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1 DISCOVERING USING SPSS STATISTICS THIRD EDITION (and sex and drugs and rock 'n' roll) ANDY FIELD

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

3 vi DISCOVERING STATISTICS USING SPSS 2 Everything you ever wanted to know about statistics (well, sort of) What will this chapter tell me? CD Building statistical mod eis CD Populations and samples CD Simple statistical modeis CD The mean a very simple statistical model CD Assessing the fit of the mean: sums of squares, variance and standard deviations CD Expressing the mean as amodel Going beyond the data CD The standard error CD Confidence intervals Using statistical modeis to test research questions CD Test statistics CD One- and two-tailed tests CD Type I and Type II errors CD Effect sizes Statistical power 58 What have I discovered about statistics? CD Smart Alex's stats quiz The SPSS environment 3.1. What will this chapter tell me? CD 3.2. Versions of SPSS CD 3.3. Getting started CD 3.4. The data editor CD Entering data into the data editor CD The 'Variable View' CD Missing values CD 3.5. The SPSS viewer CD 3.6. The SPSS SmartViewer CD 3.7. The syntax 3.8. Saving files CD 3.9. Retrieving a file CD What have I discovered about statistics? CD Online tutoriais Exploring data with graphs 4.1. What will this chapter tell me? CD 4.2. The art of presenting data CD What makes a good graph? CD Ues, damned lies, and... erm graphs CD

4 CONTENTS vii 4.3. The SPSS Chart Builder CD 4.4. Histograms a good way to spot obvious problems CD 4.5. Boxplots (box-whisker diagrams) CD 4.6. Graphing means: bar charts and error bars CD Simple bar charts for independent means CD Clustered bar charts for independent means CD Simple bar charts for related means CD Clustered bar charts for related means CD Clustered bar charts for 'mixed' designs CD 4.7. Line charts CD 4.8. Graphing relationships the scatterplot CD Simple scatterplot CD Grouped scatterplot CD Simple and grouped 3-0 scatterplots CD Matrix scatterplot CD Simple dot plot or density plot CD orop-line graph CD 4.9. Editing graphs CD What have I discovered about statistics? CD 5 ExpLoring assumptions 5.1. What will this chapter tell me? CD 5.2. What are assumptions? CD 5.3. Assumptions of parametric data CD 5.4. The assumption of normality CD Oh no, it's that pesky frequency distribution again checking normality visually CD Quantifying normality with numbers CD Exploring groups of data CD 5.5. Testing whether a distribution is normal CD ooing the Kolmogorov-Smirnov test on SPSS CD Output from the explore procedure CD Reporting the K-S test CD 5.6. Testing for homogeneity of variance CD Levene's test CD Reporting Levene's test CD 5.7. Correcting problems in the data oealing with outliers oealing with non-normality and unequal variances Transforming the data using SPSS When it all goes horribly What have I discovered about statistics? CD

5 viii DISCOVERING STATISTICS USING SPSS 6 Correlation 6.1. What will this chapter tell me? CD 6.2. Looking at relationships CD 6.3. How do we measure relationships? CD A detour into the murky world of covariance CD Standardization and the correlation coefficient CD The significance of the correlation Confidence intervals for A word of warning about interpretation: causality CD 6.4. Data entry for correlation analysis using SPSS CD 6.5. Bivariate correlation CD General procedure for running correlations on SPSS CD Pearson's correlation coefficient CD Spearman's correlation coefficient CD Kendall's tau (non-parametric) CD Biserial and point-biserial 6.6. Partial correlation The theory behind part and partial correlation Partial correlation using SPSS Semi-partial (or part) correlations 6.7. Comparing Comparing independent Comparing dependent 6.8. Calculating the effect size CD 6.9. How to report correlation coefficents CD What have I discovered about statistics? CD Regression 7.1. What will this chapter tell me? CD 7.2. An introduction to regression CD Some important information about straight lines ed The method of least squares CD Assessing the goodness of fit: sums of squares, R and R2 CD Assessing individual predictors CD 7.3. Doing simple regression on SPSS CD 7.4. Interpreting a simple regression CD Overall fit of the model CD Model parameters CD Using the model CD 7.5. Multiple regression: the basics An example of a multiple regression model SulTisof squares, R and R Methods of regression 7.6. How accurate is my regression model?

