Discovering statistics using IBM SPSS statistics

Title
Copyright
Contents
Preface
How to use this book
Acknowledgements
Dedication
Symbols used in this book
Some maths revision
1 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
		1.2.1. The research process
	1.3. Initial observation: finding something that needs explaining
	1.4. Generating theories and testing them
	1.5. Collect data to test your theory
		1.5.1. Variables
		1.5.2. Measurement error
		1.5.3. Validity and reliability
		1.5.4. Correlational research methods
		1.5.5. Experimental research methods
		1.5.6. Randomization
	1.6. Analysing data
		1.6.1. Frequency distributions
		1.6.2. The centre of a distribution
		1.6.3. The dispersion in a distribution
		1.6.4. Using a frequency distribution to go beyond the data
		1.6.5. Fitting statistical models to the data
	1.7. Reporting data
		1.7.1. Dissemination of research
		1.7.2. Knowing how to report data
		1.7.3. Some initial guiding principles
	1.8. Brian’s attempt to woo Jane
	1.9. What next?
	1.10. Key terms that I’ve discovered
	1.11. Smart Alex’s tasks
	1.12. Further reading
2 Everything you never wanted to know about statistics
	2.1. What will this chapter tell me?
	2.2. Building statistical models
	2.3. Populations and samples
	2.4. Statistical models
		2.4.1. The mean as a statistical model
		2.4.2. Assessing the fit of a model: sums of squares and variance revisited
		2.4.3. Estimating parameters
	2.5. Going beyond the data
		2.5.1. The standard error
		2.5.2. Confidence intervals
	2.6. Using statistical models to test research questions
		2.6.1. Null hypothesis significance testing
		2.6.2. Problems with NHST
	2.7. Modern approaches to theory testing
		2.7.1. Effect sizes
		2.7.2. Meta-analysis
	2.8. Reporting statistical models
	2.9. Brian’s attempt to woo Jane
	2.10. What next?
	2.11. Key terms that I’ve discovered
	2.12. Smart Alex’s tasks
	2.13. Further reading
3 The IBM SPSS Statistics environment
	3.1. What will this chapter tell me?
	3.2. Versions of IBM SPSS Statistics
	3.3. Windows versus MacOS
	3.4. Getting started
	3.5. The data editor
		3.5.1. Entering data into the data editor
		3.5.2. The variable view
		3.5.3. Missing values
	3.6. Importing data
	3.7. The SPSS viewer
	3.8. Exporting SPSS output
	3.9. The syntax editor
	3.10. Saving files
	3.11. Retrieving a file
	3.12. Brian’s attempt to woo Jane
	3.13. What next?
	3.14. Key terms that I’ve discovered
	3.15. Smart Alex’s tasks
	3.16. Further reading
4 Exploring data with graphs
	4.1. What will this chapter tell me?
	4.2. The art of presenting data
		4.2.1. What makes a good graph?
		4.2.2. Lies, damned lies, and … erm … graphs
	4.3. The SPSS chart builder
	4.4. Histograms
	4.5. Boxplots (box–whisker diagrams)
	4.6. Graphing means: bar charts and error bars
		4.6.1. Simple bar charts for independent means
		4.6.2. Clustered bar charts for independent means
		4.6.3. Simple bar charts for related means
		4.6.4. Clustered bar charts for related means
		4.6.5. Clustered bar charts for ‘mixed’ designs
	4.7. Line charts
	4.8. Graphing relationships: the scatterplot
		4.8.1. Simple scatterplot
		4.8.2. Grouped scatterplot
		4.8.3. Simple and grouped 3-D scatterplots
		4.8.4. Matrix scatterplot
		4.8.5. Simple dot plot or density plot
		4.8.6. Drop-line graph
	4.9. Editing graphs
	4.10. Brian’s attempt to woo Jane
	4.11. What next?
	4.12. Key terms that I’ve discovered
	4.13. Smart Alex’s tasks
	4.14. Further reading
5 The beast of bias
