9 discovering statistics using SPSS

DISCOVERING STATISTICS USING Spss T H I R D E D I T I O N (and sex and drugs and rock ’n’ roll) ANDY FIELD © Andy Field 2009 First edition published 2000 Second edition published 2005 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act, 1988, this publication may be reproduced, stored or transmitted in any form, or by any means, only with the prior permission in writing of the publishers, or in the case of reprographic reproduction, in accordance with the terms of licences issued by the Copyright Licensing Agency Enquiries concerning reproduction outside those terms should be sent to the publishers SAGE Publications Ltd Oliver’s Yard 55 City Road London EC1Y 1SP SAGE Publications Inc 2455 Teller Road Thousand Oaks, California 91320 SAGE Publications India Pvt Ltd B 1/I Mohan Cooperative Industrial Area Mathura Road New Delhi 110 044 SAGE Publications Asia-Pacific Pte Ltd 33 Pekin Street #02-01 Far East Square Singapore 048763 Library of Congress Control Number: 2008930166 British Library Cataloguing in Publication data A catalogue record for this book is available from the British Library ISBN 978-1-84787-906-6 ISBN 978-1-84787-907-3 Typeset by C&M Digitals (P) Ltd, Chennai, India Printed by Oriental Press, Dubai Printed on paper from sustainable resources CONTENTS Preface xix How to use this book xxiv Acknowledgements xxviii Dedication xxx Symbols used in this book xxxi Some maths revision xxxiii Why is my evil lecturer forcing me to learn statistics? 1.1 1.2 1.3 1.4 1.5 What will this chapter tell me? What the hell am I doing here? I don’t belong here 1.2.1 The research process 1.5.1 Variables 1.5.2 Measurement error 1.5.3 Validity and reliability 1.6 1.7 Initial observation: finding something that needs explaining Generating theories and testing them Data collection 1: what to measure 1 1 Data collection 2: how to measure 1.6.1 Correlational research methods 1.6.2 Experimental research methods 1.6.3 Randomization Analysing data 1 1.7.1 Frequency distributions 1.7.2 The centre of a distribution 1.7.3 The dispersion in a distribution 1.7.4 Using a frequency distribution to go beyond the data 1.7.5 Fitting statistical models to the data What have I discovered about statistics? Key terms that I’ve discovered Smart Alex’s stats quiz Further reading Interesting real research 1 1 3 7 10 11 12 12 13 17 18 18 20 23 24 26 28 28 29 29 30 vi D I S C O VE R I N G STAT I ST I C S US I N G S PSS 2 Everything you ever wanted to know about statistics (well, sort of) 2.1 2.2 2.3 2.4 What will this chapter tell me? Building statistical models Populations and samples Simple statistical models 1 2.4.1 The mean: a very simple statistical model 31 32 34 35 35 2.4.2 Assessing the fit of the mean: sums of squares, variance and standard 2.4.3 Expressing the mean as a model deviations 2.5 Going beyond the data 2.5.1 The standard error 2.5.2 Confidence intervals 2.6 2.6.1 Test statistics 2.6.2 One- and two-tailed tests 2.6.3 Type I and Type II errors 2.6.4 Effect sizes 2.6.5 Statistical power The spss environment 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 Using statistical models to test research questions 2 What have I discovered about statistics? Key terms that I’ve discovered Smart Alex’s stats quiz Further reading Interesting real research 3.4.2 The ‘Variable View’ 61 62 62 63 69 70 77 78 81 82 83 84 The spss viewer The spss SmartViewer The syntax window Saving files Retrieving a file What have I discovered about statistics? 85 Key terms that I’ve discovered   85 Smart Alex’s tasks 85 Further reading 86 Online tutorials 86 Exploring data with graphs 4.1 4.2 59 59 59 60 60 3.4.1 Entering data into the data editor 35 38 40 40 43 48 52 54 55 56 58 61 What will this chapter tell me? Versions of spss Getting started The data editor 3.4.3 Missing values 31 What will this chapter tell me? The art of presenting data 87 4.2.1 What makes a good graph? 4.2.2 Lies, damned lies, and … erm … graphs 87 88 88 90 vii C ontents 4.3 4.4 4.5 4.6 4.7 4.8 The spss Chart Builder Histograms: a good way to spot obvious problems Boxplots (box–whisker diagrams) Graphing means: bar charts and error bars 4.6.1 4.6.2 4.6.3 4.6.4 4.6.5 4.9 Exploring assumptions 5.1 5.2 5.3 5.4 5.5 5.6 5.7 Simple scatterplot Grouped scatterplot Simple and grouped 3-D scatterplots Matrix scatterplot Simple dot plot or density plot Drop-line graph Simple bar charts for independent means Clustered bar charts for independent means Simple bar charts for related means Clustered bar charts for related means Clustered bar charts for ‘mixed’ designs Line charts Graphing relationships: the scatterplot 4.8.1 4.8.2 4.8.3 4.8.4 4.8.5 4.8.6 Editing graphs What have I discovered about statistics? Key terms that I’ve discovered Smart Alex’s tasks Further reading Online tutorial Interesting real research 129 130 130 130 130 130 131 What will this chapter tell me? What are assumptions? Assumptions of parametric data The assumption of normality 5.4.1 Oh no, it’s that pesky frequency distribution again: checking normality visually 5.4.2 Quantifying normality with numbers 5.4.3 Exploring groups of data Testing whether a distribution is normal 5.5.1 Doing the Kolmogorov–Smirnov test on spss 5.5.2 Output from the explore procedure 5.5.3 Reporting the K–S test Testing for homogeneity of variance 5.6.1 Levene’s test 5.6.2 Reporting Levene’s test 1 1 Correcting problems in the data 5.7.1 5.7.2 5.7.3 5.7.4 91 93 99 103 105 107 109 111 113 115 116 117 119 121 123 125 126 126 Dealing with outliers Dealing with non-normality and unequal variances Transforming the data using spss When it all goes horribly wrong 131 132 132 133 134 136 140 144 145 146 148 149 150 152 153 153 153 156 162 What have I discovered about statistics? 164 Key terms that I’ve discovered   164 Smart Alex’s tasks 165 Online tutorial 165 Further reading 165 viii D I S C O VE R I N G STAT I ST I C S US I N G S PSS Correlation 6.1 6.2 6.3 166 What will this chapter tell me? Looking at relationships How we measure relationships? 