THIRD EDITIONI

DISCOVERING STATISTICSUSING SPSS(and sex and drugs and rock 'n' roll)

ANDY FIELD

($)SAGELos Angeles . Lonccn s New Deth! • Sinqapc re • Washingt on DC

(ONTEN S

Preface

How to use this book

Acknowledgements

Dedication

Symbols used in this book

Some maths revision

xix

xxiv

xxvii i

xxx

xxxi

xxxiii

1 Why is my eviL Lecturer forcing me to learn statistics?

1.1. What will this chapter tell me? CD1.2. What the hell am I do ing here? I don't belong here CD

1.2.1. The research process CD1.3. Initial obs ervation finding something that needs explaining CD1.4. Generating theories and testing them CD1.5. Data co llection 1: what to measure CD

1.5.1. Variables CD1.5.2. Measurement error CD1.5.3. Validity and reliability CD

1.6. Data collect ion 2: how to measure CD1.6.1. Correlational research methods CD1.6.2. Experimental research methods CD1.6.3. Randomization CD

1.7. Analysing da ta CD1.7.1. Frequency distributions CD1.7.2. The centre 01 a distribution CD1.7.3. The dispersion in a d istribution CD1.7.4. Using a frequency distribution to go beyond the data CD1.7.5. Fitting statistical models to the data CD

What have I discovered about statistics? CDKey terms that I've discovered

Smart Alex's stats quiz

Further reading

Interesting real research

1

1

2334

77

10

11

12

12

13

17

18

18

2023

2426

2828292930

DISCOVE RING STATlSTlCS US ING SPSS

2 Everything you ever wanted to know about statistics(weLl, sort of) 31

2.1. What will this chapter tell rne? <D 312.2. Build ing statistical models <D 322.3. Pop ulations and sampies <D 342.4. Simple statistica l models <D 35

2.4.1. The mean: a very simple statistical model <D 352.4.2. Assessing the fit 01the mean: sums of squares, variance and standard

deviations <D 352.4.3. Expressing the mean as a model ® 38

2.5. Go ing beyon d the data <D 402.5.1. The standard error <D 402.5.2. Conlidence intervals ® 43

2.6. Using stat istica l mo dels to test research questio ns <D 482.6.1. Test statistics <D 522.6.2. One- and two-tailed tests <D 542.6.3. Type I and Type 11 errors <D 552.6.4. Effect sizes ® 562.6.5. Statistical power ® 58

What have I discovered about statistics? <D 59Key terms that I've dis covered 59Sma rt Alex's stats q uiz 59Further read ing 60Interesting rea l research 60

3 The SPSS environment 61

3.1. What will this chapter tell rne? <D 613.2. Vers ions of SPSS <D 623.3. Getti ng started <D 623.4 . The data ed itor <D 63

3.4.1. Entering data into the data editor <D 693.4.2. The 'Variable View' <D 703.4.3. Missing values <D 77

3.5. The SPSS viewer <D 783.6. The SPSS SmartViewe r <D 813.7. The synt ax window @ 823.8 . Sav ing files <D 833.9. Retrievin g a fi le <D 84

What have I di scovered about statistics? <D 85Key terms that I've discovered 85Smart Alex's tasks 85Furthe r read ing 86Online tuto rials 86

4 ExpLoring data with graphs 87

4 .1. What wi ll this chapter tell me? <D 874.2. The art of pre sen ting da ta <D 88

4.2.1. What makes a good graph? <D 884.2.2. Lies, damned lies, and .. . erm ... graphs <D 90

CONTENT S

4.3. The SPSS Cha rt Builder CD4.4. Histog rams: a good way to spot obvious problems CD4.5 . Boxpl ots (box- whiske r diagram s) CD4.6. Graphing means: bar charts and error ba rs CD

4.6 .1. Simple bar charts for independent means CD4.6 .2. C1ustered bar charts tor independent means CD4.6.1 Simple bar charts Ior related means CD4.6.4. C1ustered bar charts for related means CD4.6.5 C1ustered bar charts for 'mixed' designs CD

4.7. Line charts CD4 .8. Graphing relati on ships: the scatterp lot CD

4.8.1. Simple scatterplot CD4.8.2. Grouped scatterplot CD4.8.1 Simple and grouped 3-D scatterplots CD4.8.4 . Matrix scatterplol CD4.8.5. Simple dot plot or density plot CD4.8.6. Drop-line graph CD