	5.1. What will this chapter tell me?
	5.2. What is bias?
		5.2.1. Assumptions
		5.2.2. Outliers
		5.2.3. Additivity and linearity
		5.2.4. Normally distributed something or other
		5.2.5. Homoscedasticity/homogeneity of variance
		5.2.6. Independence
	5.3 Spotting bias
		5.3.1. Spotting outliers
		5.3.2. Spotting normality
		5.3.3. Spotting linearity and heteroscedasticity/heterogeneity of variance
	5.4. Reducing bias
		5.4.1. Trimming the data
		5.4.2. Winsorizing
		5.4.3. Robust methods
		5.4.4. Transforming data
	5.5. Brian’s attempt to woo Jane
	5.6. What next?
	5.7. Key terms that I’ve discovered
	5.8. Smart Alex’s tasks
	5.9. Further reading
6 Non-parametric models
	6.1. What will this chapter tell me?
	6.2. When to use non-parametric tests
	6.3. General procedure of non-parametric tests in SPSS
	6.4. Comparing two independent conditions: the Wilcoxon rank-sum test and Mann–Whitney test
		6.4.1. Theory
		6.4.2. Inputting data and provisional analysis
		6.4.3. The Mann–Whitney test using SPSS
		6.4.4. Output from the Mann–Whitney test
		6.4.5. Calculating an effect size
		6.4.6. Writing the results
	6.5. Comparing two related conditions: the Wilcoxon signed-rank test
		6.5.1. Theory of the Wilcoxon signed-rank test
		6.5.2. Running the analysis
		6.5.3. Output for the ecstasy group
		6.5.4. Output for the alcohol group
		6.5.5. Calculating an effect size
		6.5.6. Writing the results
	6.6. Differences between several independent groups: the Kruskal–Wallis test
		6.6.1. Theory of the Kruskal–Wallis test
		6.6.2. Follow-up analysis
		6.6.3. Inputting data and provisional analysis
		6.6.4. Doing the Kruskal–Wallis test in SPSS
		6.6.5. Output from the Kruskal–Wallis test
		6.6.6. Testing for trends: the Jonckheere–Terpstra test
		6.6.7. Calculating an effect size
		6.6.8. Writing and interpreting the results
	6.7. Differences between several related groups: Friedman’s ANOVA
		6.7.1. Theory of Friedman’s ANOVA
		6.7.2. Inputting data and provisional analysis
		6.7.3. Doing Friedman’s ANOVA in SPSS
		6.7.4. Output from Friedman’s ANOVA
		6.7.5. Following-up Friedman’s ANOVA
		6.7.6. Calculating an effect size
		6.7.7. Writing and interpreting the results
	6.8. Brian’s attempt to woo Jane
	6.9. What next?
	6.10. Key terms that I’ve discovered
	6.11. Smart Alex’s tasks
	6.12. Further reading
7 Correlation
	7.1. What will this chapter tell me?
	7.2. Modelling relationships
		7.2.1. A detour into the murky world of covariance
		7.2.2. Standardization and the correlation coefficient
		7.2.3. The significance of the correlation coefficient
		7.2.4. Confidence intervals for r
		7.2.5. A word of warning about interpretation: causality
	7.3. Data entry for correlation analysis using SPSS
	7.4. Bivariate correlation
		7.4.1. General procedure for running correlations in SPSS
		7.4.2. Pearson’s correlation coefficient
		7.4.3. Spearman’s correlation coefficient
		7.4.4. Kendall’s tau (non-parametric)
		7.4.5. Biserial and point-biserial correlations
	7.5. Partial correlation
		7.5.1. The theory behind part and partial correlation
		7.5.2. Partial correlation in SPSS
		7.5.3. Semi-partial (or part) correlations
	7.6. Comparing correlations
		7.6.1. Comparing independent rs
		7.6.2. Comparing dependent rs
	7.7. Calculating the effect size
	7.8. How to report correlation coefficients
	7.9. Brian’s attempt to woo Jane
	7.10. What next?
	7.11. Key terms that I’ve discovered
	7.12. Smart Alex’s tasks
	7.13. Further reading
8 Regression