6.3.1 A detour into the murky world of covariance 6.3.2 Standardization and the correlation coefficient 6.3.3 The significance of the correlation coefficient 6.3.4 Confidence intervals for r 6.4 6.5 6.6 Data entry for correlation analysis using spss Bivariate correlation 1 6.5.2 Pearson’s correlation coefficient 6.5.3 Spearman’s correlation coefficient 6.5.4 Kendall’s tau (non-parametric) 1 6.5.5 Biserial and point–biserial correlations 6.6.3 Semi-partial (or part) correlations 6.8 6.9 6.6.2 Partial correlation using spss 6.5.1 General procedure for running correlations on spss 6.6.1 The theory behind part and partial correlation 6.7 6.3.5 A word of warning about interpretation: causality Partial correlation 166 167 167 167 169 171 172 173 174 175 175 177 179 181 182 186 186 188 190 191 191 191 192 193 Comparing correlations 2 6.7.1 Comparing independent rs 3 6.7.2 Comparing dependent rs Calculating the effect size How to report correlation coefficents What have I discovered about statistics? Key terms that I’ve discovered Smart Alex’s tasks Further reading Online tutorial Interesting real research 195 195 195 196 196 196 Regression 7.1 7.2 7.3 7.4 7.5 7.6 197 What will this chapter tell me? An introduction to regression 7.2.1 7.2.2 7.2.3 7.2.4 Some important information about straight lines The method of least squares Assessing the goodness of fit: sums of squares, R and R2 Assessing individual predictors Doing simple regression on spss Interpreting a simple regression 7.4.1 Overall fit of the model 7.4.2 Model parameters 7.4.3 Using the model 1 Multiple regression: the basics 7.5.1 An example of a multiple regression model 7.5.2 Sums of squares, R and R2 7.5.3 Methods of regression How accurate is my regression model? 197 198 199 200 201 204 205 206 206 207 208 209 210 211 212 214 ix C ontents 7.7 7.8 How to multiple regression using spss 7.7.1 7.7.2 7.7.3 7.7.4 7.7.5 7.7.6 Interpreting multiple regression 7.8.1 7.8.2 7.8.3 7.8.4 7.8.5 7.8.6 7.8.7 2 214 220 225 225 225 227 229 230 231 233 233 234 237 241 241 244 247 251 252 253 253 256 Some things to think about before the analysis Main options Statistics Regression plots Saving regression diagnostics Further options 2 Descriptives Summary of model Model parameters Excluded variables Assessing the assumption of no multicollinearity Casewise diagnostics Checking assumptions 2 7.9 What if I violate an assumption? 7.10 How to report multiple regression 7.11 Categorical predictors and multiple regression 7.6.1 Assessing the regression model I: diagnostics 7.6.2 Assessing the regression model II: generalization 7.11.1 Dummy coding 7.11.2 Spss output for dummy variables 3 What have I discovered about statistics? Key terms that I’ve discovered Smart Alex’s tasks Further reading Online tutorial Interesting real research 261 261 262 263 263 263 Logistic regression 8.1 8.2 8.3 8.4 8.5 8.6 264 What will this chapter tell me? Background to logistic regression What are the principles behind logistic regression? 8.3.1 8.3.2 8.3.3 8.3.4 8.3.5 Assumptions and things that can go wrong 8.4.1 8.4.2 8.4.3 8.4.4 Assessing the model: the log-likelihood statistic Assessing the model: R and R2 Assessing the contribution of predictors: the Wald statistic The odds ratio: Exp(B) Methods of logistic regression Assumptions Incomplete information from the predictors Complete separation Overdispersion Binary logistic regression: an example that will make you feel eel 8.5.1 8.5.2 8.5.3 8.5.4 8.5.5 The main analysis Method of regression Categorical predictors Obtaining residuals Further options Interpreting logistic regression 264 265 265 267 268 269 270 271 273 273 273 274 276 277 278 279 279 280 281 282 x D I S C O VE R I N G STAT I ST I C S US I N G S PSS 8.7 8.8 8.9 8.6.1 The initial model 8.6.3 Listing predicted probabilities 8.6.4 Interpreting residuals 8.6.5 Calculating the effect size How to report logistic regression Testing assumptions: another example 8.8.1 Testing for linearity of the logit 8.8.2 Testing for multicollinearity Predicting several categories: multinomial logistic regression 8.9.1 Running multinomial logistic regression in spss 8.9.2 Statistics 282 284 291 292 294 294 294 296 297 300 301 304 305 306 312 8.6.2 Step 1: intervention 3 8.9.3 Other options 8.9.4 Interpreting the multinomial logistic regression output 8.9.5 Reporting the results What have I discovered about statistics? Key terms that I’ve discovered Smart Alex’s tasks Further reading Online tutorial Interesting real research 313 313 313 315 315 315 Comparing two means 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 316 What will this chapter tell me? Looking at differences 1 9.2.1 A problem with error bar graphs of repeated-measures designs 9.2.2 Step 1: calculate the mean for each participant 9.2.3 Step 2: calculate the grand mean 9.2.4 Step 3: calculate the adjustment factor 9.2.5 Step 4: create adjusted values for each variable The t-test 9.3.1 Rationale for the t-test 9.3.2 Assumptions of the t-test The dependent t-test 1 9.4.1 Sampling distributions and the standard error 9.4.2 The dependent t-test equation explained 1 9.4.3 The dependent t-test and the assumption of normality 9.4.4 Dependent t-tests using spss 9.4.5 Output from the dependent t-test 9.4.6 Calculating the effect size 9.4.7 Reporting the dependent t-test The independent t-test 1 9.5.1 The independent t-test equation explained 9.5.2 The independent t-test using spss 9.5.3 Output from the independent t-test 9.5.4 Calculating the effect size 9.5.5 Reporting the independent t-test Between groups or repeated measures? The t-test as a general linear model What if my data are not normally distributed? 316 317 317 320 320 322 323 324 325 326 326 327 327 329 329 330 332 333 334 334 337 339 341 341 342 342 344 xi C ontents What have I discovered about statistics? Key terms that I’ve discovered Smart Alex’s task Further reading Online tutorial Interesting real research 345 345 346 346 346 346 10 Comparing several means: anova (glm 1) 10.1 What will this chapter tell me? 10.2 The theory behind anova 10.2.2 10.2.3 10.2.4 10.2.5 10.2.6 10.2.7 10.2.8 10.2.9 Inflated error rates Interpreting f Anova as regression Logic of the f-ratio Total sum of squares (sst) Model sum of squares (ssm) Mean squares The F-ratio 2 10.2.12 Post hoc procedures Planned comparisons using spss Post hoc tests in spss 10.4.1 Output for the main analysis 2 Options 10.4.3 10.3.3 10.4.2 10.4 Output from one-way anova 10.2.11 Planned contrasts 10.3.2 10.2.10 Assumptions of anova 10.3.1 Residual sum of squares (ssr) 10.3 Running one-way anova on spss 10.2.1 347 2 Output for planned comparisons Output for post hoc tests 2 10.5 Calculating the effect size 10.6 Reporting results from one-way independent anova 10.7 Violations of assumptions in one-way independent anova What have I discovered about statistics? Key terms that I’ve discovered Smart Alex’s tasks Further reading Online tutorials Interesting real research 392 392 393 394 394 394 11 Analysis of covariance, ancova (glm 2) 11.1 What will this chapter tell me? 11.2 What is ancova? 