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2 Everything you never wanted to know about statistics
2.1. What will this chapter tell me? ①
2.2. Building statistical models ①
2.3. Populations and samples ①
2.4. Statistical models ①
2.4.1. The mean as a statistical model ①
2.4.2. Assessing the fit of a model: sums of squares and variance revisited ①
2.4.3. Estimating parameters ①
2.5. Going beyond the data ①
2.5.1. The standard error ①
2.5.2. Confidence intervals ②
2.6. Using statistical models to test research questions ①
2.6.1. Null hypothesis significance testing ①
2.6.2. Problems with NHST ②
2.7. Modern approaches to theory testing ②
2.7.1. Effect sizes ②
2.7.2. Meta-analysis ②
2.8. Reporting statistical models ②
2.9. Brian’s attempt to woo Jane ①
2.10. What next? ①
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? ①
3.2. Versions of IBM SPSS Statistics ①
3.3. Windows versus MacOS ①
3.4. Getting started ①
3.5. The data editor ①
3.5.1. Entering data into the data editor ①
3.5.2. The variable view ①
3.5.3. Missing values ①
3.6. Importing data ①
3.7. The SPSS viewer ①
3.8. Exporting SPSS output ①
3.9. The syntax editor ③
3.10. Saving files ①
3.11. Retrieving a file ①
3.12. Brian’s attempt to woo Jane ①
3.13. What next? ①
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? ①
 4.2. The art of presenting data ①
4.2.1. What makes a good graph? ①
4.2.2. Lies, damned lies, and … erm … graphs ①
4.3. The SPSS chart builder ①
4.4. Histograms ①
4.5. Boxplots (box–whisker diagrams) ①
4.6. Graphing means: bar charts and error bars ①
4.6.1. Simple bar charts for independent means ①
4.6.2. Clustered bar charts for independent means ①
4.6.3. Simple bar charts for related means ①
4.6.4. Clustered bar charts for related means ①
4.6.5. Clustered bar charts for ‘mixed’ designs ①
4.7. Line charts ①
4.8. Graphing relationships: the scatterplot ①
4.8.1. Simple scatterplot ①
4.8.2. Grouped scatterplot ①
4.8.3. Simple and grouped 3-D scatterplots ①
4.8.4. Matrix scatterplot ①
4.8.5. Simple dot plot or density plot ①
4.8.6. Drop-line graph ①
4.9. Editing graphs ①
4.10. Brian’s attempt to woo Jane ①
4.11. What next? ①
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? ①
5.2. What is bias? ①
5.2.1. Assumptions ①
5.2.2. Outliers ①
5.2.3. Additivity and linearity ①
5.2.4. Normally distributed something or other ①
5.2.5. Homoscedasticity/homogeneity of variance ②
5.2.6. Independence ②
5.3 Spotting bias ②
5.3.1. Spotting outliers ②
5.3.2. Spotting normality ①
5.3.3. Spotting linearity and heteroscedasticity/heterogeneity of variance ②
5.4. Reducing bias ②
5.4.1. Trimming the data ②
5.4.2. Winsorizing ①
5.4.3. Robust methods ③
5.4.4. Transforming data ②
5.5. Brian’s attempt to woo Jane ①
5.6. What next? ①
 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? ①
6.2. When to use non-parametric tests ①
6.3. General procedure of non-parametric tests in SPSS ①
6.4. Comparing two independent conditions: the Wilcoxon rank-sum test and Mann–Whitney test ①
6.4.1. Theory ②
6.4.2. Inputting data and provisional analysis ①
6.4.3. The Mann–Whitney test using SPSS ①
6.4.4. Output from the Mann–Whitney test ①
6.4.5. Calculating an effect size ②
6.4.6. Writing the results ①
6.5. Comparing two related conditions: the Wilcoxon signed-rank test ①
6.5.1. Theory of the Wilcoxon signed-rank test ②
6.5.2. Running the analysis ①
6.5.3. Output for the ecstasy group ①
6.5.4. Output for the alcohol group ①
6.5.5. Calculating an effect size ②
6.5.6. Writing the results ①
6.6. Differences between several independent groups: the Kruskal–Wallis test ①
6.6.1. Theory of the Kruskal–Wallis test ②
6.6.2. Follow-up analysis ②
6.6.3. Inputting data and provisional analysis ①
6.6.4. Doing the Kruskal–Wallis test in SPSS ①
6.6.5. Output from the Kruskal–Wallis test ①
6.6.6. Testing for trends: the Jonckheere–Terpstra test ②
6.6.7. Calculating an effect size ②
6.6.8. Writing and interpreting the results ①
6.7. Differences between several related groups: Friedman’s ANOVA ①
6.7.1. Theory of Friedman’s ANOVA ②
6.7.2. Inputting data and provisional analysis ①
6.7.3. Doing Friedman’s ANOVA in SPSS ①
6.7.4. Output from Friedman’s ANOVA ①
6.7.5. Following-up Friedman’s ANOVA ②
6.7.6. Calculating an effect size ②
6.7.7. Writing and interpreting the results ①
6.8. Brian’s attempt to woo Jane ①
6.9. What next? ①
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? ①
 7.2. Modelling relationships ①
7.2.1. A detour into the murky world of covariance ①
7.2.2. Standardization and the correlation coefficient ①
7.2.3. The significance of the correlation coefficient ③
7.2.4. Confidence intervals for r ③
7.2.5. A word of warning about interpretation: causality ①
7.3. Data entry for correlation analysis using SPSS ①
7.4. Bivariate correlation ①
7.4.1. General procedure for running correlations in SPSS ①
7.4.2. Pearson’s correlation coefficient ①
7.4.3. Spearman’s correlation coefficient ①
7.4.4. Kendall’s tau (non-parametric) ①
7.4.5. Biserial and point-biserial correlations ③
7.5. Partial correlation ②
7.5.1. The theory behind part and partial correlation ③
7.5.2. Partial correlation in SPSS ③
7.5.3. Semi-partial (or part) correlations ②
7.6. Comparing correlations ③
7.6.1. Comparing independent rs ③
7.6.2. Comparing dependent rs ③
7.7. Calculating the effect size ①
7.8. How to report correlation coefficients ①
7.9. Brian’s attempt to woo Jane ①
7.10. What next? ①
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? ①
8.2. An introduction to regression ①
8.2.1. The simple linear model ①
8.2.2. The linear model with several predictors ②
8.2.3. Estimating the model ②
8.2.4. Assessing the goodness of fit, sums of squares, R and R2 ①
8.2.5. Assessing individual predictors ①
8.3. Bias in regression models? ②
8.3.1. Is the model biased by unusual cases? ②
8.3.2. Generalizing the model ②
8.3.3. Sample size in regression ③
8.4. Regression using SPSS: One Predictor ①
8.4.1. Regression: the general procedure ①
8.4.2. Running a simple regression using SPSS ①
8.4.3. Interpreting a simple regression ①
8.4.4. Using the model ①
8.5. Multiple regression ②
8.5.1. Methods of regression ②
 8.5.2. Comparing models ②
8.5.3. Multicollinearity ②
8.6. Regression with several predictors using SPSS ②
8.6.1. Main options ②
8.6.2. Statistics ②
8.6.3. Regression plots ②
8.6.4. Saving regression diagnostics ②
8.6.5. Further options ②
8.6.6. Robust regression ②
8.7. Interpreting multiple regression ②
8.7.1. Descriptives ②
8.7.2. Summary of model ②
8.7.3. Model parameters ②
8.7.4. Excluded variables ②
8.7.5. Assessing multicollinearity ②
8.7.6. Bias in the model: casewise diagnostics ②
8.7.7. Bias in the model: assumptions ②
8.8. What if I violate an assumption? Robust regression ②
8.9. How to report multiple regression ②
8.10. Brian’s attempt to woo Jane ①
8.11. What next? ①
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? ①
9.2. Looking at differences ①
9.2.1. An example: are invisible people mischievous? ①