	8.1. What will this chapter tell me?
	8.2. An introduction to regression
		8.2.1. The simple linear model
		8.2.2. The linear model with several predictors
		8.2.3. Estimating the model
		8.2.4. Assessing the goodness of fit, sums of squares, R and R2
		8.2.5. Assessing individual predictors
	8.3. Bias in regression models?
		8.3.1. Is the model biased by unusual cases?
		8.3.2. Generalizing the model
		8.3.3. Sample size in regression
	8.4. Regression using SPSS: One Predictor
		8.4.1. Regression: the general procedure
		8.4.2. Running a simple regression using SPSS
		8.4.3. Interpreting a simple regression
		8.4.4. Using the model
	8.5. Multiple regression
		8.5.1. Methods of regression
		8.5.2. Comparing models
		8.5.3. Multicollinearity
	8.6. Regression with several predictors using SPSS
		8.6.1. Main options
		8.6.2. Statistics
		8.6.3. Regression plots
		8.6.4. Saving regression diagnostics
		8.6.5. Further options
		8.6.6. Robust regression
	8.7. Interpreting multiple regression
		8.7.1. Descriptives
		8.7.2. Summary of model
		8.7.3. Model parameters
		8.7.4. Excluded variables
		8.7.5. Assessing multicollinearity
		8.7.6. Bias in the model: casewise diagnostics
		8.7.7. Bias in the model: assumptions
	8.8. What if I violate an assumption? Robust regression
	8.9. How to report multiple regression
	8.10. Brian’s attempt to woo Jane
	8.11. What next?
	8.12. Key terms that I’ve discovered
	8.13. Smart Alex’s tasks
	8.14. Further reading
9 Comparing two means
	9.1. What will this chapter tell me?
	9.2. Looking at differences
		9.2.1. An example: are invisible people mischievous?
		9.2.2. Categorical predictors in the linear model
	9.3. The t-test
		9.3.1. Rationale for the t-test
		9.3.2. The independent t-test equation explained
		9.3.3. The paired-samples t-test equation explained
	9.4. Assumptions of the t-test
	9.5. The independent t-test using SPSS
		9.5.1. The general procedure
		9.5.2. Exploring data and testing assumptions
		9.5.3. Compute the independent t-test
		9.5.4. Output from the independent t-test
		9.5.5. Calculating the effect size
		9.5.6. Reporting the independent t-test
	9.6. Paired-samples t-test using SPSS
		9.6.1. Entering data
		9.6.2. Exploring data and testing assumptions
		9.6.3. Computing the paired-samples t-test
		9.6.4. Calculating the effect size
		9.6.5. Reporting the paired-samples t-test
	9.7. Between groups or repeated measures?
	9.8. What if I violate the test assumptions?
	9.9. Brian’s attempt to woo Jane
	9.10. What next?
	9.11. Key terms that I’ve discovered
	9.12. Smart Alex’s tasks
	9.13. Further reading
10 Moderation, mediation and more regression
	10.1. What will this chapter tell me?
	10.2. Installing custom dialog boxes in SPSS
	10.3. Moderation: interactions in regression
		10.3.1. The conceptual model
		10.3.2. The statistical model
		10.3.3. Centring variables
		10.3.4. Creating interaction variables
		10.3.5. Following up an interaction effect
		10.3.6. Running the analysis
		10.3.7. Output from moderation analysis
		10.3.8. Reporting moderation analysis
	10.4. Mediation
		10.4.1. The conceptual model
		10.4.2. The statistical model
		10.4.3. Effect sizes of mediation
		10.4.4. Running the analysis
		10.4.5. Output from mediation analysis
		10.4.6. Reporting mediation analysis
	10.5. Categorical predictors in regression
		10.5.1. Dummy coding
		10.5.2. SPSS output for dummy variables
	10.6. Brian’s attempt to woo Jane
	10.7. What next?
	10.8. Key terms that I’ve discovered