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

7 x DISCOVERING STATISTICS USING SPSS The initial model Step l' Listing predicted probabilities Interpreting residuals Calculating the effect size How to report logistic regression Testing assumptions another example Testing for linearity of the Testing for Predicting several categories multinomiallogistic Running multinomiallogistic regression in Other Interpreting the multinomiallogistic regression Reporting the results What have I discovered about statistics? ed Comparing two means 9.1. What will this chapter tell me? ed 9.2. Looking at differences ed A problem with error bar graphs of repeated-measures designs ed Step 1. calculate the mean for each participant Step 2 calculate the grand mean Step 3 calculate the adjustment factor Step 4. create adjusted values for each variable 9.3. The t-test ed Rationale for the t-test ed Assumptions of the t-test ed 9.4. The dependent t-test ed Sampling distributions and the standard error ed The dependent t-test equation explained ed The dependent t-test and the assumption of normality ed Dependent t-tests using SPSS ed Output from the dependent t-test ed Calculating the effect size Reporting the dependent t-test ed 9.5. The independent t-test ed The independent t-test equation explained ed The independent t-test using SPSS ed Output from the independent t-test ed Calculating the effect size Reporting the independent t-test ed 9.6. Between groups or repeated measures? ed 9.7. The t-test as a generallinear model 9.8. What if my data are not normally distributed?

8 CONTENTS xi What have I discovered about statistics? CD Smart Alex's task 10 Comparing several means: ANOVA (GLM 1) What will this chapter tell me? CD The theory behind ANOVA Inflated error rates Interpreting F ANOVA as regression Logic of the F-ratio Total sum of squares (SST) Model sum of squares (SSM) Residual sum of squares (SSR) Mean squares The F-ratio Assumptions of Planned contrasts Post hoc procedures Running one-way ANOVA on SPSS Planned comparisons using SPSS Post hoc tests in SPSS Options Output from one-way ANOVA Output for the main analysis Output for planned comparisons Output for post hoc tests Calculating the effect size Reporting results from one-way independent ANOVA Violations of assumptions in one-way independent ANOVA What have I discovered about statistics? CD Online tutoriais 11 Analysis of covariance, ANCOVA (GLM 2) What will this chapter tell me? What is ANCOVA? Assumptions and issues in Independence of the covariate and treatment Homogeneity of regression Conducting ANCOVA on SPSS Inputting data CD Initial considerations: testing the independence of the independent variable and covariate

9 xii DISCDVERING STATISTICS USING SPSS The main analysis Contrasts and other options Interpreting the output from ANCOVA What happens when the covariate is exciuded The main analysis Contrasts Interpreting the covariate ANCOVA run as a multiple regression Testing the assumption of homogeneity of regression slopes Calculating the effect size Reporting results What to do when assumptions are violated in ANCOVA What have I discovered about statistics? Online tutoriais FactoriaL ANOVA (GLM 3) What will this chapter tell me? Theory of factorial ANOVA (between-groups) Factorial designs An example with two independent variables Total sums of squares (SST) The model sum of squares (SSM) The residual sum of squares (SSR) The F-ratios Factorial ANOVA using SPSS Entering the data and accessing the main dialog box Graphing interactions Contrasts Post hoc tests Options Output from factorial ANOVA Output for the preliminary analysis Levene's test The main ANOVA table Contrasts Simple effects analysis Post hoc analysis Interpreting interaction graphs Calculating effect sizes Reporting the results of two-way ANOVA Factorial ANOVA as regression What to do when assumptions are violated in factorial ANOVA What have I discovered about statistics?