9.2.2. Categorical predictors in the linear model ①
9.3. The t-test ①
9.3.1. Rationale for the t-test ①
9.3.2. The independent t-test equation explained ①
9.3.3. The paired-samples t-test equation explained ①
9.4. Assumptions of the t-test ①
9.5. The independent t-test using SPSS ①
9.5.1. The general procedure ①
9.5.2. Exploring data and testing assumptions ①
9.5.3. Compute the independent t-test ①
9.5.4. Output from the independent t-test ①
9.5.5. Calculating the effect size ②
9.5.6. Reporting the independent t-test ①
9.6. Paired-samples t-test using SPSS ①
9.6.1. Entering data ①
9.6.2. Exploring data and testing assumptions ①
9.6.3. Computing the paired-samples t-test ①
9.6.4. Calculating the effect size ①
 9.6.5. Reporting the paired-samples t-test ①
9.7. Between groups or repeated measures? ①
9.8. What if I violate the test assumptions? ②
9.9. Brian’s attempt to woo Jane ①
9.10. What next? ①
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? ①
10.2. Installing custom dialog boxes in SPSS ②
10.3. Moderation: interactions in regression ③
10.3.1. The conceptual model ③
10.3.2. The statistical model ②
10.3.3. Centring variables ②
10.3.4. Creating interaction variables ②
10.3.5. Following up an interaction effect ②
10.3.6. Running the analysis ②
10.3.7. Output from moderation analysis ②
10.3.8. Reporting moderation analysis ②
10.4. Mediation ②
10.4.1. The conceptual model ②
10.4.2. The statistical model ②
10.4.3. Effect sizes of mediation ③
10.4.4. Running the analysis ②
10.4.5. Output from mediation analysis ②
10.4.6. Reporting mediation analysis ②
10.5. Categorical predictors in regression ③
10.5.1. Dummy coding ③
10.5.2. SPSS output for dummy variables ③
10.6. Brian’s attempt to woo Jane ①
10.7. What next? ①
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? ①
11.2. The theory behind ANOVA ②
11.2.1. Using a linear model to compare means ②
11.2.2. Logic of the F-ratio ②
11.2.3. Total sum of squares (SST) ②
11.2.4. Model sum of squares (SSM) ②
11.2.5. Residual sum of squares (SSR) ②
11.2.6. Mean squares ②
11.2.7. The F-ratio ②
 11.2.8. Interpreting F ②
11.3. Assumptions of ANOVA ③
11.3.1. Homogeneity of variance ②
11.3.2. Is ANOVA robust? ③
11.3.3. What to do when assumptions are violated ②
11.4. Planned contrasts ②
11.4.1. Choosing which contrasts to do ②
11.4.2. Defining contrasts using weights ②
11.4.3. Non-orthogonal comparisons ②
11.4.4. Standard contrasts ②
11.4.5. Polynomial contrasts: trend analysis ②
11.5. Post hoc procedures ②
11.5.1. Type I and Type II error rates for post hoc tests ②
11.5.2. Are post hoc procedures robust? ②
11.5.3. Summary of post hoc procedures ②
11.6. Running one-way ANOVA in SPSS ②
11.6.1. General procedure of one-way ANOVA ②
11.6.2. Planned comparisons using SPSS ②
11.6.3. Post hoc tests in SPSS ②
11.6.4. Options ②
11.6.5. Bootstrapping ②
11.7. Output from one-way ANOVA ②
11.7.1. Output for the main analysis ②
11.7.2. Output for planned comparisons ②
11.7.3. Output for post hoc tests ②
11.8. Calculating the effect size ②
11.9. Reporting results from one-way independent ANOVA ②
11.10. Key terms that I’ve discovered
11.11. Brian’s attempt to woo Jane ①
11.12. What next? ①
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? ②
12.2. What is ANCOVA? ②
12.3. Assumptions and issues in ANCOVA ③
12.3.1. Independence of the covariate and treatment effect ③
12.3.2. Homogeneity of regression slopes ③
12.3.3. What to do when assumptions are violated ②
12.4. Conducting ANCOVA in SPSS ②
12.4.1. General procedure ①
12.4.2. Inputting data ①
12.4.3. Testing the independence of the treatment variable and covariate ②
12.4.4. The main analysis ②
12.4.5. Contrasts
12.4.6. Other options ②
 12.4.7. Bootstrapping and plots ②
12.5. Interpreting the output from ANCOVA ②
12.5.1. What happens when the covariate is excluded? ②
12.5.2. The main analysis ②
12.5.3. Contrasts ②
12.5.4. Interpreting the covariate ②
12.6. Testing the assumption of homogeneity of regression slopes ③
12.7. Calculating the effect size ②
12.8. Reporting results ②
12.9. Brian’s attempt to woo Jane ①
12.10. What next? ②
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? ②
13.2. Theory of factorial ANOVA (independent designs) ②
13.2.1. Factorial designs ②
13.2.2. Guess what? Factorial ANOVA is a linear model ③
13.2.3. Two-way ANOVA: behind the scenes ②
13.2.4. Total sums of squares (SST)②
13.2.5. Model sum of squares, SSM②
13.2.6. The residual sum of squares, SSR②
13.2.7. The F-ratios ②
13.3. Assumptions of factorial ANOVA ③
13.4. Factorial ANOVA using SPSS ②
13.4.1. General procedure for factorial ANOVA ①
13.4.2. Entering the data and accessing the main dialog box ②
13.4.3. Graphing interactions ②
13.4.4. Contrasts ②
13.4.5. Post hoc tests ②
13.4.6. Bootstrapping and other options ②
13.5. Output from factorial ANOVA ②
13.5.1. Levene’s test ②
13.5.2. The main ANOVA table ②
13.5.3. Contrasts ②
13.5.4. Simple effects analysis ③
13.5.5. Post hoc analysis ②
13.6. Interpreting interaction graphs ②
13.7. Calculating effect sizes ③
13.8. Reporting the results of two-way ANOVA ②
13.9. Brian’s attempt to woo Jane ①
13.10. What next? ②
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? ②
14.2. Introduction to repeated-measures designs ②
14.2.1. The assumption of sphericity ②
14.2.2. How is sphericity measured? ②
14.2.3. Assessing the severity of departures from sphericity ②
14.2.4. What is the effect of violating the assumption of sphericity? ③
14.2.5. What do you do if you violate sphericity? ②
14.3. Theory of one-way repeated-measures ANOVA ②
14.3.1. The total sum of squares, SST②
14.3.2. The within-participant sum of squares, SSW②
14.3.3. The model sum of squares, SSM②
14.3.4. The residual sum of squares, SSR②
14.3.5. The mean squares ②
14.3.6. The F-ratio ②
14.3.7. The between-participants sum of squares ②
14.4. Assumptions in repeated-measures ANOVA ③
14.5. One-way repeated-measures ANOVA using SPSS ②
14.5.1. Repeated-measures ANOVA: the general procedure ②
14.5.2. The main analysis ②
14.5.3. Defining contrasts for repeated measures ②
14.5.4. Post hoc tests and additional options ③
14.6. Output for one-way repeated-measures ANOVA ②
14.6.1. Descriptives and other diagnostics ①
14.6.2. Assessing and correcting for sphericity: Mauchly’s test ②
14.6.3. The main ANOVA ②
14.6.4. Contrasts ②
14.6.5. Post hoc tests ②
14.7. Effect sizes for repeated-measures ANOVA ③
14.8. Reporting one-way repeated-measures ANOVA ②
14.9. Factorial repeated-measures designs ②
14.9.1. The main analysis ②
14.9.2. Contrasts ②
14.9.3. Simple effects analysis ③
14.9.4. Graphing interactions ②
14.9.5. Other options ②
14.10. Output for factorial repeated-measures ANOVA ②
14.10.1. Descriptives and main analysis ②
14.10.2. Contrasts for repeated-measures variables ②
14.11. Effect sizes for factorial repeated-measures ANOVA ③
14.12. Reporting the results from factorial repeated-measures ANOVA ②
14.13. Brian’s attempt to woo Jane ①
14.14. What next? ②
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? ①