4.9. Editing graphs CD

Wh at have I di sco vered abo ut statistics? CDKey term s that I've discove red

Smart Ale x's tasks

Further read ing

Online tutorial

Inte restin g real resea rch

919399

10310510710911111 3115116117119121123125126126

129130130130130130

5 Exploring assumptions

5.1 . Wh at will this ch apter tell me? CD5.2. What are assumptions? CD5.3. Assum pti on s of pa rametric data CD5.4. The assum ption of nor mality CD

5.4.1. Oh no, lt's that pesky frequency distribution again: checking

normality visually CD5.4.2. Ouantifying normality with numbers CD5.4.3 . Exploring groups of data CD

5.5. Testin g whethe r a distribution is normal CD5.5.1. Doing the Kolmogorov-Smirnov test on SPSSCD5.5.2. Output from the explore procedure CD5.5.1 Reporting the K-S test CD

5.6 . Testing for homogeneity o f va riance CD5.6.1. Levene's test CD5.6.2. Reporting Levene's test CD

5.7. Corr ecting probl ems in the data ®5.7.1. Dealing with outliers ®5.7.2. Dealing with non-normality and unequal variances ®5.7.3. Transforming the cata using SPSS®5.7.4. When it all goes horribly wrong@

What have I d iscovered about statis tics? CDKey terms that I've di scovered

Sma rt Alex's tasks

Online tutorial

Furth er reading

131

131132132133

134136140144145146148149150152153153153156162

164164165165165

viii

6 CorreLation

DISCOVERING STATlSTIC S USING SP SS

166

7

6.1. What will this chapter tell rne? CD6.2. Looking at relationships CD6.3. How do we measure relationships? CD

6.3.1. A detour into the murky world 01 covariance CD6.3.2. Standardization and the correlation coe flicient CD6.3.3. The significance of the correlation coefiicient @

63.4. Confidence intervals for r@

6.3.5. A word of warning about interpretation causality CD6.4. Data entry for correlation analysis using SPSS CD6.5. Bivariate correlation CD

6.5.1. General procedure for running correlations on SPSS CD6.5.2. Pearson's correlation coefficient CD6.5.3. Spearman's correlation coefiicient CD6.5.4. Kendall's tau (non-parametric) CD6.5.5. Biserial and point-biserial correlations @

6.6. Partial correlation @

6.6.1. The theory behind part and partial correlation @

6.6.2. Partial correlation using SPSS @

6.6.3. Semi-partial (or part) correlations @

6.1. Compar ing correlations @

6.7.1. Comparing independent rs @

6.7.2. Compar ing dependent rs @

6.8. Calculating the effect size CD6.9. How to report correlation coeffi cents CD

What have I discovered about statistics? CDKey terms that I've discoveredSmart Alex's tasksFurther reading

Online tutorialInteresting real research

Regression

7.1. What will this chapter tell me? CD1.2. An introduction to regress ion CD

7.2.1. Some important information about straight lines CD7.2.2. The method of least squares CD7.2.3. Assessing the goo dness of fit: sums of squares, R and R2CD7.2.4. Assessing individua l predictors CD

7.3. Doing simple regression on SPSS CD7.4 . Interpreting a simple regression CD

7.4 .1. Overall fit 01the model CD7.4.2. Model paramete rs CD7.4.3. Using the model CD

1.5. Multiple regression the basics @

7.5.1. An example of a multiple regression mode l @

7.5.2. Sums 01 squares, R and R2@

7.5.3 . Methods of regression @

7.6. How accurate is my regression rnodel? @

166167167167169171172

173174175175177179181182186186188190191191191192193

195195195196196196

197197198199200201204205206206207208209210211212214

CONTENTS

7.7.

7.8.

7.9.

7.10 .

7.11.

