering data into the data editor The 'Variable View' Missing values The SPSS viewer The SPSS SmartViewer The syntax window Saving files Retrieving a file 84 What have I discovered about statistics? 85 Key terms that I've discovered 85 Smart Alex's tasks 85 Further reading 86 Online tutorials 86 4 Exploring data with graphs What will this chapter tell me? The art of presenting data What makes a good graph? Lies, damned lies, and... erm... graphs 90

4 CONTENTS 4.3. The SPSS Chart Builder 4.4. Histograms: a good way to spot obvious problems 4.5. Boxplots (box-whisker diagrams) 4.6. Graphing means: bar charts and error bars Simple bar charts for independent means Clustered bar charts for independent means Simple bar charts for related means Clustered bar charts for related means Clustered bar charts for 'mixed' designs Line charts 4.8. Graphing relationships: the scatterplot Simple scatterplot Grouped scatterplot Simple and grouped 3-D scatterplots Matrix scatterplot Simple dot plot or density plot Drop-line graph 4.9. Editing graphs What have I discovered about statistics? Key terms that I've discovered Smart Alex's tasks Further reading Online tutorial Interesting real research Exploring assumptions 5.1. What will this chapter tell me? 5.2. What are assumptions? 5.3. Assumptions of parametric data 5.4. The assumption of normality Oh no, it's that pesky frequency distribution again: checking normality visually Quantifying normality with numbers Exploring groups of data 5.5. Testing whether a distribution is normal Doing the Kolmogorov-Smirnov test on SPSS Output from the explore procedure Reporting the K-S test 5.6. Testing for homogeneity of variance Levene's test Reporting Levene's test 5.7. Correcting problems in the data Dealing with outliers Dealing with non-normality and unequal variances Transforming the data using SPSS When it all goes horribly wrong What have I discovered about statistics? Key terms that I've discovered Smart Alex's tasks Online tutorial Further reading

5 DISCOVERING STATISTICS USING SPSS 6 Correlation What will this chapter tell me? Looking at relationships How do we measure relationships? A detour into the murky world of covariance Standardization and the correlation coefficient The significance of the correlation coefficient Confidence intervals for r A word of warning about interpretation: causality Data entry for correlation analysis using SPSS Bivariate correlation General procedure for running correlations on SPSS Pearson's correlation coefficient Spearman's correlation coefficient Kendall's tau (non-parametric) Biserial and point-biserial correlations Partial correlation The theory behind part and partial correlation Partial correlation using SPSS Semi-partial (or part) correlations Comparing correlations Comparing independent re Comparing dependent re Calculating the effect size How to report correlation coefficents 193 What have I discovered about statistics? 195 Key terms that I've discovered 195 Smart Alex's tasks 195 Further reading 196 Online tutorial 196 Interesting real research Regression What will this chapter tell me? An introduction to regression Some important information about straight lines The method of least squares Assessing the goodness of fit: sums of squares, R and Я Assessing individual predictors Doing simple regression on SPSS Interpreting a simple regression Overall fit of the model Model parameters Using the model Multiple regression: the basics An example of a multiple regression model Sums of squares, R and R Methods of regression How accurate is my regression model? 214

6 CONTENTS Assessing the regression model I: diagnostics Assessing the regression model II: generalization How to do multiple regression using SPSS Some things to think about before the analysis Main options Statistics Regression plots Saving regression diagnostics Further options Interpreting multiple regression Descriptives Summary of model Model parameters Excluded variables Assessing the assumption of no multicollinearity Casewise diagnostics Checking assumptions What if I violate an assumption? How to report multiple regression Categorical predictors and multiple regression Dummy coding SPSS output for dummy variables 256 What have I discovered about statistics? 261 Key terms that I've discovered 261 Smart Alex's tasks 262 Further reading 263 Online tutorial 263 Interesting real research Logistic regression What will this chapter tell me? Background to logistic regression What are the principles behind logistic regression? Assessing the model: the log-likelihood statistic Assessing the model: R and R Assessing the contribution of predictors: the Wald statistic The odds ratio: Exp(B) Methods of logistic regression Assumptions and things that can go wrong Assumptions Incomplete information from the Complete Overdispersion Binary logistic regression: an example that will make you feel eel The main analysis Method of regression Categorical predictors Obtaining residuals Further options Interpreting logistic regression 282