11.3 Assumptions and issues in ancova 11.3.1 11.3.2 Homogeneity of regression slopes 11.4.1 Inputting data 395 Independence of the covariate and treatment effect 11.4 Conducting ancova on spss 3 11.4.2 Initial considerations: testing the independence of the independent variable and covariate 347 348 348 349 349 354 356 356 357 358 358 359 360 372 375 376 378 379 381 381 384 385 389 390 391 395 396 397 397 399 399 399 400 xii D I S C O VE R I N G STAT I ST I C S US I N G S PSS 11.6 11.7 11.8 11.9 11.10 11.5.1 11.5.2 11.5.3 11.5.4 401 401 404 404 405 407 408 408 413 415 417 418 11.5 Interpreting the output from ancova 11.4.3 The main analysis 11.4.4 Contrasts and other options What happens when the covariate is excluded? The main analysis Contrasts Interpreting the covariate 2 Ancova run as a multiple regression Testing the assumption of homogeneity of regression slopes Calculating the effect size Reporting results What to when assumptions are violated in ancova What have I discovered about statistics? Key terms that I’ve discovered Smart Alex’s tasks Further reading Online tutorials Interesting real research 418 419 419 420 420 420 12 Factorial anova (glm 3) 12.1 What will this chapter tell me? 12.2 Theory of factorial anova (between-groups) 12.2.1 12.2.2 12.2.3 12.2.4 12.2.5 12.2.6 Factorial designs 12.3.1 12.3.2 12.3.3 12.3.4 12.3.5 Total sums of squares (sst) 12.4.1 12.4.2 12.4.3 2 The residual sum of squares (ssr) 2 The model sum of squares (ssm) The F-ratios Entering the data and accessing the main dialog box Graphing interactions Contrasts 2 Output for the preliminary analysis Levene’s test 2 The main anova table 12.4.4 Contrasts Post hoc tests Options 12.4 Output from factorial anova An example with two independent variables 12.3 Factorial anova using spss 421 12.4.5 Simple effects analysis 12.4.6 Post hoc analysis 12.5 12.6 12.7 12.8 12.9 Interpreting interaction graphs Calculating effect sizes Reporting the results of two-way anova Factorial anova as regression What to when assumptions are violated in factorial anova What have I discovered about statistics? Key terms that I’ve discovered Smart Alex’s tasks 421 422 422 423 424 426 428 429 430 430 432 432 434 434 435 435 436 436 439 440 441 443 446 448 450 454 454 455 455 808 D I S C O VE R I N G STAT I ST I C S US I N G S PSS A.4.  Critical values of the chi-square distribution p p df 0.05 0.01 df  1   3.84   6.63    25 37.65 44.31  2   5.99   9.21    26 38.89 45.64  3   7.81 11.34    27 40.11 46.96  4   9.49 13.28    28 41.34 48.28  5 11.07 15.09    29 42.56 49.59  6 12.59 16.81    30 43.77 50.89  7 14.07 18.48    35 49.80 57.34  8 15.51 20.09    40 55.76 63.69  9 16.92 21.67    45 61.66 69.96 10 18.31 23.21    50 67.50 76.15 11 19.68 24.72    60 79.08 88.38 12 21.03 26.22    70 90.53 100.43 13 22.36 27.69    80 101.88 112.33 14 23.68 29.14    90 113.15 124.12 15 25.00 30.58   100 124.34 135.81 16 26.30 32.00   200 233.99 249.45 17 27.59 33.41   300 341.40 359.91 18 28.87 34.81   400 447.63 468.72 19 30.14 36.19   500 553.13 576.49 20 31.41 37.57   600 658.09 683.52 21 32.67 38.93   700 762.66 789.97 22 33.92 40.29   800 866.91 895.98 23 35.17 41.64   900 970.90 1001.63 24 36.42 42.98 1000 1074.68 1106.97 All values computed by the author using SPSS 0.05 0.01 References Agresti, A., & Finlay, B (1986) Statistical methods for the social sciences (2nd ed.) San Francisco: Dellen Algina, J., & Olejnik, S F (1984) Implementing the Welch-James procedure with factorial designs Educational and Psychological Measurement, 44, 39–48 Arrindell, W A., & van der Ende, J (1985) An empirical test of the utility of the observer-to-variables ratio in factor and components analysis Applied Psychological Measurement, 9, 165–178 Baguley, T (2004) Understanding statistical power in the context of applied research Applied Ergonomics, 35(2), 73–80 Bale, C., Morrison, R., & Caryl, P G (2006) Chat-up lines as male sexual displays Personality and Individual Differences, 40(4), 655–664 Bargman, R E (1970) Interpretation and use of a generalized discriminant function In R C Bose et al (eds.), Essays in probability and statistics Chapel Hill: University of North Carolina Press Barnard, G A (1963) Ronald Aylmer Fisher, 1890–1962: Fisher’s contributions to mathematical statistics Journal of the Royal Statistical Society, Series A (General), 126, 162–166 Barnett, V., & Lewis, T (1978) Outliers in statistical data New York: Wiley Beckham, A S (1929) Is the Negro happy? A psychological analysis Journal of Abnormal and Social Psychology, 24, 186–190 Belsey, D A., Kuh, E., & Welsch, R (1980) Regression diagnostics: Identifying influential data and sources of collinearity New York: Wiley Bemelman, M., & Hammacher, E R (2005) Rectal impalement by pirate ship: A case report Injury Extra, 36, 508–510 Berger, J O (2003) Could Fisher, Jeffreys and Neyman have agreed on testing? Statistical Science, 18(1), 1–12 Berry, W D (1993) Understanding regression assumptions Sage university paper series on quantitative applications in the social sciences, 07-092 Newbury Park, CA: Sage Berry, W D., & Feldman, S (1985) Multiple regression in practice Sage university paper series on quantitative applications in the social sciences, 07-050 Beverly Hills, CA: Sage Board, B J., & Fritzon, K (2005) Disordered personalities at work Psychology, Crime & Law, 11(1), 17–32 Bock, R D (1975) Multivariate statistical methods in behavioural research New York: McGraw-Hill Boik, R J (1981) A priori tests in repeated measures designs: Effects of nonsphericity Psychometrika, 46(3), 241–255 Bowerman, B L., & O’Connell, R T (1990) Linear statistical models: An applied approach (2nd ed.) Belmont, CA: Duxbury Bray, J H., & Maxwell, S E (1985) Multivariate analysis of variance Sage university paper series on quantitative applications in the social sciences, 07-054 Newbury Park, CA: Sage Brown, M B., & Forsythe, A B (1974) The small sample behaviour of some statistics which test the equality of several means Technometrics, 