7.6.1. Assessing the regression modell : diagnostics ®7.6.2. Assessing the regression modet 11: generalization ®How to do multiple regression using SPSS ®7.7.1. Some things to think about betö re the analysis ®7.7.2. Main options ®7.7.3. Statistics ®7.7.4. Regression plots ®7.7.5. Saving regression diagnostics ®7.7.6. Further options ®Interpreting multiple regression ®7.8.1. Descriptives ®7.8.2. Summary of model ®7.8.3. Model parameters ®7.8.4. Excluded variables ®7.8.5. Assessing the assumption of no multicollinearity ®7.8.6. Casewise diagnostics ®7.8.7. Checking assumptions ®What if I violate an as surnption? ®How to report multiple regression ®Categorical predi ctor s and multiple regression @

7.11.1. Dummy coding ®7.11.2. SPSS output tor dummy variables @

What have I discovered about statistics? CDKey terms that I've discoveredSmart Alex's tasks

Further readingOnline tutorialInteresting real research

214

220225225225227229230231

233233234237241241

244247251

252253253256

261261262263

263263

8 Logistic regression 264

8.1. What will this chapter tell me? CD 2648.2 . Background to logistic regression CD 2658.3. What are the principles behind logistic reqres sion? ® 265

8.3.1. Assessing the model : the log-likelihood statistic@ 2678.3.2. Assessing the model: Rand R2@ 2688.3.3. Assessing the contribution of predictors: the Wald statistic ® 2698.3.4. The odd s ratio: Exp(B) @ 270

8.3.5. Methods of logistic regression ® 2718.4. Assumptions and things that can go wrong @ 273

8.4.1. Assumption s ® 2738.4.2. Incomplete information from the predictors @ 2738.4.3. Complete separation @ 2748.4.4. Overdispersion @ 276

8.5. Binary logistic regression: an example that will make you feel eel ® 27785.1 The main analysis ® 27885.2. Method of regression ® 2798.5.3. Categorical predictors ® 2798.5.4. Obtaining residuals ® 28085.5. Further options ® 281

8.6. Interpreting logistic regression ® 282

OI SCOVERING STATlSTIC S IJSI NG SPSS

9

8.6 .1. The initial model ®8 6 2. Step 1: intervention @

8.6.3. Listing predicted probabilities ®8.6.4 . Interpreting residuals ®8.6.5. Calculating the effect size ®

8.7. How to report logistic regression ®8.8. Testing assumptions ano ther exam ple ®

8.8.1. Testing for linearity of the logit @

8.8.2. Testing far multico llinearity @

8.9. Predicti ng severa l catego ries multinomial logistic reqressio n @

8.9.1. Running multinomiallogi stic regression in SPSS @

8.9.2. Statistics @

8.9.3. Other options @

8.9 .4. Interpreting the multinomial logistic regression output @

8.9.5. Report ing the results

What have I discovered about statistics? CDKey terms that I've discovered

Smart Alex's tasks

Further reading

Online tutorial

Interest ing real research

Comparing two means

9.1. What will this cha pter tell me? CD9.2. Lookin g at differences CD

9.2.1. A problem with error bar graphs of repeated-measures designs CD9.22. Step 1: calculate the mean far each participant ®9.2.3. Step 2 : calculate the grand mean ®9.2.4. Step 3: calculate the adjustment factar ®9.2.5. Step 4 create adjus ted values for each variable ®

9.3. The r-test CD9.3.1. Rationale Ior the r-test CD9.3.2. Assumptions of the r-test CD

9.4. The depe ndent r-Iest CD9.4 .1. Sampling distri butions and the standard error CD9.4 .2. The dependent r-Iest equation explained CD9.4.3. The dependen t r-iest and the assumption of narma lity CD9.4.4. Dependent r-tests using SPSS CD9.4 .5. Output from the depe ndent I-test CD9.4.6. Calculating the effect size ®9.4 .7. Reporting the dependent r-test CD

9.5. The independent r-test CD9.5.1. The independent r-test equation explained CD9.5.2 The independent r-test using SPSS CD9.5.3. Output from the independent r-test CD9.5.4 . Calculating the effect size ®9.5.5 Reporting the indepen dent r-iest CD

9.6. Between groups or repeated measures? CD9.7. The [-test as a general linear model ®9.8. What if my data are not normally dis tributed ? ®

282284291292294294294296297300301304305306312

313313313315315315

316316317317320320322323324325326326327327329329330332333334334337339341341342342344

......... ..........