	10.9. Smart Alex’s tasks
	10.10. Further reading
11 Comparing several means: ANOVA (GLM 1)
	11.1. What will this chapter tell me?
	11.2. The theory behind ANOVA
		11.2.1. Using a linear model to compare means
		11.2.2. Logic of the F-ratio
		11.2.3. Total sum of squares (SST)
		11.2.4. Model sum of squares (SSM)
		11.2.5. Residual sum of squares (SSR)
		11.2.6. Mean squares
		11.2.7. The F-ratio
		11.2.8. Interpreting F
	11.3. Assumptions of ANOVA
		11.3.1. Homogeneity of variance
		11.3.2. Is ANOVA robust?
		11.3.3. What to do when assumptions are violated
	11.4. Planned contrasts
		11.4.1. Choosing which contrasts to do
		11.4.2. Defining contrasts using weights
		11.4.3. Non-orthogonal comparisons
		11.4.4. Standard contrasts
		11.4.5. Polynomial contrasts: trend analysis
	11.5. Post hoc procedures
		11.5.1. Type I and Type II error rates for post hoc tests
		11.5.2. Are post hoc procedures robust?
		11.5.3. Summary of post hoc procedures
	11.6. Running one-way ANOVA in SPSS
		11.6.1. General procedure of one-way ANOVA
		11.6.2. Planned comparisons using SPSS
		11.6.3. Post hoc tests in SPSS
		11.6.4. Options
		11.6.5. Bootstrapping
	11.7. Output from one-way ANOVA
		11.7.1. Output for the main analysis
		11.7.2. Output for planned comparisons
		11.7.3. Output for post hoc tests
	11.8. Calculating the effect size
	11.9. Reporting results from one-way independent ANOVA
	11.10. Key terms that I’ve discovered
	11.11. Brian’s attempt to woo Jane
	11.12. What next?
	11.13. Smart Alex’s tasks
	11.14. Further reading
12 Analysis of covariance, ANCOVA (GLM 2)
	12.1. What will this chapter tell me?
	12.2. What is ANCOVA?
	12.3. Assumptions and issues in ANCOVA
		12.3.1. Independence of the covariate and treatment effect
		12.3.2. Homogeneity of regression slopes
		12.3.3. What to do when assumptions are violated
	12.4. Conducting ANCOVA in SPSS
		12.4.1. General procedure
		12.4.2. Inputting data
		12.4.3. Testing the independence of the treatment variable and covariate
		12.4.4. The main analysis
		12.4.5. Contrasts
		12.4.6. Other options
		12.4.7. Bootstrapping and plots
	12.5. Interpreting the output from ANCOVA
		12.5.1. What happens when the covariate is excluded?
		12.5.2. The main analysis
		12.5.3. Contrasts
		12.5.4. Interpreting the covariate
	12.6. Testing the assumption of homogeneity of regression slopes
	12.7. Calculating the effect size
	12.8. Reporting results
	12.9. Brian’s attempt to woo Jane
	12.10. What next?
	12.11. Key terms that I’ve discovered
	12.12. Smart Alex’s tasks
	12.13. Further reading
13 Factorial ANOVA (GLM 3)
	13.1. What will this chapter tell me?
	13.2. Theory of factorial ANOVA (independent designs)
		13.2.1. Factorial designs
		13.2.2. Guess what? Factorial ANOVA is a linear model
		13.2.3. Two-way ANOVA: behind the scenes
		13.2.4. Total sums of squares (SST)
		13.2.5. Model sum of squares, SSM
		13.2.6. The residual sum of squares, SSR
		13.2.7. The F-ratios
	13.3. Assumptions of factorial ANOVA
	13.4. Factorial ANOVA using SPSS
		13.4.1. General procedure for factorial ANOVA
		13.4.2. Entering the data and accessing the main dialog box
		13.4.3. Graphing interactions
		13.4.4. Contrasts
		13.4.5. Post hoc tests
		13.4.6. Bootstrapping and other options
	13.5. Output from factorial ANOVA
		13.5.1. Levene’s test
		13.5.2. The main ANOVA table
		13.5.3. Contrasts
		13.5.4. Simple effects analysis
		13.5.5. Post hoc analysis
	13.6. Interpreting interaction graphs
	13.7. Calculating effect sizes