16, 129–132 Brown, W (1910) Some experimental results in the correlation of mental abilities British Journal of Psychology, 3, 296–322 Budescu, D V (1982) The power of the F test in normal populations with heterogeneous variances Educational and Psychological Measurement, 42, 609–616 Budescu, D V., & Appelbaum, M I (1981) Variance stabilizing transformations and the power of the F test Journal of Educational Statistics, 6(1), 55–74 Cattell, R B (1966a) The scientific analysis of personality Chicago: Aldine Cattell, R B (1966b) The scree test for the number of factors Multivariate Behavioral Research, 1, 245–276 Çetinkaya, H., & Domjan, M (2006) Sexual fetishism in a quail (Coturnix japonica) model system: Test of reproductive success Journal of Comparative Psychology, 120(4), 427–432 Chamorro-Premuzic, T., Furnham, A., Christopher, A N., Garwood, J., & Martin, N (2008) Birds of a feather: Students’ preferences for lecturers’ personalities as predicted by their own personality and learning approaches Personality and Individual Differences, 44, 965–976 Chen, P Y., & Popovich, P M (2002) Correlation: Parametric 809 810 and nonparametric measures Thousand Oaks, CA: Sage Clarke, D L., Buccimazza, I., Anderson, F A., & Thomson, S R (2005) Colorectal foreign bodies Colorectal Disease, 7(1), 98–103 Cliff, N (1987) Analyzing multivariate data New York: Harcourt Brace Jovanovich Cohen, J (1968) Multiple regression as a general dataanalytic system Psychological Bulletin, 70(6), 426–443 Cohen, J (1988) Statistical power analysis for the behavioural sciences (2nd ed.) New York: Academic Press Cohen, J (1990) Things I have learned (so far) American Psychologist, 45(12), 1304–1312 Cohen, J (1992) A power primer Psychological Bulletin, 112(1), 155–159 Cohen, J (1994) The Earth is round (p < 05) American Psychologist, 49(12), 997–1003 Cole, D A., Maxwell, S E., Arvey, R., & Salas, E (1994) How the power of MANOVA can both increase and decrease as a function of the intercorrelations among the dependent variables Psychological Bulletin, 115(3), 465–474 Collier, R O., Baker, F B., Mandeville, G K., & Hayes, T F (1967) Estimates of test size for several test procedures based on conventional variance ratios in the repeated measures design Psychometrika, 32(2), 339–352 Comrey, A L., & Lee, H B (1992) A first course in factor analysis (2nd ed.) Hillsdale, NJ: Erlbaum Cook, R D., & Weisberg, S (1982) Residuals and influence in regression New York: Chapman & Hall Cook, S A., Rosser, R., & Salmon, P (2006) Is cosmetic surgery an effective psychotherapeutic intervention? A systematic review of the evidence Journal of Plastic, Reconstructive & Aesthetic Surgery, 59, 1133–1151 Cook, S A., Rossera, R., Toone, H., James, M I., & Salmon, P (2006) The psychological D I S C O VE R I N G STAT I ST I C S US I N G S PSS and social characteristics of patients referred for NHS cosmetic surgery: Quantifying clinical need Journal of Plastic, Reconstructive & Aesthetic Surgery 59, 54–64 Cooper, C L., Sloan, S J., & Williams, S (1988) Occupational Stress Indicator Management Guide Windsor, UK: NFER-Nelson Cooper, M., O’Donnell, D., Caryl, P G., Morrison, R., & Bale, C (2007) Chat-up lines as male displays: Effects of content, sex, and personality Personality and Individual Differences, 43(5), 1075–1085 Cortina, J M (1993) What is coefficient alpha? An examination of theory and applications Journal of Applied Psychology, 78, 98–104 Cox, D R., & Snell, D J (1989) The analysis of binary data (2nd ed.) London: Chapman & Hall Cronbach, L J (1951) Coefficient alpha and the internal structure of tests Psychometrika, 16, 297–334 Cronbach, L J (1957) The two disciplines of scientific psychology American Psychologist, 12, 671–684 Dalgaard, P (2002) Introductory Statistics with R New York: Springer Davey, G C L., Startup, H M., Zara, A., MacDonald, C B., & Field, A P (2003) Perseveration of checking thoughts and moodas-input hypothesis Journal of Behavior Therapy & Experimental Psychiatry, 34, 141–160 Davidson, M L (1972) Univariate versus multivariate tests in repeated-measures experiments Psychological Bulletin, 77, 446–452 DeCarlo, L T (1997) On the meaning and use of kurtosis Psychological Methods, 2(3), 292–307 Domjan, M., Blesbois, E., & Williams, J (1998) The adaptive significance of sexual conditioning: Pavlovian control of sperm release Psychological Science, 9(5), 411–415 Donaldson, T S (1968) Robustness of the F-test to errors of both kinds and the correlation between the numerator and denominator of the F-ratio Journal of the American Statistical Association, 63, 660–676 Dunlap, W P., Cortina, J M., Vaslow, J B., & Burke, M J (1996) Meta-analysis of experiments with matched groups or repeated measures designs Psychological Methods, 1(2), 170–177 Dunteman, G E (1989) Principal components analysis Sage university paper series on quantitative applications in the social sciences, 07-069 Newbury Park, CA: Sage Durbin, J., & Watson, G S (1951) Testing for serial correlation in least squares regression, II Biometrika, 30, 159–178 Easterlin, R A (2003) Explaining Happiness Proceedings of the National Academy of Sciences., 100(19), 11176–11183 Efron, B., & Tibshirani, R (1993) An introduction to the bootstrap: Chapman and Hall Eriksson, S.-G., Beckham, D., & Vassell, D (2004) Why are the English so shit at penalties? A review Journal of Sporting Ineptitude, 31, 231–1072 Erlebacher, A (1977) Design and analysis of experiments contrasting the within- and between-subjects manipulations of the independent variable Psychological Bulletin, 84, 212–219 Eysenck, H J (1953) The structure of human personality New York: Wiley Fesmire, F M (1988) Termination of intractable hiccups with digital rectal massage Annals of Emergency Medicine, 17(8), 872 Field, A P (1998) A bluffer’s guide to sphericity Newsletter of the mathematical, statistical and computing section of the British Psychological Society, 6(1)13–22 Field, A P (2000) Discovering statistics using SPSS for Windows: Advanced techniques for the beginner London: Sage 811 References Field, A P (2001) Meta-analysis of correlation coefficients: A Monte Carlo comparison of fixedand random-effects methods Psychological Methods, 6(2), 161–180 Field, A P (2005a) Intraclass correlation In B Everitt & D C Howell (eds.), Encyclopedia of Statistics in Behavioral Science (Vol 2, pp 948–954) New