CO NTEN TS

What have I discovered about sla tis lics? CD 345Key terms that l've discovered 345Smart Alex' s task 346Furth er read ing 346Online tutor ial 346Interes ting real rese arch 346

10 Comparing several means: ANOVA (GLM 1) 347

10.1 . What will this chapter tell me? CD 34710.2. The theory behind ANOVA ® 348

10.2.1. Inflated errar rates ® 34810.2.2. Interpreting F® 34910.2.3. ANOVAas regression ® 34910.2.4. Logic 01the F-ratio ® 35410.2.5. Total sum of squares (SST) ® 35610.2.6. Model sum 01 squares (SS,) ® 35610.2.7. Residual sum of squares (SSR) ® 35710.2.8. Mean squares® 35810.2.9. The F-ratio ® 35810.2.10. Assumptions of ANOVA@ 35910.2.11. Planned contrasts ® 36010.2.12. Post hoc procedures ® 372

10.3. Running one-way ANOVA on SPSS ® 37510.3.1. Planned comparisons using SPSS® 37610.3.2. Post hoc tests in SPSS® 37810.3.3. Options ® 379

10.4 . Output l ram one-way AI\JOVA® 38110.4 .1. Output tor the main analysis® 38110.4 .2. Output lar planned comparisons ® 38410.4-3. Output for post hoc tests ® 385

10.5. Calculatin g the ellect size ® 38910.6. Reporting results Iro m one -way independ ent ANOVA ® 39010.7. Violat ion s 01 assumptions in on e-way independent ANOVA ® 391

What have I di scovered about statistics? CD 392Key terms tha t I've di scovered 392Smart Alex's tasks 393Further readi ng 394Online tutorials 394Interest ing real research 394

11 Analysis of covariance, ANCOVA (GLM 2) 395

11.1. What will this chap ter tell rne? ® 39511.2 . What is ANCOVA?® 39611.3. Assumptions and issues in AN COVA@ 397

11.3.1. Independence of the covariate and treatment eflect @ 39711.3.2. Homogeneity of regression slopes @ 399

11.4 . Conducting ANCOVA on SPSS ® 39911.4.1. Inputting data CD 39911.4 .2. Initial considerations: testing the independence 01 the independent

variable and covariate ® 400

xii DISCDVERING STATlSTIC S USING SP SS

11.5.

11.6.

11.7 .11.8.

11.9.11.10.

11.4 .3. The main analysis @

11.4 .4. Contrasts and other options @

Interpret ing the outp ut from AN COVA @11.5.1. What happens when the covariate is excluded? @

11.5.2. The main analysis @

11.5.3. Contrasts @

11.5.4 . Interpreting the covariate @

ANCOVA run as a multiple regression @

Testing the assumption of homogeneity of regression slopes @

Calculat ing the effec t size @

Rep orting result s @

What to do when assumptions are viol ated in ANCOVA @

Wh at have I discovered about statistics? @

Key term s that I've discovered

Sm art Ale x's tasks

Further reading

Onlin e tutorials

Interestin g real rese arch

40140140440440540740840841 3415417418

418419419420420420

12 Factorial ANOVA (GLM 3) 421

12.1.

12.2 .

12.3 .

12.4.

12.5.

12.6 .

12.7 .

12.8.

12.9.

What will this ch apter tell me? @

Theory of fac tori al ANOVA (be tween-g roups) @

12.2.1. Factorial designs @

12.2.2, An example with two independent variables @

12.2.3. Total sums of squares (SSr) @

12.2.4 , The rnodel sum of squares (SS,) @

12.2.5. The residual sum of squares (SSA) @

12.2.6. The F-ratios @

Factorial ANOVA using SPSS @

12.3.1. Entering the data and accessing the main dialog box @

12.3.2. Graphing interactions @

12.3.3. Contrasts @

12.3.4. Post hoc tests @

12.3.5. Options @

Output from factorial ANOVA @

12.4 .1. Output for the preliminary analysis @

12.4 .2. Levene's test @

12.4 .3. The main ANOVA table @

12.4.4 . Contrasts @

12.4 .5. Simple effects analysis @

12.4.6. Post hoc analysis @

Interpreting inter action graphs @

Calculating effec t sizes @

Reporting the results of two-way ANOVA @

Factoriai ANOVA as reg ressi on @

What to do when assum ptions are vio lated in factorial ANOVA @

What have I discovered about stati stics? @

Key term s that l've di scovered

Smart Alex 's tasks

421422422423424426428429430430432432434434435435436436439440441443446448450454

454455455

CO NT ENTS

Furth er read ing

Onl ine tutorials

Interestin g real research

13 Repeated-measures designs (GLM 4)

456456456

457

xiii

13.1.