	13.8. Reporting the results of two-way ANOVA
	13.9. Brian’s attempt to woo Jane
	13.10. What next?
	13.11. Key terms that I’ve discovered
	13.12. Smart Alex’s tasks
	13.13. Further reading
14 Repeated-measures designs (GLM 4)
	14.1. What will this chapter tell me?
	14.2. Introduction to repeated-measures designs
		14.2.1. The assumption of sphericity
		14.2.2. How is sphericity measured?
		14.2.3. Assessing the severity of departures from sphericity
		14.2.4. What is the effect of violating the assumption of sphericity?
		14.2.5. What do you do if you violate sphericity?
	14.3. Theory of one-way repeated-measures ANOVA
		14.3.1. The total sum of squares, SST
		14.3.2. The within-participant sum of squares, SSW
		14.3.3. The model sum of squares, SSM
		14.3.4. The residual sum of squares, SSR
		14.3.5. The mean squares
		14.3.6. The F-ratio
		14.3.7. The between-participants sum of squares
	14.4. Assumptions in repeated-measures ANOVA
	14.5. One-way repeated-measures ANOVA using SPSS
		14.5.1. Repeated-measures ANOVA: the general procedure
		14.5.2. The main analysis
		14.5.3. Defining contrasts for repeated measures
		14.5.4. Post hoc tests and additional options
	14.6. Output for one-way repeated-measures ANOVA
		14.6.1. Descriptives and other diagnostics
		14.6.2. Assessing and correcting for sphericity: Mauchly’s test
		14.6.3. The main ANOVA
		14.6.4. Contrasts
		14.6.5. Post hoc tests
	14.7. Effect sizes for repeated-measures ANOVA
	14.8. Reporting one-way repeated-measures ANOVA
	14.9. Factorial repeated-measures designs
		14.9.1. The main analysis
		14.9.2. Contrasts
		14.9.3. Simple effects analysis
		14.9.4. Graphing interactions
		14.9.5. Other options
	14.10. Output for factorial repeated-measures ANOVA
		14.10.1. Descriptives and main analysis
		14.10.2. Contrasts for repeated-measures variables
	14.11. Effect sizes for factorial repeated-measures ANOVA
	14.12. Reporting the results from factorial repeated-measures ANOVA
	14.13. Brian’s attempt to woo Jane
	14.14. What next?
	14.15. Key terms that I’ve discovered
	14.16. Smart Alex’s tasks
	14.17. Further reading
15 Mixed design ANOVA (GLM 5)
	15.1 What will this chapter tell me?
	15.2. Mixed designs
	15.3. Assumptions in mixed designs
	15.4. What do men and women look for in a partner?
	15.5. Mixed ANOVA in SPSS
		15.5.1. Mixed ANOVA: the general procedure
		15.5.2. Entering data
		15.5.3. The main analysis
		15.5.4. Other options
	15.6. Output for mixed factorial ANOVA
		15.6.1. The main effect of gender
		15.6.2. The main effect of looks
		15.6.3. The main effect of charisma
		15.6.4. The interaction between gender and looks
		15.6.5. The interaction between gender and charisma
		15.6.6. The interaction between attractiveness and charisma
		15.6.7. The interaction between looks, charisma and gender
		15.6.8. Conclusions
	15.7. Calculating effect sizes
	15.8. Reporting the results of mixed ANOVA
	15.9. Brian’s attempt to woo Jane
	15.10. What next?
	15.11. Key terms that I’ve discovered
	15.12. Smart Alex’s tasks
	15.13. Further reading
16 Multivariate analysis of variance (MANOVA)
	16.1. What will this chapter tell me?
	16.2. When to use MANOVA
	16.3. Introduction
		16.3.1. Similarities to and differences from ANOVA
		16.3.2. Choosing outcomes
		16.3.3. The example for this chapter
	16.4. Theory of MANOVA
		16.4.1. Introduction to matrices
		16.4.2. Some important matrices and their functions
		16.4.3. Calculating MANOVA by hand: a worked example