15.2. Mixed designs ②
15.3. Assumptions in mixed designs ②
15.4. What do men and women look for in a partner? ②
15.5. Mixed ANOVA in SPSS ②
15.5.1. Mixed ANOVA: the general procedure ②
15.5.2. Entering data ②
15.5.3. The main analysis ②
15.5.4. Other options ②
15.6. Output for mixed factorial ANOVA ③
15.6.1. The main effect of gender ②
15.6.2. The main effect of looks ②
15.6.3. The main effect of charisma ②
15.6.4. The interaction between gender and looks ②
15.6.5. The interaction between gender and charisma ②
15.6.6. The interaction between attractiveness and charisma ②
15.6.7. The interaction between looks, charisma and gender ③
15.6.8. Conclusions ③
15.7. Calculating effect sizes ③
15.8. Reporting the results of mixed ANOVA ②
15.9. Brian’s attempt to woo Jane ①
15.10. What next? ②
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? ②
16.2. When to use MANOVA ②
16.3. Introduction
16.3.1. Similarities to and differences from ANOVA ②
16.3.2. Choosing outcomes ②
16.3.3. The example for this chapter ②
16.4. Theory of MANOVA ③
16.4.1. Introduction to matrices ③
16.4.2. Some important matrices and their functions ③
16.4.3. Calculating MANOVA by hand: a worked example ③
16.4.4. Principle of the MANOVA test statistic ④
16.5. Practical issues when conducting MANOVA ③
16.5.1. Assumptions and how to check them ③
16.5.2. What to do when assumptions are violated ③
16.5.3. Choosing a test statistic ③
 16.5.4. Follow-up analysis ③
16.6. MANOVA using SPSS ②
16.6.1. General procedure of one-way ANOVA ②
16.6.2. The main analysis ②
16.6.3. Multiple comparisons in MANOVA ②
16.6.4. Additional options ③
16.7. Output from MANOVA ③
16.7.1. Preliminary analysis and testing assumptions ③
16.7.2. MANOVA test statistics ③
16.7.3. Univariate test statistics ②
16.7.4. SSCP matrices ③
16.7.5. Contrasts ③
16.8. Reporting results from MANOVA ②
16.9. Following up MANOVA with discriminant analysis ③
16.10. Output from the discriminant analysis ④
16.11. Reporting results from discriminant analysis ②
16.12. The final interpretation ④
16.13. Brian’s attempt to woo Jane ①
16.14. What next? ②
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? ①
17.2. When to use factor analysis ②
17.3. Factors and components ②
17.3.1. Graphical representation ②
17.3.2. Mathematical representation ②
17.3.3. Factor scores ②
17.4. Discovering factors ②
17.4.1. Choosing a method ②
17.4.2. Communality ②
17.4.3. Factor analysis or PCA? ②
17.4.4. Theory behind PCA ③
17.4.5. Factor extraction: eigenvalues and the scree plot ②
17.4.6. Improving interpretation: factor rotation ③
17.5. Research example ②
17.5.1. General procedure ①
17.5.2. Before you begin ②
17.6. Running the analysis ②
17.6.1. Factor extraction in SPSS ②
17.6.2. Rotation ②
17.6.3. Scores ②
17.6.4. Options ②
17.7. Interpreting output from SPSS ②
17.7.1. Preliminary analysis ②
 17.7.2. Factor extraction ②
17.7.3. Factor rotation ②
17.7.4. Factor scores ②
17.7.5. Summary ②
17.8. How to report factor analysis ①
17.9. Reliability analysis ②
17.9.1. Measures of reliability ③
17.9.2. Interpreting Cronbach’s a (some cautionary tales) ②
17.9.3. Reliability analysis in SPSS ②
17.9.4. Reliability analysis output ②
17.10. How to report reliability analysis ②
17.11. Brian’s attempt to woo Jane ①
17.12. What next? ②
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? ①
18.2. Analysing categorical data ①
18.3. Theory of analysing categorical data ①
18.3.1. Pearson’s chi-square test ①
18.3.2. Fisher’s exact test ①
18.3.3. The likelihood ratio ②
18.3.4. Yates’s correction ②
18.3.5. Other measures of association ①
18.3.6. Several categorical variables: loglinear analysis ③
18.4. Assumptions when analysing categorical data ①
18.4.1. Independence ①
18.4.2. Expected frequencies ①
18.4.3. More doom and gloom ①
18.5. Doing chi-square in SPSS ①
18.5.1. General procedure for analysing categorical outcomes ①
18.5.2. Entering data ①
18.5.3. Running the analysis ①
18.5.4. Output for the chi-square test ①
18.5.5. Breaking down a significant chi-square test with standardized residuals ②
18.5.6. Calculating an effect size ②
18.5.7. Reporting the results of chi-square ①
18.6. Loglinear analysis using SPSS ②
18.6.1. Initial considerations ②
18.6.2. Running loglinear analysis ②
18.6.3. Output from loglinear analysis ③
18.6.4. Following up loglinear analysis ②
18.7. Effect sizes in loglinear analysis ②
18.8. Reporting the results of loglinear analysis ②
18.9. Brian’s attempt to woo Jane ①
 18.10. What next? ①
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? ①
19.2. Background to logistic regression ①
19.3. What are the principles behind logistic regression? ③
19.3.1. Assessing the model: the log-likelihood statistic ③
19.3.2. Assessing the model: the deviance statistic ③
19.3.3. Assessing the model: R and R2 ③
19.3.4. Assessing the contribution of predictors: the Wald statistic ②
19.3.5. The odds ratio: exp(B) ③
19.3.6. Model building and parsimony ②
19.4. Sources of bias and common problems ④
19.4.1. Assumptions ②
19.4.2. Incomplete information from the predictors ④
19.4.3. Complete separation ④
19.4.4. Overdispersion ④
19.5. Binary logistic regression: an example that will make you feel eel ②
19.5.1. Building a model ①
19.5.2. Logistic regression: the general procedure ①
19.5.3. Data entry ①
19.5.4. Building the models in SPSS ②
19.5.5. Method of regression ②
19.5.6. Categorical predictors ②
19.5.7. Comparing the models ②
19.5.8. Rerunning the model ①
19.5.9. Obtaining residuals ②
19.5.10. Further options ②
19.5.11. Bootstrapping ②
19.6. Interpreting logistic regression ②
19.6.1. Block 0 ②
19.6.2. Model summary ②
19.6.3. Listing predicted probabilities ②
19.6.4. Interpreting residuals ②
19.6.5. Calculating the effect size ②
19.7. How to report logistic regression ②
19.8. Testing assumptions: another example ②
19.8.1. Testing for linearity of the logit ③
19.8.2. Testing for multicollinearity ③
19.9. Predicting several categories: multinomial logistic regression ③
19.9.1. Running multinomial logistic regression in SPSS ③
19.9.2. Statistics ③
19.9.3. Other options ③
19.9.4. Interpreting the multinomial logistic regression output ③
 19.9.5. Reporting the results ②
19.10. Brian’s attempt to woo Jane ①
19.11. What next? ①
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? ①
20.2. Hierarchical data ②
20.2.1. The intraclass correlation ②
20.2.2. Benefits of multilevel models ②
20.3 Theory of multilevel linear models ③
20.3.1. An example ②
20.3.2. Fixed and random coefficients ③
20.4 The multilevel model ④
20.4.1. Assessing the fit and comparing multilevel models ④
20.4.2. Types of covariance structures ④
20.5 Some practical issues ③
20.5.1. Assumptions ③
20.5.2. Robust multilevel models ③
20.5.3. Sample size and power ③
20.5.4. Centring predictors ③
20.6 Multilevel modelling using SPSS ④
20.6.1. Entering the data ②
20.6.2. Ignoring the data structure: ANOVA ②
20.6.3. Ignoring the data structure: ANCOVA ②
20.6.4. Factoring in the data structure: random intercepts ③
20.6.5. Factoring in the data structure: random intercepts and slopes ④
20.6.6. Adding an interaction to the model ④
20.7. Growth models ④
20.7.1. Growth curves (polynomials) ④
20.7.2. An example: the honeymoon period ②
20.7.3. Restructuring the data ③
20.7.4. Running a growth model on SPSS ④
20.7.5. Further analysis ④
20.8. How to report a multilevel model ③
20.9. A message from the octopus of inescapable despair ①
20.10. Brian’s attempt to woo Jane ①
20.11. What next? ②
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
 PREFACE