13.2.

13.3.

13.4 .

13.5 .

13.6.

13.7.

13.8.

13.9 .

13.10 .

13.11.

13.12 .

What wi ll this chapter tell me? ®Int roduction to repeated -measures designs ®13.2.1. The assumption of sphericity ®13.2.2. How is sphericity measured? ®13.2.3. Assessing the severity of departures from sphericity ®13.2.4. What is the effect 01violating the assumpl ion 01 sphericily? @

13.2.5. What do you do if you violate sphericity? ®Theory of one-way repeated-m easur es AN OVA ®13.3.1. The total sum 01 squares (SST) ®13.3.2. The within-participant (SS",) ®13.3.3. The model sum of squares (SS,,) ®13.3.4 . The residual sum of squares (SSR) ®13.3.5. The mean squares ®13.3.6. The F-ratio ®13.3.7. The between-participant sum 01squares ®On e-way repeated-measu res AN OVA usi ng SPSS ®13.4 .1. The main analysis ®13.4.2. Defining contrasts for repeated-measures ®13.4.3. Post hoc tests and additional options @

Output for one -way repeated-measures ANOVA ®13.5.1. Descriptives and other diagnostics CD13.5.2. Assessing and correcting for sphericity: Mauchly's test ®13.5.3. The main ANOVA ®13.5.4. Contrasls ®13.5.5 Post ho c tests ®Effec t sizes for repeated -m easur es ANOVA @

Reporting one-way repeated-measu res ANOVA ®Repeated-measures w ith several indepe ndent va riab les ®13.8.1. The main analysis ®13.8.2. Contrasts ®13.8.3. Simple etlects analysis @

13.8.4 . Graphing interactions ®13.8.5. Other options ®Output fo r fact orial repeated-measures ANOVA ®13.9.1. Descriplives and main analysis ®13.9.2. The elfect of drink ®13.9.3. The effecl 01imagery ®13.9.4 . The interaction effect (drink x imagery) ®13.9.5. Contrasls for repealed-measures variables ®Effect sizes for factorial repeated-measures AN OVA @

Reporting the results from fac torial rep eated-measures ANOVA ®What to do when ass umptions are vio lated in repeated-measures AN OVA @

What have I discovered about statistics? ®Key terms that I've discovered

457458459459460460461462464465466467467467468468468471471474474474475477478479481482484488488490491492492493495496498501502503

503504

xiv

Sm art Alex's tasks

Further read ing

Online tutorials

Interestin g real research

14 Mixed design ANOVA (GLM 5)

DI SCOVERING STATISTICS USING SPSS

504505505505

506

14 .1.

14 .2.

14. 3.

14.4.

14.5 .

14 .6.

14 .7.

14 .8.

What will thi s chapter te ll rne? CDMixed de sign s ®Wh at do men and women look for in a partner? ®Mixed AN OVA on SPSS ®14.41. The main analysis ®14.42. Other options ®Output Ior mixed lactori al ANOVA : main ana lys is @

14.5.1. The main eflect 01gender ®14.5.2. The main eflect 01 looks ®14.5.3. The main ettect of charisma ®14.5.4. The interaction between gender and looks ®14.5.5. The interaction between gender and charisma ®14.5.6. The interaction between attractiveness and charisma ®14.5.7. The interaction between looks, charisma and gender @

14 .5.8. Conclusions @

Calculating ellect sizes @

Reporting the result s 01 mixed ANOVA ®Wh at to do when assumptions are violated in m ixed ANOVA @

Wh at have I discovered about stati sti cs? ®Key terms that I've discovered

Smart Alex' s tasks

Further reading

Online tutorial s

Interesting real research

50650750850850851351451 7518520521523524527530531533536

536537537538538538

15 Non-parametric tests 539

15.1 .

15.2.

15.3.

15.4 .