York: Wiley Field, A P (2005b) Is the metaanalysis of correlation coefficients accurate when population correlations vary? Psychological Methods, 10(4), 444–467 Field, A P (2005c) Learning to like (and dislike): Associative learning of preferences In A J Wills (ed.), New Directions in Human Associative Learning (pp 221–252) Mahwah, NJ: LEA Field, A P (2005d) Sir Ronald Aylmer Fisher In B S Everitt & D C Howell (eds.), Encyclopedia of Statistics in Behavioral Science (Vol 2, pp 658–659) Chichester: Wiley Field, A P (2006) The behavioral inhibition system and the verbal information pathway to children’s fears Journal of Abnormal Psychology, 115(4), 742–752 Field, A P (2009) Discovering statistics using SPSS (and sex and drugs and rock’ n’ roll) (3rd ed.) London: Sage Field, A P., & Davey, G C L (1999) Reevaluating evaluative conditioning: A nonassociative explanation of conditioning effects in the visual evaluative conditioning paradigm Journal of Experimental Psychology – Animal Behavior Processes, 25(2), 211–224 Field, A P., & Hole, G J (2003) How to design and report experiments London: Sage Field, A P., & Moore, A C (2005) Dissociating the effects of attention and contingency awareness on evaluative conditioning effects in the visual paradigm Cognition and Emotion, 19(2), 217–243 Fisher, R A (1921) On the probable error of a coefficient of correlation deduced from a small sample Metron, 1, 3–32 Fisher, R A (1922) On the interpretation of chi square from contingency tables, and the calculation of P Journal of the Royal Statistical Society, 85, 87–94 Fisher, R A (1925) Statistical methods for research workers Edinburgh: Oliver & Boyd Fisher, R A (1925/1991) Statistical methods, experimental design, and scientific inference Oxford: Oxford University Press (This reference is for the 1991 reprint.) Fisher, R A (1956) Statistical methods and scientific inference New York: Hafner Flanagen, J C (1937) A proposed procedure for increasing the efficiency of objective tests Journal of Educational Psychology, 28, 17–21 Friedman, M (1937) The use of ranks to avoid the assumption of normality implicit in the analysis of variance Journal of the American Statistical Association, 32, 675–701 Gallup, G G J., Burch, R L., Zappieri, M L., Parvez, R., Stockwell, M., & Davis, J A (2003) The human penis as a semen displacement device Evolution and Human Behavior, 24, 277–289 Games, P A (1983) Curvilinear transformations of the dependent variable Psychological Bulletin, 93(2), 382–387 Games, P A (1984) Data transformations, power, and skew: A rebuttal to Levine and Dunlap Psychological Bulletin, 95(2), 345–347 Games, P A., & Lucas, P A (1966) Power of the analysis of variance of independent groups on non-normal and normally transformed data Educational and Psychological Measurement, 26, 311–327 Girden, E R (1992) ANOVA: Repeated measures Sage university paper series on quantitative applications in the social sciences, 07-084 Newbury Park, CA: Sage Glass, G V (1966) Testing homogeneity of variances American Educational Research Journal, 3(3), 187–190 Glass, G V., Peckham, P D., & Sanders, J R (1972) Consequences of failure to meet assumptions underlying the fixed effects analyses of variance and covariance Review of Educational Research, 42(3), 237–288 Graham, J M., Guthrie, A C., & Thompson, B (2003) Consequences of not interpreting structure coefficients in published CFA research: A reminder Structural Equation Modeling, 10(1), 142–153 Grayson, D (2004) Some myths and legends in quantitative psychology Understanding Statistics, 3(1), 101–134 Green, S B (1991) How many subjects does it take to a regression analysis? Multivariate Behavioral Research, 26, 499–510 Greenhouse, S W., & Geisser, S (1959) On methods in the analysis of profile data Psychometrika, 24, 95–112 Guadagnoli, E., & Velicer, W F (1988) Relation of sample size to the stability of component patterns Psychological Bulletin, 103(2), 265–275 Haitovsky, Y (1969) Multicollinearity in regression analysis: A comment Review of Economics and Statistics, 51(4), 486–489 Hakstian, A R., Roed, J C., & Lind, J C (1979) Two-sample T2 procedure and the assumption of homogeneous covariance matrices Psychological Bulletin, 86, 1255–1263 Halekoh, U., & Højsgaard, S (2007) Overdispersion Retrieved March 18, 2007 from http://gbi agrsci.dk/statistics/courses/phd07/ material/Day7/overdispersionhandout.pdf Hardy, M A (1993) Regression with dummy variables Sage university 812 paper series on quantitative applications in the social sciences, 07-093 Newbury Park, CA: Sage Harman, B H (1976) Modern factor analysis (3rd ed., rev.) Chicago: University of Chicago Press Harris, R J (1975) A primer of multivariate statistics New York: Academic Press Hill, C., Abraham, C., & Wright, D B (2007) Can theory-based messages in combination with cognitive prompts promote exercise in classroom settings? Social Science & Medicine, 65, 1049–1058 Hoaglin, D., & Welsch, R (1978) The hat matrix in regression and ANOVA American Statistician, 32, 17–22 Hoddle, G., Batty, D., & Ince, P (1998) How not to take penalties in important soccer matches Journal of Cretinous Behaviour, 1, 1–2 Horn, J L (1965) A rationale and test for the number of factors in factor analysis Psychometrika, 30, 179–185 Hosmer, D W., & Lemeshow, S (1989) Applied logistic regression New York: Wiley Howell, D C (1997) Statistical methods for psychology (4th ed.) Belmont, CA: Duxbury Howell, D C (2006) Statistical methods for psychology (6th ed.) Belmont, CA: Thomson Huberty, C J., & Morris, J D (1989) Multivariate analysis versus multiple univariate analysis Psychological Bulletin, 105(2), 302–308 Hughes, J P., Marice, H P., & Gathright, J B (1976) Method of removing a hollow object from the rectum Diseases of the Colon & Rectum, 19(1), 44–45 Hume, D (1739–40) A treatise of human nature (ed L A Selby-Bigge) Oxford: Clarendon Press, 1965 Hume, D (1748) An enquiry concerning human understanding Chicago: Open Court, 1927 Hutcheson, G., & Sofroniou, N (1999) The multivariate social scientist London: Sage D I S C O VE R I N G STAT I ST I C S US I N G S PSS Huynh, H., & Feldt, L S (1976) Estimation of the Box correction for degrees of freedom from sample data in randomised block and split-plot designs Journal of Educational Statistics, 1(1), 69–82 Iverson, G R., & Norpoth, H (1987) ANOVA (2nd ed.) Sage University