7 DISCOVERING STATISTICS USING SPSS The initial model Step 1: intervention Listing predicted probabilities Interpreting residuals Calculating the effect size How to report logistic regression Testing assumptions: another example Testing for linearity of the logit Testing for multicollinearity Predicting several categories: multinomial logistic regression Running multinomial logistic regression in SPSS Statistics Other options Interpreting the multinomial logistic regression output Reporting the results 312 What have I discovered about statistics? 313 Key terms that I've discovered 313 Smart Alex's tasks 313 Further reading 315 Online tutorial 315 Interesting real research Comparing two means What will this chapter tell me? Looking at differences A problem with error bar graphs of repeated-measures designs Step 1: calculate the mean for each participant Step 2: calculate the grand mean Step 3: calculate the adjustment factor Step 4: create adjusted values for each variable The f-test Rationale for the f-test Assumptions of the f-test The dependent f-test Sampling distributions and the standard error The dependent f-test equation explained The dependent f-test and the assumption of normality Dependent f-tests using SPSS Output from the dependent f-test Calculating the effect size Reporting the dependent f-test The independent f-test The independent f-test equation explained The independent f-test using SPSS Output from the independent f-test Calculating the effect size Reporting the independent f-test Between groups or repeated measures? The f-test as a general linear model What if my data are not normally distributed? 344

8 CONTENTS What have I discovered about statistics? 345 Key terms that I've discovered 345 Smart Alex's task 346 Further reading 346 Online tutorial 346 Interesting real research Comparing several means: ANOVA (GLM 1) What will this chapter tell me? The theory behind ANOVA Inflated error rates Interpreting F ANOVA as regression Logic of the F-ratio Total sum of squares (SS T ) Model sum of squares (SS M ) Residual sum of squares (SS R ) Mean squares The F-ratio Assumptions of ANOVA Planned contrasts Posf hoc procedures 372 Running one-way ANOVA on SPSS Planned comparisons using SPSS Posf hoc tests in SPSS Options Output from one-way ANOVA Output for the main analysis Output for planned comparisons Output for post hoc tests Calculating the effect size Reporting results from one-way independent ANOVA Violations of assumptions in one-way independent ANOVA 391 What have I discovered about statistics? 392 Key terms that I've discovered 392 Smart Alex's tasks 393 Further reading 394 Online tutorials 394 Interesting real research Analysis of covariance, ANC0VA (GLM 2) What will this chapter tell me? What is ANCOVA? Assumptions and issues in ANCOVA Independence of the covariate and treatment effect Homogeneity of regression slopes Conducting ANCOVA on SPSS Inputting data Initial considerations: testing the independence of the independent variable and covariate 400

9 DISCOVERING STATISTICS USING SPSS The main analysis Contrasts and other options Interpreting the output from ANCOVA What happens when the covariate is excluded? The main analysis Contrasts Interpreting the covariate ANCOVA run as a multiple regression Testing the assumption of homogeneity of regression slopes Calculating the effect size Reporting results What to do when assumptions are violated in ANCOVA 418 What have I discovered about statistics? 418 Key terms that I've discovered 419 Smart Alex's tasks 419 Further reading 420 Online tutorials 420 Interesting real research Factorial ANOVA (GLM 3) What will this chapter tell me? Theory of factorial ANOVA (between-groups) Factorial designs An example with two independent variables Total sums of sguares (SS T ) The model sum of squares (SSJ The residual sum of squares (SS R ) The F-ratios Factorial ANOVA using SPSS Entering the data and accessing the main dialog box Graphing interactions Contrasts Post hoc tests Options Output from factorial ANOVA Output for the preliminary analysis Levene's test The main ANOVA table Contrasts Simple effects analysis Post hoc analysis Interpreting interaction graphs Calculating effect sizes Reporting the results of two-way ANOVA Factorial ANOVA as regression What to do when assumptions are violated in factorial ANOVA 454 What have I discovered about statistics? 454 Key terms that I've discovered 455 Smart Alex's tasks 455