		16.4.4. Principle of the MANOVA test statistic
	16.5. Practical issues when conducting MANOVA
		16.5.1. Assumptions and how to check them
		16.5.2. What to do when assumptions are violated
		16.5.3. Choosing a test statistic
		16.5.4. Follow-up analysis
	16.6. MANOVA using SPSS
		16.6.1. General procedure of one-way ANOVA
		16.6.2. The main analysis
		16.6.3. Multiple comparisons in MANOVA
		16.6.4. Additional options
	16.7. Output from MANOVA
		16.7.1. Preliminary analysis and testing assumptions
		16.7.2. MANOVA test statistics
		16.7.3. Univariate test statistics
		16.7.4. SSCP matrices
		16.7.5. Contrasts
	16.8. Reporting results from MANOVA
	16.9. Following up MANOVA with discriminant analysis
	16.10. Output from the discriminant analysis
	16.11. Reporting results from discriminant analysis
	16.12. The final interpretation
	16.13. Brian’s attempt to woo Jane
	16.14. What next?
	16.15. Key terms that I’ve discovered
	16.16. Smart Alex’s tasks
	16.17. Further reading
17 Exploratory factor analysis
	17.1. What will this chapter tell me?
	17.2. When to use factor analysis
	17.3. Factors and components
		17.3.1. Graphical representation
		17.3.2. Mathematical representation
		17.3.3. Factor scores
	17.4. Discovering factors
		17.4.1. Choosing a method
		17.4.2. Communality
		17.4.3. Factor analysis or PCA?
		17.4.4. Theory behind PCA
		17.4.5. Factor extraction: eigenvalues and the scree plot
		17.4.6. Improving interpretation: factor rotation
	17.5. Research example
		17.5.1. General procedure
		17.5.2. Before you begin
	17.6. Running the analysis
		17.6.1. Factor extraction in SPSS
		17.6.2. Rotation
		17.6.3. Scores
		17.6.4. Options
	17.7. Interpreting output from SPSS
		17.7.1. Preliminary analysis
		17.7.2. Factor extraction
		17.7.3. Factor rotation
		17.7.4. Factor scores
		17.7.5. Summary
	17.8. How to report factor analysis
	17.9. Reliability analysis
		17.9.1. Measures of reliability
		17.9.2. Interpreting Cronbach’s a (some cautionary tales)
		17.9.3. Reliability analysis in SPSS
		17.9.4. Reliability analysis output
	17.10. How to report reliability analysis
	17.11. Brian’s attempt to woo Jane
	17.12. What next?
	17.13. Key terms that I’ve discovered
	17.14. Smart Alex’s tasks
	17.15. Further reading
18 Categorical data
	18.1. What will this chapter tell me?
	18.2. Analysing categorical data
	18.3. Theory of analysing categorical data
		18.3.1. Pearson’s chi-square test
		18.3.2. Fisher’s exact test
		18.3.3. The likelihood ratio
		18.3.4. Yates’s correction
		18.3.5. Other measures of association
		18.3.6. Several categorical variables: loglinear analysis
	18.4. Assumptions when analysing categorical data
		18.4.1. Independence
		18.4.2. Expected frequencies
		18.4.3. More doom and gloom
	18.5. Doing chi-square in SPSS
		18.5.1. General procedure for analysing categorical outcomes
		18.5.2. Entering data
		18.5.3. Running the analysis
		18.5.4. Output for the chi-square test
		18.5.5. Breaking down a significant chi-square test with standardized residuals
		18.5.6. Calculating an effect size
		18.5.7. Reporting the results of chi-square
	18.6. Loglinear analysis using SPSS
		18.6.1. Initial considerations
		18.6.2. Running loglinear analysis
		18.6.3. Output from loglinear analysis
		18.6.4. Following up loglinear analysis
	18.7. Effect sizes in loglinear analysis
	18.8. Reporting the results of loglinear analysis
	18.9. Brian’s attempt to woo Jane
	18.10. What next?
	18.11. Key terms that I’ve discovered