series on quantitative applications in the social sciences, 07-001 Newbury Park, CA: Sage Jackson, S., & Brashers, D E (1994) Random factors in ANOVA Sage university paper series on quantitative applications in the social sciences, 07-098 Thousand Oaks, CA: Sage Jolliffe, I T (1972) Discarding variables in a principal component analysis, I: Artificial data Applied Statistics, 21, 160–173 Jolliffe, I T (1986) Principal component analysis New York: Springer Jonckheere, A R (1954) A distribution-free k-sample test against ordered alternatives Biometrika, 41, 133–145 Kahneman, D., & Krueger, A B (2006) Developments in the measurement of subjective wellbeing Journal of Economic Perspectives, 20(1), 3–24 Kaiser, H F (1960) The application of electronic computers to factor analysis Educational and Psychological Measurement, 20, 141–151 Kaiser, H F (1970) A secondgeneration little jiffy Psychometrika, 35, 401–415 Kaiser, H F (1974) An index of factorial simplicity Psychometrika, 39, 31–36 Kass, R A., & Tinsley, H E A (1979) Factor analysis Journal of Leisure Research, 11, 120–138 Kellett, S., Clarke, S., & McGill, P (2008) Outcomes from psychological assessment regarding recommendations for cosmetic surgery Journal of Plastic, Reconstructive & Aesthetic Surgery, 61, 512–517 Keselman, H J., & Keselman, J C (1988) Repeated measures multiple comparison procedures: Effects of violating multisample sphericity in unbalanced designs Journal of Educational Statistics, 13(3), 215–226 Kirk, R E (1996) Practical significance: A concept whose time has come Educational and Psychological Measurement, 56(5), 746–759 Kline, P (1999) The handbook of psychological testing (2nd ed.) London: Routledge Klockars, A J., & Sax, G (1986) Multiple comparisons Sage university paper series on quantitative applications in the social sciences, 07-061 Newbury Park, CA: Sage Koot, V C M., Peeters, P H M., Granath, F., Grobbee, D E., & Nyren, O (2003) Total and cause specific mortality among Swedish women with cosmetic breast implants: Prospective study British Medical Journal, 326(7388), 527–528 Kreft, I G G., & De Leeuw, J (1998) Introducing multilevel modeling London: Sage Kreft, I G G., De Leew, J., & Aiken, L S (1995) The effect of different forms of centering in hierarchical linear models Multivariate Behavioral Research, 30, 1–21 Kruskal, W H., & Wallis, W A (1952) Use of ranks in onecriterion variance analysis Journal of the American Statistical Association, 47, 583–621 Lacourse, E., Claes, M., & Villeneuve, M (2001) Heavy metal music and adolescent suicidal risk Journal of Youth and Adolescence, 30(3), 321–332 Lehmann, E L (1993) The Fisher, Neyman–Pearson theories of testing hypotheses: One theory or two? Journal of the American Statistical Association, 88, 1242–1249 Lenth, R V (2001) Some practical guidelines for effective sample size determination American Statistician, 55(3), 187–193 Levene, H (1960) Robust tests for equality of variances In I Olkin, 813 References S G Ghurye, W Hoeffding, W G Madow, & H B Mann (eds.), Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling (pp 278–292) Stanford, CA: Stanford University Press Levine, D W., & Dunlap, W P (1982) Power of the F test with skewed data: Should one transform or not? Psychological Bulletin, 92(1), 272–280 Levine, D W., & Dunlap, W P (1983) Data transformation, power, and skew: A rejoinder to Games Psychological Bulletin, 93(3), 596–599 Lo, S F., Wong, S H., Leung, L S., Law, I C., & Yip, A W C (2004) Traumatic rectal perforation by an eel Surgery, 135(1), 110–111 Loftus, G R., & Masson, M E J (1994) Using confidence intervals in within-subject designs Psychonomic Bulletin and Review, 1(4), 476–490 Lord, F M (1967) A paradox in the interpretation of group comparisons Psychological Bulletin, 68(5), 304–305 Lord, F M (1969) Statistical adjustments when comparing preexisting groups Psychological Bulletin, 72(5), 336–337 Lunney, G H (1970) Using analysis of variance with a dichotomous dependent variable: An empirical study Journal of Educational Measurement, 7(4), 263–269 MacCallum, R C., Widaman, K F., Zhang, S., & Hong, S (1999) Sample size in factor analysis Psychological Methods, 4(1), 84–99 MacCallum, R C., Zhang, S., Preacher, K J., & Rucker, D D (2002) On the practice of dichotomization of quantitative variables Psychological Methods, 7(1), 19–40 Mann, H B., & Whitney, D R (1947) On a test of whether one of two random variables is stochastically larger than the other Annals of Mathematical Statistics, 18, 50–60 Marzillier, S L., & Davey, G C L (2005) Anxiety and disgust: Evidence for a unidirectional relationship Cognition and Emotion, 19(5), 729–75 Mather, K (1951) R A Fisher’s Statistical Methods for Research Workers: An appreciation Journal of the American Statistical Association, 46, 51–54 Matthews, R C., Domjan, M., Ramsey, M., & Crews, D (2007) Learning effects on sperm competition and reproductive fitness Psychological Science, 18(9), 758–762 Maxwell, S E (1980) Pairwise multiple comparisons in repeated measures designs Journal of Educational Statistics, 5(3), 269–287 Maxwell, S E., & Delaney, H D (1990) Designing experiments and analyzing data Belmont, CA: Wadsworth McDonald, P T., & Rosenthal, D (1977) An unusual foreign body in the rectum – A baseball: Report of a case Diseases of the Colon & Rectum, 20(1), 56–57 McGrath, R E., & Meyer, G J (2006) When effect sizes disagree: The case of r and d Psychological Methods, 11(4), 386–401 Menard, S (1995) Applied logistic regression analysis Sage university paper series on quantitative applications in the social sciences, 07-106 Thousand Oaks, CA: Sage Mendoza, J L., Toothaker, L E., & Crain, B R (1976) Necessary and sufficient conditions for F ratios in the L * J * K factorial design with two repeated factors Journal of the American Statistical Association, 71, 992–993 Mendoza, J L., Toothaker, L E., & Nicewander, W A (1974) A Monte Carlo comparison of the univariate and multivariate methods for the groups by trials repeated measures design Multivariate Behavioural Research, 9, 165–177 Miles, J N V., & Banyard, P (2007) Understanding and using statistics in psychology: a practical introduction London: Sage Miles, J N V & Shevlin, M (2001) Applying regression and correlation: a guide for students and researchers London: Sage Mill, J S (1865) A system of logic: ratiocinative and inductive