10 CONTENTS Further reading 456 Online tutorials 456 Interesting real research Repeated-measures designs (GLM 4) What will this chapter tell me? Introduction to repeated-measures designs The assumption of sphericity How is sphericity measured? Assessing the severity of departures from sphericity What is the effect of violating the assumption of sphericity? What do you do if you violate sphericity? Theory of one-way repeated-measures ANOVA The total sum of squares (SS T ) The within-participant (SSJ The model sum of squares (SS M ) The residual sum of squares (SS R ) The mean squares The F-ratio The between-participant sum of squares One-way repeated-measures ANOVA using SPSS The main analysis Defining contrasts for repeated-measures Post hoc tests and additional options Output for one-way repeated-measures ANOVA Descriptives and other diagnostics Assessing and correcting for sphericity: Mauchly's test The main ANOVA Contrasts Post hoc tests Effect sizes for repeated-measures ANOVA Reporting one-way repeated-measures ANOVA Repeated-measures with several independent variables The main analysis Contrasts Simple effects analysis Graphing interactions Other options Output for factorial repeated-measures ANOVA Descriptives and main analysis The effect of drink The effect of imagery The interaction effect (drink x imagery) Contrasts for repeated-measures variables Effect sizes for factorial repeated-measures ANOVA Reporting the results from factorial repeated-measures ANOVA What to do when assumptions are violated in repeated-measures ANOVA 503 What have I discovered about statistics? 503 Key terms that I've discovered 504

11 DISCOVERING STATISTICS USING SPSS Smart Alex's tasks 504 Further reading 505 Online tutorials 505 Interesting real research Mixed design ANOVA (GLM 5) What will this chapter tell me? Mixed designs What do men and women look for in a partner? Mixed ANOVA on SPSS The main analysis Other options Output for mixed factorial ANOVA: main analysis The main effect of gender The main effect of looks The main effect of charisma The interaction between gender and looks The interaction between gender and charisma The interaction between attractiveness and charisma The interaction between looks, charisma and gender Conclusions Calculating effect sizes Reporting the results of mixed ANOVA What to do when assumptions are violated in mixed ANOVA 536 What have I discovered about statistics? 536 Key terms that I've discovered 537 Smart Alex's tasks 537 Further reading 538 Online tutorials 538 Interesting real research Non-parametric tests What will this chapter tell me? When to use non-parametric tests Comparing two independent conditions: the Wilcoxon rank-sum test and Mann-Whitney test Theory Inputting data and provisional analysis Running the analysis Output from the Mann-Whitney test Calculating an effect size Writing the results Comparing two related conditions: the Wilcoxon signed-rank test Theory of the Wilcoxon signed-rank test Running the analysis Output for the ecstasy group Output for the alcohol group Calculating an effect size Writing the results 558

12 CONTENTS Differences between several independent groups: the Kruskal-Wallis test Theory of the Kruskal-Wallis test Inputting data and provisional analysis Doing the Kruskal-Wallis test on SPSS Output from the Kruskal-Wallis test Posf hoc tests for the Kruskal-Wallis test Testing for trends: the Jonckheere-Terpstra test Calculating an effect size Writing and interpreting the results Differences between several related groups: Friedman's ANOVA Theory of Friedman's ANOVA Inputting data and provisional analysis Doing Friedman's ANOVA on SPSS Output from Friedman's ANOVA Posf hoc tests for Friedman's ANOVA Calculating an effect size Writing and interpreting the results 580 What have I discovered about statistics? 581 Key terms that I've discovered 582 Smart Alex's tasks 582 Further reading 583 Online tutorial 583 Interesting real research Multivariate analysis of variance (MANOVA) What will this chapter tell me? When to use MANOVA Introduction: similarities and differences to ANOVA Words of warning The example for this chapter Theory of MANOVA Introduction to matrices Some important matrices and their functions Calculating MANOVA by hand: a worked example Principle of the MANOVA test statistic Practical issues when conducting MANOVA Assumptions and how to check them Choosing a test statistic Follow-up analysis MANOVA on SPSS The main analysis Multiple comparisons in MANOVA Additional options Output from MANOVA Preliminary analysis and testing assumptions MANOVA test statistics Univariate test statistics SSCP Matrices Contrasts 613