Karma Police, arrest this man, he talks in maths, he buzzes like a fridge, he’s like a detuned radio

Radiohead, ‘Karma Police’, OK Computer (1997)

Introduction

Many behavioural and social science students (and researchers for that matter) despise statistics. Most
of us have a non-mathematical background, which makes understanding complex statistical equations
very difficult. Nevertheless, the evil goat-warriors of Satan force our non-mathematical brains to
apply themselves to what is the very complex task of becoming a statistics expert. The end result, as
you might expect, can be quite messy. The one weapon that we have is the computer, which allows us
to neatly circumvent the considerable disability of not understanding mathematics. Computer
programs such as IBM SPSS Statistics, SAS, R and the like provide an opportunity to teach statistics
at a conceptual level without getting too bogged down in equations. The computer to a goat-warrior of
Satan is like catnip to a cat: it makes them rub their heads along the ground and purr and dribble
ceaselessly. The only downside of the computer is that it makes it really easy to make a complete idiot
of yourself if you don’t really understand what you’re doing. Using a computer without any statistical
knowledge at all can be a dangerous thing. Hence this book.
My first aim is to strike a good balance between theory and practice: I want to use the computer as
a tool for teaching statistical concepts in the hope that you will gain a better understanding of both
theory and practice. If you want theory and you like equations then there are certainly better books:
Howell (2012), Stevens (2002) and Tabachnick and Fidell (2012) have taught (and continue to teach)
me more about statistics than you could possibly imagine. (I have an ambition to be cited in one of
these books, but I don’t think that will ever happen.) However, if you want a stats book that also
discusses digital rectal stimulation then you have just spent your money wisely.
Too many books create the impression that there is a ‘right’ and ‘wrong’ way to do statistics. Data
analysis is more subjective than is often made out. Therefore, although I make recommendations,
within the limits imposed by the senseless destruction of rainforests, I hope to give you enough
background in theory to enable you to make your own decisions about how best to conduct your
analysis.
A second (ridiculously ambitious) aim is to make this the only statistics book that you’ll ever need
to buy. It’s a book that I hope will become your friend from first year at university right through to
your professorship. The start of the book is aimed at first-year undergraduates (Chapters 1–9), and
then we move onto second-year undergraduate level material (Chapters 5, 8 and 10–15) before a
dramatic climax that should keep postgraduates tickled (Chapters 16–20). There should be something
for everyone in each chapter also, and to help you gauge the difficulty of material, I flag the level of
each section within each chapter (more on that in a moment).
My final and most important aim is to make the learning process fun. I have a sticky history with
maths. This extract is from my school report at the age of 11:
The ‘27’ in the report is to say that I came equal 27th with another student out of a class of 29. That’s
pretty much bottom of the class. The 43 is my exam mark as a percentage. Oh dear. Four years later
(at 15) this was my school report:

The catalyst of this remarkable change was having a good teacher: my brother, Paul. I owe my life as
an academic to Paul’s ability to teach me stuff in an engaging way – something my maths teachers
failed to do. Paul’s a great teacher because he cares about bringing out the best in people, and he was
able to make things interesting and relevant to me. He got the ‘good teaching’ genes in the family, but
wasted them by not becoming a teacher; however, they’re a little less wasted because his approach
inspires mine. I strongly believe that people appreciate the human touch, and so I try to inject a lot of
my own personality and sense of humour (or lack of) into Discovering Statistics Using … books.
Many of the examples in this book, although inspired by some of the craziness that you find in the real
world, are designed to reflect topics that play on the minds of the average student (i.e., sex, drugs,
rock and roll, celebrity, people doing crazy stuff). There are also some examples that are there simply
because they made me laugh. So, the examples are light-hearted (some have said ‘smutty’, but I prefer
‘light-hearted’) and by the end, for better or worse, I think you will have some idea of what goes on in
my head on a daily basis. I apologize to those who think it’s crass, hate it, or think that I’m
undermining the seriousness of science, but, come on, what’s not funny about a man putting an eel up
his anus?
I never believe that I meet my aims, but previous editions have certainly been popular. I enjoy the
rare luxury of having complete strangers emailing me to tell me how wonderful I am. (Admittedly,
there are also emails calling me a pile of gibbon excrement, but you have to take the rough with the
smooth.) The second edition of this book also won the British Psychological Society book award in
2007. However, with every new edition, I fear that the changes I make will ruin all of my previous
hard work. Let’s see what those changes are.