London: Longmans, Green Miller, G A., & Chapman, J P (2001) Misunderstanding analysis of covariance Journal of Abnormal Psychology, 110(1), 40–48 Miller, G., Tybur, J M., & Jordan, B D (2007) Ovulatory cycle effects on tip earnings by lap dancers: economic evidence for human estrus? Evolution and Human Behavior, 28, 375–381 Mitzel, H C., & Games, P A (1981) Circularity and multiple comparisons in repeated measures designs British Journal of Mathematical and Statistical Psychology, 34, 253–259 Muris, P., Huijding, J., Mayer, B., & Hameetman, M (2008) A space odyssey: Experimental manipulation of threat perception and anxiety-related interpretation bias in children Child Psychiatry and Human Development 39(4), 469–480 Myers, R (1990) Classical and modern regression with applications (2nd ed.) Boston, MA: Duxbury Nagelkerke, N J D (1991) A note on a general definition of the coefficient of determination Biometrika, 78, 691–692 Namboodiri, K (1984) Matrix algebra: an introduction Sage university paper series on quantitative applications in the social sciences, 07-38 Beverly Hills, CA: Sage Nichols, L A., & Nicki, R (2004) Development of a psychometrically sound internet addiction scale: A preliminary step Psychology of Addictive Behaviors, 18(4), 381–384 Nunnally, J C (1978) Psychometric theory New York: McGraw-Hill 814 Nunnally, J C., & Bernstein, I H (1994) Psychometric Theory (3rd ed.) New York: McGraw-Hill O’Brien, M G., & Kaiser, M K (1985) MANOVA method for analyzing repeated measures designs: An extensive primer Psychological Bulletin, 97(2), 316–333 O’Connor, B P (2000) SPSS and SAS programs for determining the number of components using parallel analysis and Velicer’s MAP test Behavior Research Methods, Instrumentation, and Computers, 32, 396–402 Olson, C L (1974) Comparative robustness of six tests in multivariate analysis of variance Journal of the American Statistical Association, 69, 894–908 Olson, C L (1976) On choosing a test statistic in multivariate analysis of variance Psychological Bulletin, 83, 579–586 Olson, C L (1979) Practical considerations in choosing a MANOVA test statistic: A rejoinder to Stevens Psychological Bulletin, 86, 1350–1352 Pearson, E S., & Hartley, H O (1954) Biometrika tables for statisticians, volume I New York: Cambridge University Press Pearson, K (1894) Science and Monte Carlo The Fortnightly Review, 55, 183–193 Pearson, K (1900) On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling Philosophical Magazine, 50(5), 157–175 Pedhazur, E., & Schmelkin, L (1991) Measurement, design and analysis: an integrated approach Hillsdale, NJ: Erlbaum Plackett, R L (1983) Karl Pearson and the chi-squared test International Statistical Review, 51(1), 59–72 Ramsey, P H (1982) Empirical power of procedures for comparing two groups on p variables Journal of Educational Statistics, 7, 139–156 D I S C O VE R I N G STAT I ST I C S US I N G S PSS Raudenbush, S W., & Bryk, A S (2002) Hierarchical linear models (2nd ed.) Thousand Oaks, CA: Sage Rockwell, R C (1975) Assessment of multicollinearity: The Haitovsky test of the determinant Sociological Methods and Research, 3(4), 308–320 Rosenthal, R (1991) Metaanalytic procedures for social research (2nd ed.) Newbury Park, CA: Sage Rosenthal, R., Rosnow, R L., & Rubin, D B (2000) Contrasts and effect sizes in behavioural research: a correlational approach Cambridge: Cambridge University Press Rosnow, R L., Rosenthal, R., & Rubin, D B (2000) Contrasts and correlations in effect-size estimation Psychological Science, 11, 446–453 Rosnow, R L., & Rosenthal, R (2005) Beginning behavioural research: a conceptual primer (5th ed.) Englewood Cliffs, NJ: Pearson/Prentice Hall Rouanet, H., & Lépine, D (1970) Comparison between treatments in a repeated-measurement design: ANOVA and multivariate methods British Journal of Mathematical and Statistical Psychology, 23, 147–163 Rulon, P J (1939) A simplified procedure for determining the reliability of a test by split-halves Harvard Educational Review, 9, 99–103 Rutherford, A (2000) Introducing ANOVA and ANCOVA: A GLM approach London: Sage Sacco, W P., Levine, B., Reed, D., & Thompson, K (1991) Attitudes about condom use as an AIDS-relevant behavior: Their factor structure and relation to condom use Psychological Assessment: A Journal of Consulting and Clinical Psychology, 3(2), 265–272 Sacco, W P., Rickman, R L., Thompson, K., Levine, B., & Reed, D L (1993) Gender differences in aids-relevant condom attitudes and condom use AIDS Education and Prevention, 5(4), 311–326 Sachdev, Y V (1967) An unusual foreign body in the rectum Diseases of the Colon & Rectum, 10(3), 220–221 Salsburg, D (2002) The lady tasting tea: How statistics revolutionized science in the twentieth century New York: Owl Books Savage, L J (1976) On re-reading R A Fisher Annals of Statistics, 4, 441–500 Scariano, S M., & Davenport, J M (1987) The effects of violations of independence in the one-way ANOVA American Statistician, 41(2), 123–129 Schützwohl, A (2008) The disengagement of attentive resources from task-irrelevant cues to sexual and emotional infidelity Personality and Individual Differences, 44, 633–644 Shackelford, T K., LeBlanc, G J., & Drass, E (2000) Emotional reactions to infidelity Cognition & Emotion, 14(5), 643–659 Shee, J C (1964) Pargyline and the cheese reaction British Medical Journal, 1(539), 1441 Siegel, S., & Castellan, N J (1988) Nonparametric statistics for the behavioral sciences (2nd ed.) New York: McGraw-Hill Spearman, C (1910) Correlation calculated with faulty data British Journal of Psychology, 3, 271–295 Stevens, J P (1979) Comment on Olson: Choosing a test statistic in multivariate analysis of variance Psychological Bulletin, 86, 365–360 Stevens, J P (1980) Power of the multivariate analysis of variance tests Psychological Bulletin, 88, 728–737 Stevens, J P (2002) Applied multivariate statistics for the social sciences (4th ed.) Hillsdale, NJ: Erlbaum Strahan, R F (1982) Assessing magnitude of effect from rankorder correlation coeffients Educational and Psychological Measurement, 42, 763–765 815 References Stuart, E W., Shimp, T A., & Engle, R W (1987) Classicalconditioning of consumer attitudes – Experiments in an advertising context Journal of Consumer Research, 14(3), 334–349 Studenmund, A H., & Cassidy, H J (1987) Using econometrics: a practical guide Boston: Little Brown