	18.12. Smart Alex’s tasks
	18.13. Further reading
19 Logistic regression
	19.1. What will this chapter tell me?
	19.2. Background to logistic regression
	19.3. What are the principles behind logistic regression?
		19.3.1. Assessing the model: the log-likelihood statistic
		19.3.2. Assessing the model: the deviance statistic
		19.3.3. Assessing the model: R and R2
		19.3.4. Assessing the contribution of predictors: the Wald statistic
		19.3.5. The odds ratio: exp(B)
		19.3.6. Model building and parsimony
	19.4. Sources of bias and common problems
		19.4.1. Assumptions
		19.4.2. Incomplete information from the predictors
		19.4.3. Complete separation
		19.4.4. Overdispersion
	19.5. Binary logistic regression: an example that will make you feel eel
		19.5.1. Building a model
		19.5.2. Logistic regression: the general procedure
		19.5.3. Data entry
		19.5.4. Building the models in SPSS
		19.5.5. Method of regression
		19.5.6. Categorical predictors
		19.5.7. Comparing the models
		19.5.8. Rerunning the model
		19.5.9. Obtaining residuals
		19.5.10. Further options
		19.5.11. Bootstrapping
	19.6. Interpreting logistic regression
		19.6.1. Block 0
		19.6.2. Model summary
		19.6.3. Listing predicted probabilities
		19.6.4. Interpreting residuals
		19.6.5. Calculating the effect size
	19.7. How to report logistic regression
	19.8. Testing assumptions: another example
		19.8.1. Testing for linearity of the logit
		19.8.2. Testing for multicollinearity
	19.9. Predicting several categories: multinomial logistic regression
		19.9.1. Running multinomial logistic regression in SPSS
		19.9.2. Statistics
		19.9.3. Other options
		19.9.4. Interpreting the multinomial logistic regression output
		19.9.5. Reporting the results
	19.10. Brian’s attempt to woo Jane
	19.11. What next?
	19.12. Key terms that I’ve discovered
	19.13. Smart Alex’s tasks
	19.14. Further reading
20 Multilevel linear models
	20.1. What will this chapter tell me?
	20.2. Hierarchical data
		20.2.1. The intraclass correlation
		20.2.2. Benefits of multilevel models
	20.3 Theory of multilevel linear models
		20.3.1. An example
		20.3.2. Fixed and random coefficients
	20.4 The multilevel model
		20.4.1. Assessing the fit and comparing multilevel models
		20.4.2. Types of covariance structures
	20.5 Some practical issues
		20.5.1. Assumptions
		20.5.2. Robust multilevel models
		20.5.3. Sample size and power
		20.5.4. Centring predictors
	20.6 Multilevel modelling using SPSS
		20.6.1. Entering the data
		20.6.2. Ignoring the data structure: ANOVA
		20.6.3. Ignoring the data structure: ANCOVA
		20.6.4. Factoring in the data structure: random intercepts
		20.6.5. Factoring in the data structure: random intercepts and slopes
		20.6.6. Adding an interaction to the model
	20.7. Growth models
		20.7.1. Growth curves (polynomials)
		20.7.2. An example: the honeymoon period
		20.7.3. Restructuring the data
		20.7.4. Running a growth model on SPSS
		20.7.5. Further analysis
	20.8. How to report a multilevel model
	20.9. A message from the octopus of inescapable despair
	20.10. Brian’s attempt to woo Jane
	20.11. What next?
	20.12. Key terms that I’ve discovered
	20.13. Smart Alex’s tasks
	20.14. Further reading
21 Epilogue: life after discovering statistics
	21.1. Nice emails
	21.2. Everybody thinks that I’m a statistician
	21.3. Craziness on a grand scale
		21.3.1. Catistics
		21.3.2. Cult of underlying numerical truths
		21.3.3. And then it got really weird
Glossary
Appendix
References
Index