10 CONTENTS xiii Online tutoriais Repeated-measures designs (GLM 4) What will this chapter tell me? Introduction to repeated-measures designs The assumption of sphericity How is sphericity measured? Assessing the severity of departures from sphericity What is the effect of violating the assumption of sphericity? What do you do if you violate sphericity? Theory of one-way repeated-measures ANOVA The total sum of squares (SST) The within-participant (SSw) The model sum of squares (SSM) The residual sum of squares (SSR) The mean squares The F-ratio The between-participant sum of squares One-way repeated-measures ANOVA using SPSS The main analysis Defining contrasts for repeated-measures Post hoc tests and additional options Output fo\ one-way repeated-measures ANOVA Descriptives and other diagnostics CD Assessing and correcting for sphericity: Mauchly's test The main ANOVA Contrasts Post hoc tests Effect sizes for repeated-measures ANOVA Reporting one-way repeated-measures ANOVA Repeated-measures with several independent variables The main analysis Contrasts Simple effects analysis Graphing interactions Other options Output for factorial repeated-measures ANOVA Descriptives and main analysis The effect of drink The effect of imagery The interaction effect (drink x imagery) Contrasts for repeated-measures variables Effect sizes for factorial repeated-measures ANOVA Reporting the results from factorial repeated-measures ANOVA What to do when assumptions are violated in repeated-measures ANOVA What have I discovered about statistics?

11 xiv OISCOVERING STATISTICS USING SPSS Online tutoriais 14 Mixed design ANOVA (GLM 5) What will this chapter tell me? ed Mixed designs What do men and women look for in a partner? Mixed ANOVA on SPSS The main analysis Other options Output for mixed factorial ANOVA: main The main effect of gender The main effect of looks The main effect of charisma The interaction between gender and looks The interaction between gender and charisma The interaction between attractiveness and charisma The interaction between looks, charisma and Calculating effect Reporting the results of mixed ANOVA What to do when assumptions are violated in mixed What have I discovered about statistics? Online tutoriais Non-parametric tests What will this chapter tell me? ed When to use non-parametric tests ed Comparing two independent conditions: the Wilcoxon rank-sum test and Mann-Whitney test ed Theory Inputting data and provisional analysis ed Running the analysis ed Output from the Mann-Whitney test ed Calculating an etfect size Writing the results ed Comparing two related conditions: the Wilcoxon signed-rank test ed Theory of the Wilcoxon signed-rank test Running the analysis ed Output for the ecstasy group ed Output for the alcohol group ed Calculating an effect size Writing the results ed

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

13 xvi DISCDVERING STATISTICS USING SPSS A Reporting Following Univariate linai up ANOVA results MANOVA from MANOVA with discriminant analysis? analysis Exploratory What When Reliability Discovering Research Running How Factors Graphical Choosing Communality Theory Options Summary Mathematical Improving Before Rotation Scores Preliminary Measures fleliability Interpreting will extraction: scores you rotation behind report use this analysisa of example interpretation: begin Cronbach's the method output factors reliability analysis representation chapter principai vs. output eigenvalues principai from SPSS analysis tell 01 a component factor (some SPSS me? lactors 01and rotation lactors <D <D cautionary the scree analysis tales plot... )

14 CONTENTS xvii What have I discovered about statistics? CategoricaL data What will this chapter tell me? ed Analysing categorical data ed Theory of analysing categorical data ed Pearson's chi-square test ed Fisher's exact test ed The Iikelihood ratio Yates' correction Assumptions of the chi-square test ed Doing chi-square on SPSS ed Entering data raw scores ed Entering data weight cases ed Running the analysis ed Output for the chi-square test ed Breaking down a significant chi-square test with standardized residuals Calculating an effect size Reporting the results of chi-square ed Several categorical variables: loglinear analysis Chi-square as Loglinear analysis Assumptions in loglinear analysis Loglinear analysis using SPSS Initial considerations The loglinear analysis Output from loglinear analysis Following up loglinear analysis Effect sizes in loglinear analysis Reporting the results of loglinear analysis What have I discovered about statistics? ed MuLtiLeveLLinear models What will this chapter tell me? ed Hierarchical data The ij;1traclasscorrelation Benefits of multilevel modeis Theory of multilevellinear modeis

15 xviii DISCOVERING STATISTICS USING SPSS An example Fixed and random The multilevel Assessing the fit and comparing multilevel Types of covariance Some practical Sampie size and Centring Multilevel modelling on Entering the data Ignoring the data structure ANOVA Ignoring the data structure ANCOVA Factoring in the data structure: random Factoring in the data structure: random intercepts and Adding an interaction to the Growth Growth curves An example: the honeymoon period Restructuring the Running a growth model on Further How to report a multilevel What have I discovered about statistics? Epilogue Glossary Appendix A.l. A.2. A.3. A.4. Table of the standard normal distribution Critical values of the t-distribution Critical values of the F-distribution Critical values of the chi-square distribution References Index

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