13 DISCOVERING STATISTICS USING SPSS Reporting results from MANOVA Following up MANOVA with discriminant analysis Output from the discriminant analysis Reporting results from discriminant analysis Some final remarks The final interpretation Univariate ANOVA or discriminant analysis? What to do when assumptions are violated in MANOVA 624 What have I discovered about statistics? 624 Key terms that I've discovered 625 Smart Alex's tasks 625 Further reading 626 Online tutorials 626 Interesting real research Exploratory factor analysis What will this chapter tell me? When to use factor analysis Factors Graphical representation of factors Mathematical representation of factors Factor scores Discovering factors Choosing a method Communality Factor analysis vs. principal component analysis Theory behind principal component analysis Factor extraction: eigenvalues and the scree plot Improving interpretation: factor rotation Research example Before you begin Running the analysis Factor extraction on SPSS Rotation Scores Options Interpreting output from SPSS Preliminary analysis Factor extraction Factor rotation Factor scores Summary How to report factor analysis Reliability analysis Measures of reliability Interpreting Cronbach's a (some cautionary tales...) Reliability analysis on SPSS Interpreting the output How to report reliability analysis 681

14 CONTENTS What have I discovered about statistics? 682 Key terms that I've discovered 682 Smart Alex's tasks 683 Further reading 685 Online tutorial 685 Interesting real research Categorical data What will this chapter tell me? Analysing categorical data Theory of analysing categorical data Pearson's chi-square test Fisher's exact test The likelihood ratio Yates'correction Assumptions of the chi-square test Doing chi-square on SPSS Entering data: raw scores Entering data: weight cases Running the analysis Output for the chi-square test Breaking down a significant chi-square test with standardized residuals Calculating an effect size Reporting the results of chi-square Several categorical variables: loglinear analysis Chi-square as Loglinear analysis Assumptions in loglinear analysis Loglinear analysis using SPSS Initial considerations The loglinear analysis Output from loglinear analysis Following up loglinear analysis Effect sizes in loglinear analysis Reporting the results of loglinear analysis 721 What have I discovered about statistics? 722 Key terms that I've discovered 722 Smart Alex's tasks 722 Further reading 724 Online tutorial 724 Interesting real research Multilevel linear models What will this chapter tell me? Hierarchical data The intraclass correlation Benefits of multilevel models Theory of multilevel linear models 730

15 XVIII DISCOVERING STATISTICS USING SPSS An example Fixed and random coefficients The multilevel model Assessing the fit and comparing multilevel Types of covariance structures Some practical issues Assumptions Sample size and power Centring variables Multilevel modelling on SPSS Entering the data Ignoring the data structure: ANOVA Ignoring the data structure: ANCOVA Factoring in the data structure: random intercepts Factoring in the data structure: random intercepts and slopes Adding an interaction to the model Growth models Growth curves (polynomials) An example: the honeymoon period Restructuring the data Running a growth model on SPSS Further analysis How to report a multilevel model What have I discovered about statistics? Key terms that I've discovered Smart Alex's tasks Further reading Online tutorial Interesting real research Epilogue Glossary Appendix А.1. A.2. A.3. A.4. Table of the standard normal distribution Critical values of the ^-distribution Critical values of the F-distribution Critical values of the chi-square distribution References Index