Wh at w ill thi s chapter tell me? CDWh en to use non-p aram etric tests CDComparin g two independent conditions the Wilc oxon rank-sum test and

Mann-Whitney test CD15.31. Theory®15.3.2. Inputting data and provisional analysis CD15.3.3. Running the analysls CD15.3.4. Output lrom the Mann-Whitney test CD15.3.5. Calculating an effect size ®15.3.6. Writing the results CDCo mparing two related cond itio ns : the Wilcoxon signed-rank tes t CD15.4.1. Theory 01 the Wilcoxon signed-rank test ®15.4.2. Running the analysis CD15.4.3. Output Ior the ecstasy group CD15.4.4 Output Ior the alcohol group CD15.45. Calculating an effect size ®15.46. Writing the results CD

539540

540542545546548550550552552554556557558558

CONTENTS

15.5. Differences between several independent groups the Kruskal-Walli s test CD 559

15.5.1. Theory of the Kruskal-Wallis test @ 560

15.5.2. Inputting data and provisional analysis CD 562

15.5.3. Doing the Kruskal- Wallis test on SPSS CD 562

15.5.4. Output from the Kruskal- Wallis test CD 564

15.5.5. Post hoc tests for the Kruskal- Wallis test @ 565

15.5.5. Testing for trends: the Jonckheere-Terpstra test @ 568

15.5.7. Calculating an eHect size @ 570

15.5.8. Writing and interpreting the results CD 571

15.6 . Differences between several related groups: Friedman 's ANOVA CD 573

15.5.1. Theory of Friedman's ANOVA @ 573

15.5.2. Inputting data and provisional analysis CD 575

15.5.3. Doing Friedman's ANOVA on SPSS CD 575

155.4. Output from Friedman's ANOVA CD 576

15.5.5. Post hoc tests for Friedman' s ANOVA @ 577

155.5. Calculating an effect size @ 579

15.5.7. Writing and interpreting the results CD 580

xv

What have I discovered about statistics? CDKey terms that l've discovered

Smart Alex's tasks

Further reading

Online tutorial

Interesting real research

16 Multivariate analysis of variance (MANOVA)

581

582

582

583

583

583

584

16.1.

16.2.

16.3.

16.4 .

16.5 .

16.6 .

16 .7.

What will this chapter tell rne? ®When to use MANOVA @

Introdu ction : similarities and differences to ANOVA @

15.31. Words of warning ®15.3.2. The example for this chapter @

Theory of MANOVA @

15.4.1. Introduction to matrices @

15.4.2. Some important matrices and their functions @

15.4.3. Calculating MANOVA by hand : a worked example @

15.4.4. Principle of the MANOVA test statistic @

Practical issues when conducting MANOVA @

15.5.1. Assumptions and how to check them @

15.5.2. Choosing a test statistic @

15.5.3. Follow-up analysis @

MANOVA on SPSS ®15.5.1. The main analysis @

15.5.2. Multiple comparisons in MANOVA @

15.5.3. Addition al options @

Output from MANOVA @

15.7.1. Preliminary analysis and testing assumpti ons @

15.7.2. MANOVA test statistics @

15.7.3. Univariate test statistics ®15.7.4 SSCP Matrices @

157.5. Contrasts @

584

585

585

587

587

588

588

590

591

598

603

603

604

605

605

606

607

607

608

608

608

609611

613

xvi OISCOVER ING STATlSTICS USING SPS S

16.8. Reporting results from MANOVA ® 61416.9. Following up MANOVA with discriminant analysis @ 61516.10 . Output from the discriminant ana lys is @ 61816.11. Reporting results from discriminant analysis ® 62116.12. Some final remarks @ 622

16.12.1. The final interpretation @ 62216.12.2. Univariate ANOVAor discriminant ana lysis? 624

16.13 . What to do when assumptions are violated in MAN OVA @ 624

What have I discovered about statistics? ® 624Key terms that I've discovered 625Smart Alex' s ta sks 625Further read ing 626Onl ine tuto rials 626Interestin g real research 626

17 Exploratory factor analysis 62717.1. Wh at w ill this chapter tell me? Q) 62717.2. When to use fac tor analys is ® 62817.3. Factors ® 628

17.3.1. Graphical representation of factors ® 630173.2. Mathematical representation of factors ® 631173.3. Factor scores ® 633

17.4 . Discovering factors ® 63617.4.1. Choosing a method ® 63617.4.2. Communality ® 63717.4.3. Factor analysis vs. principal component analysis ® 63817.4.4. Theory behind principal component analysis @ 63817.4 .5. Factor extraction: eigenvalues and the scree plot ® 63917.4.6. Improving interpretation: factor rotation @ 642