What do you get for your money?

This book takes you on a journey (and I try my best to make it a pleasant one) not just of statistics but
also of the weird and wonderful contents of the world and my brain. It’s full of daft, bad jokes, and
smut. Aside from the smut, I have been forced reluctantly to include some academic content. In
essence it contains everything I know about statistics (actually, more than I know …). It also has these
features:

Everything you’ll ever need to know: I want this book to be good value for money, so it guides
you from complete ignorance (Chapter 1 tells you the basics of doing research) to being an expert
on multilevel modelling (Chapter 20). Of course no book that it’s physically possible to lift will
contain everything, but I think this one has a fair crack. It’s pretty good for developing your
biceps also.
Stupid faces: You’ll notice that the book is riddled with stupid faces, some of them my own. You
can find out more about the pedagogic function of these ‘characters’ in the next section, but even
without any useful function they’re nice to look at.
Data sets: There are about 132 data files associated with this book on the companion website.
Not unusual in itself for a statistics book, but my data sets contain more sperm (not literally) than
other books. I’ll let you judge for yourself whether this is a good thing.
My life story: Each chapter is book-ended by a chronological story from my life. Does this help
you to learn about statistics? Probably not, but hopefully it provides some light relief between
chapters.
SPSS tips: SPSS does weird things sometimes. In each chapter, there are boxes containing tips,
hints and pitfalls related to SPSS.
Self-test questions: Given how much students hate tests, I thought the best way to commit
commercial suicide was to liberally scatter tests throughout each chapter. These range from
simple questions to test what you have just learned to going back to a technique that you read
about several chapters before and applying it in a new context. All of these questions have
answers to them on the companion website so that you can check on your progress.
Companion website: The companion website contains an absolutely insane amount of additional
material, all of which is described in the section about the companion website.
Digital stimulation: No, not the aforementioned type of digital stimulation, but brain
stimulation. Many of the features on the companion website will be accessible from tablets and
smartphones, so that when you’re bored in the cinema you can read about the fascinating world of
heteroscedasticity instead.
Reporting your analysis: Every chapter has a guide to writing up your analysis. How you write
up an analysis varies a bit from one discipline to another, but my guides should get you heading
in the right direction.
Glossary: Writing the glossary was so horribly painful that it made me stick a vacuum cleaner
into my ear to suck out my own brain. You can find my brain in the bottom of the vacuum cleaner
in my house.
Real-world data: Students like to have ‘real data’ to play with. The trouble is that real research
can be quite boring. However, just for you, I trawled the world for examples of research on really
fascinating topics (in my opinion). I then stalked the authors of the research until they gave me
their data. Every chapter has a real research example.

What do you get that you didn’t get last time?

I suppose if you have spent your hard-earned money on the previous edition it’s reasonable that you
want a good reason to spend more money on this edition. In some respects it’s hard to quantify all of
Another random document with
no related content on Scribd:
his feet, and striking wildly at his breast, his wings, and his scaly legs,
it

“... doth ever seek

Upon its enemy’s heart a mortal wound to wreak.”

Keeping his own head well back out of danger, the bird lets the
snake exhaust itself, waiting only till he can give a fatal blow with his
beak upon its upraised head, and then, soon despatching it, tears it to
pieces for a meal. Nor is even the dreaded Cobra safe from danger, for
he finds his match in the powerful Adjutant birds (see p. 128), and in
the Indian Ichneumon or Mungoos, which attacks the snake boldly,
skilfully dodging the fatal stroke until it has broken the neck of its
enemy; while in Africa the bold Secretary bird is complete master of
the dreaded poisonous snakes of that country. In fact, there is little
doubt that every kind of snake, either in youth or age, falls a victim to
some kind of bird or beast; and even the poisonous sea-snakes, which
swarm in the tropical seas, probably find their masters in the
pugnacious saw-fish and the thick-skinned shark.
 Fig. 31.

Common English viper (Pelias berus), with poison-

fangs showing in the open mouth, and the soft harmless
tongue outstretched to feel.

We see, then, that it is not without some struggle that these cold-
blooded reptiles have held their own in the world, nor is it to be
wondered at that only these four types—tortoises, lizards, crocodiles,
and snakes—should have managed to find room to live among the
myriads of warm-blooded animals which have filled the earth. These
four groups have made a good fight of it, and many of them even make
use of warm-blooded animals as food. The tortoises, it is true, feed
upon plants, except those that live in the fresh water, and feed chiefly
on fish, snakes, and frogs, while most of the lizards are insect-feeders.
But the crocodile, as he lurks near the river’s edge, and the snake,
when he fastens his glittering eye on a mouse or bird, are both on the
look-out for animals higher in the world than themselves.
 It is, perhaps, natural that we should shrink from cold-blooded
creatures, especially as they seem to show very little affection. Yet
lizards, tortoises, and snakes can all be made to know and care for
those who are kind to them; while, as we have seen, the fierce
crocodile watches over and feeds her young, and the python coils
herself over her eggs, and will take no food till they are hatched.
Moreover, we can scarcely look at the quaint shell-covered tortoise, or
examine the heavily-mailed coat of the alligator, or the poison-fangs of
the snake, without admiring the curious devices by which these
animals have managed to survive in a world which once belonged to
their ancestors, before our present swarm of warm-blooded animals
multiplied and took possession of their kingdom.
THE EARLIEST KNOWN WATERBIRDS
 CHAPTER VI.
THE FEATHERED CONQUERORS OF THE AIR.

Part I.—Their Wanderings over Sea and Marsh,

Desert and Plain.

It is a warm sunny day in early spring, one of those few bright days
which sometimes burst upon us in April, just after the swallows have
come back to us, searching out their old nooks under the eaves, or
their old corners in the chimneys, to build their new nests. There they
are, clinging with their sharp claws to the edge of the cottage thatch,
while the impudent little sparrow, which has remained hopping about
all the winter long, chirrups at them from a neighbouring apple-tree.
Upon the grass-plot near a blackbird is pecking at a worm, and from
the wood beyond a thrush trills out his clear and mellow song,
accompanied from time to time by the distant cry of the cuckoo calling
to his mate. For it is the love-time of the birds; and as we watch them
flying merrily hither and thither in the bright sunshine, we ask ourselves
whether we must not have made a great leap on leaving the cold-
blooded snakes and tortoises, since now we find ourselves among
such merry, warm-hearted, passionate little beings, with their beautiful
feathery plumage, their light rapid flight, their love for each other, their
skill in nest-building, and their patient care for their little ones.
And, indeed, we have come into quite a new life, for now we are
going to wander among the conquerors of the air, who have learned to
rise far beyond our solid ground, and to soar, like the lark, into the
clouds, or, like the eagle, to sail over the topmost crags of the
mountains, there to build his solitary eyrie.
Even the little sparrow, which flits about by the roadside, can laugh
at us with his impudent little chirp, as he flies up out of reach to the
topmost branch of a tree. And yet a glance at his skeleton will show us
that he has the same framework as a reptile, only it is altered to suit
his mode of life.

Fig. 32.

The Sparrow.
With wings raised, as in the skeleton on next page.

True, his breastbone (b, Fig. 33) is deep and thin instead of flat,
and those joints of his backbone which lie between his neck and tail
are soldered firmly together, more like those of the tortoise, and he
stands only upon two feet. Yet this last difference is merely apparent,
for if you look at the bones of his wings you will find that they are, bone
for bone, the same as those in the front legs of a lizard, only they have
been drawn backwards and upwards so as to work in the air.

Fig. 33.

Skeleton of a Sparrow (from a specimen).

q, Quadrate bone, peculiar to reptiles and birds and some

amphibia; b, breastbone; m, merrythought or collar bone; c,
coracoid bone, over which the tendon works to pull up the wing;
p, ploughshare bone, on which the tail grows.
Wing bones—a, upper arm; e, elbow; fa, fore arm; w, wrist; t,
thumb; ha, hand.
Leg bones—th, thigh bone; k, knee; l, lower part of leg; h,
heel; f, foot.
 There is the upper arm (a) answering to the same part of the
lizard’s front limb (p. 103); there is the elbow (e); then the two bones of
the fore-arm (fa); then the wrist (w), and a long hand (h), which has
lost almost all trace of separate fingers, except the little thumb (t),
which carries some feathers of its own, known as the “bastard” wing.
Now when the sparrow is resting he draws back his elbow, folds his
wrist joint, and brings the whole wing flat to his body. But when he
wishes to fly he stretches his arms out and beats the air with them, and
as his hand moves over most space, it is there that you will find the
longest quill feathers, which stretch right to the tip of his wing; then
next to these follow the feathers of his fore-arm, while those of the
upper arm are short and close to his body, and over all these are the
rows of covering feathers, which make the whole wing thick and
compact.
Here, then, we have the lizard’s front legs turned into a wonderful
flying machine in the bird, and this in quite a different way from the
flying lizards which lived long ago, and which had only a piece of
membrane to flit with, like bats. And now what has happened to the
hind legs, the only ones used as legs by the birds? Look at the
sparrow as he clasps the bough with his toes, and you will, perhaps,
be puzzled why the first joint of his leg turns back like an elbow and not
forward like a knee. Ah! but that joint is his ankle, and the knob behind
is his heel (h), for the bones of his foot have grown long and leg-like;
and he always stands upon his toes, the rest of his foot forming a firm
support to hold his body up in the air. Look at the skeleton and you will
find his true knee (k) up above; and if you go to the Zoological
Gardens and watch the Adjutant birds, you will often find them resting
their whole foot upon the ground (see Fig. 34), and comical as it looks,
it will help to explain the curious foot and leg of a bird.
 Fig. 34.

The Adjutant Bird.

Showing the foot resting from heel to toe upon the ground.