17.5. Research example ® 64517.5.1. Before you begin ® 645

17.6. Runn ing the ana lysis ® 65017.6.1. Factor extraction on SPSS® 65117.6.2. Rotation ® 65317.6.3. Scores ® 65417.6.4 . Options ® 654

17.7. Interpretin g output from SPSS ® 65517.7.1. Preliminary analysis ® 65617.7.2. Factor extraction ® 66017.7.3. Factor rotation ® 66417.7.4. Factor scores ® 66917.7.5. Summary ® 671

17.8. How to report factor analysis Q) 67117.9. Reliability analysis ® 673

17.9.1. Measures 01 reliability @ 67317.9.2. Interpreting Cronbach's Ci (some cautionary tales : .l ® 67517.9.3. Reliability analysis on SPSS ® 67617.9.4 . Interpreting the output ® 678

17.10. How to report reliability analysis ® 681

CONTENTS

What have I discovered about statistics? ®Key terms that I've discovered

Smart Alex's tasks

Further reading

Online tutorial

Interesting real research

18 Categorical data

682682683685685685

686

xvii

18.1.

18.2.

18.3 .

18.4.

18.5.

18.6.

18.7.

18.8.

18.9 .

18.10 .

18.11.

18.12.

What will this chapter tell me? CDAnalysing categor ical data CDTheory of analysing categorical data CD18.11. Pearson's chi-square test CD18.12. Fisher's exact test CD183.3. The likelihood ratio ®183.4. Yates' correction ®Assumptions of the chi-square test CDOoing chi-square on SPSS CD18.5.1. Entering data: raw scores CD18.5 .2. Entering data: weight cases CD18.53. Running the analysis CD18.5.4. Output for the chi-square test CD18.5.5. Breaking down a significant chi-square test with standardized residuals ®18.5.6. Calculating an eflect size ®18.5.7 Reporting the results of chi-square CDSeveral categoric al variables log linear analysis @

18.6.1. Chi-square as regression @)

18.6.2. Loglinear analysis @

Assumptions in loglinear analysis ®Loglinear analysis using SPSS ®18.8.1. Initial considerations ®18.8.2. The loglinear analysis ®Output from logl inear analysis @

Following up loglinear analysis ®Effect sizes in loglinear analysis ®Reporting the results of loglinear analysis ®

What have I discovered about statistics? CDKey terms that I've discovered

Smart Alex's tasks

Further reading

Online tuto rial

Interesting real research

686687687688690690691691692692692694696698699700702702708710711711712714719720721

722722722724724724

19 Multilevellinear models 725

19.1.

19.2.

19.3.

What will this chapter tell me? CDHierarchical dat a ®19.2.1. The intraclass correlation ®19.2.2. Benefits of multilevel models ®Theory of multi level linear mode ls @

725726728729730

xviii DI SCOVE RING STATlSTIC S USI NG SPS S

193.1, An example ®19,3. 2, Fixed and random coefficients @

19.4. The multil evel model @)

194 .1. Assessing the fit and comparing multilevel models @)

194,2, Types of covariance structures @)

19.5. Some practical issues @

19 5.1, Assumptions @

19.52, Sampie size and power @

19.5.3. Centring variables @)

19.6. Multilevel modelling on SPSS @)

19.6.1. Entering the data ®19.6.2. Ignoring the data structure: ANOVA®19.63. Ignoring the data structure ANCOVA®19.64. Factoring in the data structure: random intercepts @

19.6.5. Factoring in the data structure: randorn intercepts and slopes @)

19.6.6. Adding an interaction to the model @)

19.7. Growth models @)

19.7.1. Growth curves (polynomials) @)

19.7.2. An example: the honeymoon period ®19.7 3. Restructuring the data @

19.74. Running a growth model on SPSS @)

19.7.5. Further analysis @)

19.8. How to report a rnultrlevel model @

What have I discovered about statistics? ®Key terms that I've discovered

Smart Alex's tasks

Further reading

Online tutoriai

Interesting real research

730732734737737739739740740741742742746749752756761761761763767774775

776777777778778778

Epilogue

Glossary

Appendix

A.l.

A.2.

A.3.

A.4.

References

Index

Table 01 the standar d normal distr ibution

Critica l values 01 the (-distribu tion

Critical values of the F-distribution

Critical values of the chi-square distribu tion

779

781

797797803804808

809

816