Already, then, we see that the bird is using the same bones as a
reptile, though he uses them in a different way; and besides these
resemblances between the skeletons of birds and reptiles there are
two special ones easy enough for us to understand. We saw in the
snakes and the lizards that they have a separate bone (9, Figs. 23 and
26) joining the lower jaw on to the head; now you will find this same
bone in the sparrow and in all birds (see Fig. 33), but in quadrupeds
this bone is not to be found, the part representing it being changed into
one of the bones of the ear. Again, the sparrow’s skull is joined to his
backbone by a single half-moon-shaped knob, which fits into a groove
in the first joint or vertebra. This also we find in reptiles, while all higher
animals have two such knobs, so that although they can nod the head
upon these, they cannot turn it upon them, and consequently the first
joint turns with the skull upon the second vertebra.
These, then, are some of the reasons why Professor Huxley tells
us that though frogs and reptiles look in many ways so like each other,
yet in truth the frogs must be grouped with the gill-breathing and fish-
88
like animals; while the cold-blooded reptiles, when we come to look
closely into them, are linked with such different looking creatures as
89
the bright and merry birds. But we have also another and stronger
reason for thinking that reptiles and birds are distant connections; for in
those far bygone times (see p. 92), when the huge land-lizards
browsed upon the trees, the birds living among them were much more
like them in many ways than they are now. From their skeletons and
90
feathers which we find, we know that the strange land birds which
then perched on the trees had not a fan-shaped tail made of feathers,
growing on one broad bone as our birds have now (p, Fig. 33), but
they had a long tail of many joints like lizards, only that each joint
carried a pair of feathers, and like lizards too they had teeth in their
jaws, which no living bird has. They must have been poor flyers at
best, these earliest known birds, for their wings were small and the
fingers of their hand were separate more like lizard’s toes, two of them
at least having claws upon them, while their long hanging tail must
have been very awkward compared to the fan-shaped tail they now
wear. For some time they were the only birds we know of, but later on
91
we come upon the bones of water-birds telling the same story. For
92
some about the size of small gulls, though they flew with strong
wings and had fan-shaped tails, still had teeth in their horny jaws, set
in sockets like those of the crocodile, while their backbones had joints
like those of fishes rather than birds; and with them were other and
93
wingless birds rather larger than our swans, but more like swimming
fish-eating ostriches, for their breastbones were flat, not thin and sharp
like the sparrow’s, and they had scarcely any wings, short tails, long
slender necks, and jaws full of teeth, this time set in grooves like those
of lizards and snakes.
In these and many other points the early birds came very near to
the reptiles—not to the flying ones, but to those which walked on the
land. And now, perhaps, you will ask, did reptiles then turn into birds?
No, since they were both living at the same time, and those reptiles
which flew did so like bats, and not in any way like the birds which
were their companions. To explain the facts we must go much farther
back than this. If any one were to ask us whether the Australian
colonists came from the white Americans or the Americans from the
Australians, we should answer, “neither the one nor the other, and yet
they are related, for both have sprung from the English race.” In the
same way, when we see how like the ancient birds and reptiles were to
each other, so that it is very difficult to say which were bird-like reptiles
and which were reptile-like birds, we can only conclude that they, too,
once branched off from some older race which had that bone between
the jaws, that single neck joint, and the other characters which birds
and reptiles have in common.
But long ago they must have gone off each on their own road, the
reptiles filling the world for a time, flying and walking and swimming, till
they found at last that creeping was their most successful way of life;
the birds on the other hand becoming more and more masters of the
air and the water, so that, while keeping the same bones and parts as
the reptiles, they have grown into quite different beings in their form
and habits, giving up the long-jointed tail of the Archœopteryx, or
ancient-winged bird, for the compact feathered fan which helps to
balance them in their flight, and the teeth of the water-birds for the
sharp and horny beak, which, together with their claws, is their chief
weapon of attack and defence now that they have employed their front
limbs as wings.
Nor shall we have far to look for the secret of their success in life.
Just as the reptiles have an advantage over the naked frogs and newts
by having strong scaly coverings in their skin, so the birds have an
advantage over the reptiles in that beautiful feathery plumage which
covers their body, and the powerful muscles which work their limbs.
For it is by means of these that they have been able to move quickly
and travel far, and to develop that bright nervous intelligence which
has grown more and more active as they have been carried into fresh
scenes and experiences, overcoming new difficulties and enjoying new
pleasures.
Remember for a moment how weak the lizard’s limbs are, so that
his body always drags upon the ground; and then look at the bird’s
tight grasp of the bough and the rod-like legs which raise his body
above it. Watch him as he beats the air with his wings, rising and
sinking, turning and swerving at will, and you will see that he has
earned freedom, strength, and active life, by means of the strong
muscles which move these legs and wings, and the feathers which
provide him with an instrument for beating the air. Feel a sparrow’s fat
little breast, or see how much meat comes off the wing and breast of a
pigeon, and then, if you consider that all this flesh is muscle used for
moving his wings, you will not wonder at his easy flight. For the
muscles of a bird’s breast often weigh more than all his other muscles
put together, and while one enormous mass of muscle in front of the
breast works to pull down the wing, another smaller one, ending in a
cord or tendon, passing like a pulley over the top of a bone (c, Fig. 33,
p. 126), pulls it up, so that by using these, one after the other, the bird
flies.
But where have the feathers come from,—those wonderful
beautiful appendages, without which he could not fly? They are
growths of the bird’s skin, of the same nature as the scales of reptiles,
or those on the bird’s own feet and legs; and on some low birds such
as the penguins they are so stiff and scale-like that it is often difficult to
say where the scales end and the feathers begin. All feathers, even
the most delicate, are made of horny matter, though it splits up into so
many shreds as it grows that they look like the finest hair, and Dr.
Gadow has reckoned that there must be fifty-four million branches and
threads upon one good-sized eagle’s feather.
When these feathers first begin to grow they are like little grooved
pimples upon the flesh, then soon these pimples sink in till a kind of
cup is formed all round them, and into this cup the soft layer just under
the outer skin sends out fibres, which afterwards form the pith. Round
these fibres rings of horny matter form, and then within these rings, in
the grooves of the soft pimple, the true feather is fashioned. First the
tips of the feathery barbs, then the shaft, and then the quill appear, as
the feather grows from below, fed by an artery running up into the
pimple; till at last, when the whole is full-grown, the quill is drawn in at
the base, and rests in its socket, complete.
Some of these feathers are weak and soft, with slender shafts and
loose threads growing all round them, and these are the downy
feathers which lie close to the body and keep the bird warm. Others,
which cover the outside and form the wings and tail are flat, with strong
quills and shafts, and a double set of barbs growing upon each shaft;
and if you look at these wing feathers under a strong microscope you
will see that they have a special arrangement for helping them to resist
the air. For not only have all the little featherlets or barbs rows of other
featherlets or barbules growing upon them, but these again are
covered with fine horny threads, often hooked at the tip, which cling to
the next barb, so that the feather is woven together as it were, in a
close web, and if you strike it against the air you will find that it resists
it strongly.
Now in a bird’s wing the feathers are so arranged that they lap one
under the other from the outside of the wing to the body, so that when
the bird strikes downwards they are firmly pressed together, and the
whole wing, which is hollow like the bowl of a spoon, encloses a
wingful of air, and as this is forced out behind, where the tips of the
feathers are yielding and elastic, he is driven upwards and forwards.
When, however, he lifts his wing again, the feathers turn edgeways
and are separated, so that the air passes through them, and he still
rises while preparing for the next stroke. All this goes on so rapidly that
even the heron makes 300 strokes in a minute, and the wild duck 500,
while in most birds they are so rapid that it is impossible to count them;
yet all the while the little creature can direct his flight where he will, can
pause and direct his wings to the breeze so as to soar, can swoop or
hover, wheel or strike, guiding himself by the outspread tail and a
thousand delicate turns of the wing.
All this complicated machinery, however, would not have served
the bird much if his body had been as heavy, and his blood as cold, as
those of the lizard and the crocodile. But here he has made a great
step forward. In the first place, he has a heart with four chambers, two
on the right side and two on the left; and while one of those on the right
side receives the worn-out blood from the body and pumps it to the
lungs to be refreshed, one of those on the left side receives it from the
lungs when it is refreshed, and the other pumps it into the arteries to
feed the body. So here we see for the first time among our backboned
animals a creature whose good and bad blood are never mixed in the
heart (compare pp. 23 and 76), but it gets all the benefit possible from
its breathing, and the blood is kept fresh and pure.
Moreover, a bird’s lungs are large, and are continued into several
large air-sacs, which in their turn open out into tubes which carry air
actually into the bones, many of which are hollow instead of containing
94
marrow like those of other animals.
And now we begin to see how wonderfully these little creatures are
fitted for flying. With all this air within them, not only is their blood kept
hot by constant purifying, but their bodies are much lighter than if their
bones were solid, and they can present a much broader surface to
float upon the air without increasing equally in weight. Meanwhile, their
feathery covering prevents the cold air around from chilling them, so
that they are not only warm-blooded animals, but actually warmer-
blooded even than ourselves.
Thus, then, Life has spread her feathered favourites over the
world. For them there are no limits except the extreme depths of the
water below, and the height beyond the atmosphere above. Wherever
air-breathing creatures can go, there some bird may be found. On the
dizzy ledges of inaccessible cliffs, on the wide bosom of the open
ocean, on the sandy wastes of the desert, in the tops of the highest
trees, on the cloud-capped peaks of the mountains, diving or
swimming, flying or soaring, running, perching, darting, or sailing for
miles and miles without one moment’s rest, they find their way
everywhere, and there is no spot from the icebound countries of the
Arctic zone to the warm bright forests of the tropics where they do not
penetrate; while their sharp eyes, kept free from dust and harm by a
95
third eyelid moving rapidly sideways, see far into the distance, and
thus as they soar into the sky they have a power, possessed by no
other animals, of overlooking a wide domain. Nor have they been
obliged, like the reptiles, to take up strangely different forms to suit
their various habits, for so wonderfully does their body meet all their
wants that very slight changes, such as a broad body and webbed feet
for the swimmers, long bare legs for the waders, a long hind toe for
grasping in the perchers, and sharp claws and beak for the birds of
prey, fit each one for his work, and are some of the chief distinctions
we can find between them.
Even the heavy running birds, the Ostriches of Africa, the Rheas of
South America, and the Emus and Cassowaries of Australia, still
remain truly bird-like, though their wings are unfit for flight. True, their
breastbones are flat instead of keel-shaped, for they have no need of
strong muscles to move their wings, which now serve only as sails to
catch the wind as they run, and in many other ways they are an older
type than our flying birds; but their wing bones are formed as if they
were used for flying, and their feathers, though loose and downy
because they have no little booklets, are like those of other birds.

Fig. 35.

The Ostrich96 at full speed.

 Strong powerful creatures they are, even in confinement. Yet how
little can we picture to ourselves, when we see the Ostrich trotting
round his paddock in the Zoological Gardens, with his wings
outspread, what he is when he courses over the free desert!—

“Where the zebra wantonly tosses his mane,

With wild hoof scorning the desolate plain;
And the fleet-footed ostrich over the waste
Speeds like a horseman who travels in haste.”

There the soft pads under the two toes of each foot rebound from
the yielding sand as his well-bent legs straighten with a jerk one after
the other, making his body bound forward at full speed. Then he raises
his wings, sometimes on one side, sometimes on both, to balance
himself, and to serve as sails to help him; and with this help his stride
is sometimes as great as twenty feet, and he dashes along at the rate
of twenty-six miles an hour. He is not so heavy as he looks, for many,
of his bones are hollow, his feathers are downy and soft, and his wing-
bones are small; and it is to his featherless thighs that you must look
for the strong muscles to which he trusts for all his speed, as with
outstretched neck he bounds across the plain.
If we go back to long bygone times, before the lion, the leopard,
and other ferocious animals found their way into Africa, we can
imagine how this great running bird took possession of the land and
became too heavy for flight; while as time rolled on, he gained that
strength of body and leg which now is his great protection as he
dashes along, his four or five wives following in his train. The ostriches
can travel over wide distances from one oasis to another, feeding on
seeds and fruit, beetles, locusts, and small animals, and fighting
fiercely with legs and beak if attacked. And when the springtime comes
the wives lay their eggs in a hole scooped in the sand, or often in some
dry patch of ground surrounded by high grass, till sixteen or twenty are
ready; and then they take their turn (the father among the rest) of
sitting upon them, at least at night, even if they leave them to the heat
of the sun by day. And when six weeks have passed the father grows
impatient, and, pressing the large bare pad in front of his chest against
each egg in turn, breaks it, pulls out the membranous bag with the
young bird in it, shakes him out, and, swallowing the bag, goes on to
another. In this way the whole downy brood are soon set free, and
begin picking up small stones to prepare their gizzard or muscular
second stomach for grinding, while their parents scrape the sand and
find and break up food for them.
So the ostrich lives its life in Africa, from Algeria right down to
Cape Colony; while its smaller and lighter-coloured relations, the
Rheas, with their three-toed feet, course over the plains of Paraguay
and Brazil, on the other side of the Atlantic, often swimming from
island to island, in the bays or across the rivers, but quite unable to fly
with their soft hair-like feathers, though their wings are larger than
those of the ostrich. Then when we turn to the East we find other
running birds; the Cassowary, with its three toes, its horny helmet, its
five long single feathers, and its five naked pointed quills in the place
of a wing, feeding on fruit and vegetables in New Guinea, or sharing
the dreary scrubs of Australia with the almost wingless Emus
wandering in pairs, the only constant married couples among the
running birds.
Nor is New Zealand left without a representative of this family, for
there we have the curious little Apteryx or Kiwi (Fig. 36), with its thick
stumpy legs, its long beak, and its soft downy body, under which are
hidden its aborted wings. Perhaps it is because he is small and
insignificant that the apteryx has lived on till now, crouching under the
bushes by day and creeping about in the twilight, thrusting his long
nose-tipped beak into the damp ground to draw out the worms. For
long ago, though in the memory of man, as we learn from the traditions
97
of the Maories, other wingless birds called Moas, which were six or
seven feet high, lived in New Zealand, and had fierce fights with the
natives. We find their bones now, often charred from having been
cooked in the native ovens, and when they are put together they give
us skeletons which show that these birds must have been as
formidable as that great bird of Madagascar, the Æpyornis, whose
gigantic bones and eggs, three times the size of ostrich eggs, have
been found, though the bird itself has never been seen.
 But these are gone now, and
Fig. 36. their relations the Emus are fast
following them: for however well
these flightless birds may flourish on
the broad plains and deserts, where
only their wild companions are
around them, they are sadly at the
mercy of man. The proud eagle can
fly far beyond the reach of the
hunter’s gun; the little lark, if she be
only wary enough, may trill out her
song in the blue vault above and
leave the cruel destroyer far below;
but the emu and the cassowary, the
rhea and the ostrich, have lost the
power to leave the earth; and if it
were not that we prize the two last
for their feathers, they, too, like their
companions, might live to rue the
day when they became runners
instead of conquerors of the air.
Wingless birds of New * * * * *
Zealand.
It is very different, however, with
The giant Moa (Palapteryx) and the water-birds, for they have not
the tiny Apteryx. The Moa is no only kept the power of flight, but
longer to be found alive. have gained the double advantage
of also floating safely on the water.
Look at our common wild duck. We
might have taken him just as well as
the sparrow for our type of a bird, and yet while the sparrow leads a
land life in the trees, the duck’s home is on the water, and many of his
relations live cradled on the open ocean.
See his broad boat-like body which floats without any effort of his;
notice how closely it is covered with short thickly-grown feathers, which
protect him from the chilly water, while he keeps them well-oiled with
his beak, from an oil-gland which all flying birds have at the base of the
tail. Watch how he swims, drawing his webbed foot together as he
brings it forward, and spreading it like a fan to strike the water as he
drives it back. Then, as he feeds, watch him gobbling in the mud and
then shaking his head as he throws his beak up in the air. For he, like
all ducks and geese, has a set of thin horny plates inside his broad bill,
and they sift the mud, while the tender tooth-like edges of his beak and
tongue feel out the suitable morsels.
All this time he is a water animal, but when he rises and flies he is
also master of the air, for his strong wings carry him stoutly, so that he
can migrate from one pool to another; or in winter, when the pools are
frozen, to the open sea. He is by no means the best flyer of his family,
and yet he is spread over Europe and North America, and even as far
east as Japan, while his ocean-loving cousin, the eider-duck, lines her
nest and lays her eggs high up in Arctic latitudes, and dives and swims
in the open ocean. So too his relations, the wild swans and geese
which wander in the lakes and swamps of Lapland, Siberia, and
Hudson’s Bay, feeding on water-weeds, worms, and slugs, build their
nests in the summer in the far north, and then fly thousands of miles
southwards to their winter homes, their strong wings whirring in the air
as they go.
Yet these are scarcely as true sea-birds as the divers, the
Guillemots and Puffins, the Auks and Grebes, which swim out all round
our coasts, and dive deep down to feed on the fish below. How clumsy
they are on land and how skilful in the water! You may see numbers of
guillemots and puffins in summer on the high cliffs of the north of
Scotland, or of Puffin Island in the Menai Straits; the guillemots laying
their eggs on the bare ledges, and the puffins in holes which they
burrow in the cliffs face; and they sit so doggedly upon their nests, and
shuffle and hop along so awkwardly, that men climbing up, or let down
by ropes from above, knock them over as they go. But wait till the eggs
are hatched, and the little ones have broken out of their shelly prison,
each one cracking his shell from inside by means of a little horny knob,
which all baby birds have for this purpose at the end of their beak, and
which falls off when they are fairly born. Then fathers, mothers, and
young ones, able to take care of themselves as soon as hatched,
launch out into the open sea in August, and there is a sight of diving
and swimming and fishing grand to behold. The awkward legs, placed
so far back on their body, now serve as powerful oars and rudders to
drive their smooth satiny bodies through the water. Their thin narrow
legs cut through the waves like knives, while their short stumpy wings,
closely laid against their down-covered bodies, keep them from being
chilled, and so do the air-bubbles which are entangled in their short
thick feathers, and which give their backs the appearance of being
98
covered with quicksilver when they dive after the fish below.
And then when the winter comes, those which have bred in the
north fly and swim southwards to our coasts, where they are joined by
the true divers and grebes which have come from the rivers and
estuaries, where they have made their nests on some reedy bank or
floating upon the water, and lived till their young ones are strong. This
is their seafaring time; and whether near the shore, or miles out at sea,
they dive and swim and make the ocean their home till spring comes
round again.