Tabachnick, B G., & Fidell, L S (2001) Using multivariate statistics (4th ed.) Boston: Allyn & Bacon Tabachnick, B G., & Fidell, L S (2007) Using multivariate statistics (5th ed.) Boston: Allyn & Bacon Terpstra, T J (1952) The asymptotic normality and consistency of Kendall’s test against trend, when ties are present in one ranking Indagationes Mathematicae, 14, 327–333 Terrell, C D (1982a) Significance tables for the biserial and the point biserial Educational and Psychological Measurement, 42, 975–981 Terrell, C D (1982b) Table for converting the point biserial to the biserial Educational and Psychological Measurement, 42, 983–986 Tinsley, H E A., & Tinsley, D J (1987) Uses of factor analysis in counseling psychology research Journal of Counseling Psychology, 34, 414–424 Tomarken, A J., & Serlin, R C (1986) Comparison of ANOVA alternatives under variance heterogeneity and specific noncentrality structures Psychological Bulletin, 99, 90–99 Toothaker, L E (1993) Multiple comparison procedures Sage university paper series on quantitative applications in the social sciences, 07–089 Newbury Park, CA: Sage Tufte, E R (2001) The visual display of quantitative information (2nd ed.) Cheshire, CT: Graphics Press Twisk, J W R (2006) Applied multilevel analysis: a practical guide Cambridge: Cambridge University Press Umpierre, S A., Hill, J A., & Anderson, D J (1985) Effect of Coke on sperm motility New England Journal of Medicine, 313(21), 1351–1351 Wainer, H (1984) How to display data badly American Statistician, 38(2), 137–147 Welch, B L (1951) On the comparison of several mean values: An alternative approach Biometrika, 38, 330–336 Wilcox, R R (2005) Introduction to robust estimation and hypothesis testing (2nd ed.) Burlington, MA: Elsevier Wilcoxon, F (1945) Individual comparisons by ranking methods Biometrics, 1, 80–83 Wildt, A R., & Ahtola, O (1978) Analysis of covariance Sage university paper series on quantitative applications in the social sciences, 07-012 Newbury Park, CA: Sage Williams, J M G (2001) Suicide and attempted suicide London: Penguin Wright, D B (1998) Modeling clustered data in autobiographical memory research: The multilevel approach Applied Cognitive Psychology, 12, 339–357 Wright, D B (2003) Making friends with your data: Improving how statistics are conducted and reported British Journal of Educational Psychology, 73, 123–136 Wright, D B., & London, K (2009) First steps in statistics (2nd ed.) London: Sage Wright, D B., & Williams, S (2003) Producing bad results sections The Psychologist, 16, 646–648 Yates, F (1951) The influence of statistical methods for research workers on the development of the science of statistics Journal of the American Statistical Association, 46, 19–34 Zabell, S L (1992) R A Fisher and fiducial argument Statistical Science, 7(3), 369–387 Zwick, R (1985) Nonparametric one-way multivariate analysis of variance: A computational approach based on the Pillai– Bartlett trace Psychological Bulletin, 97(1), 148–152 Zwick, W R., & Velicer, W F (1986) Comparison of five rules for determining the number of components to retain Psychological Bulletin, 99(3), 432–442 Index -2LL, 268–9, 781 a-level, 56, 781 adjusted mean, 407, 781 adjusted predicted value, 217, 229, 781 adjusted R², 221–2, 781 Agresti, A., 272 Ahtola, O., 397, 420 AIC, 304, 307, 781 AICC, 737, 781 Aiken, L.S., 741 Akaike’s information criterion (AIC), 737 alcohol and imagery (repeated measures), 482–504 Algina, J., 454 alpha factoring, 637, 781 alternative (experimental) hypotheses, 27, 49, 51, 781, 785 American Psychological Association, 57 analysis of covariance see ANCOVA (analysis of covariance) analysis of variance see ANOVA (analysis of variance) ANCOVA (analysis of covariance), 396–419, 732–3, 781 assumptions homegeneity of regression slopes, 399, 413–15 independence of the covariate and treatment effect, 397–9 violations of, 418 effect size, 415–17 as a multiple regression, 408–12 reporting results, 417 using SPSS, 399–403 contrasts and other options, 401–3, 404 independence of the independent variable and covariate, 400–1 inputting data, 399–400 main analysis, 401 post hoc tests, 401, 402 using SPSS: output, 404–8 contrasts, 407–8 covariate excluded, 404–5 interpreting the covariate, 408 main analysis, 405–6 816 Anderson, D.J., 30 Anderson-Rubin method, 635, 636, 781 ANOVA (analysis of variance), 33, 65, 79, 348–92, 781 assumptions, 359–60 homogeneity of variance, 360 independence, 360 normality, 359–60 violations of, 391 compared with MANOVA, 585–6 effect size, 389–90 F-ratio, 349, 354–5, 358–9 inflated error rates, 348–9 mean squares, 358 model sum of squares, 356–7 naming ANOVAs, 423 one and two-tailed tests, 384 planned contrasts, 360–72 choosing, 361–4 defining using weights, 365–9 non-orthogonal comparisons, 369–70, 784 orthogonal, 367–8 polynomial, 372 standard, 371 post hoc tests, 372–5, 378, 385–7 as regression, 349–54 reporting results, 390–1 residual sum of squares, 257–8 total sum of squares, 356 using SPSS, 375–88 options, 379 planned contrasts, 376–8 post hoc tests, 378 using SPSS: output, 381–7 main analysis, 381–4 planned contrasts, 384–5 post hoc tests, 385–7 see also ANCOVA (analysis of covariance); factorial ANOVA; MANOVA (multivariate analysis of variance); mixed design ANOVA; repeated measures design anxiety and disgust, 615 anxiety and interpretational bias, 409 Appelbaum, M.I., 360 AR(1), 738, 781 Arindell, W.A., 647 Arvey, R., 586 assumptions, 131–64 homogeneity of variance, 133, 139–52 independence, 133, 221 interval data, 133 normality, 133–48 Asymptotic Method, 457 attractiveness of women (multilevel linear models), 775 Australian marsupials, 482 autocorrelation, 781 b-level, 56, 781 Baguley, T., 57 Baker, F.B., 461 Bale, C., 300, 315 Banyard, P., 30, 60, 170, 196, 346 bar charts, 103–15, 781 clustered, 104 3-D, 104 for independent means, 106–8 for mixed designs, 113–15 for related means, 111–12 clustered error, 104 colours or patterns, 108 simple, 104 3-D, 104 for independent means, 105–6 for related means, 109–11 simple error, 104 stacked, 104 stacked 3-D, 104 Bargman, R.E., 619 Barnard, G.A., 171 Barnett, V., 218 Bartlett’s test, 607, 612, 635, 648, 659, 660, 781–2 Batty, D., 295 Beckham, A.S., 701, 724 Beckham, D., 295 beer-goggles effect (factorial ANOVA), 424–55, 782 Belsey, D.A., 219 Berger, J.O., 51 Bernstein, I.H., 641 Berry, W.D., 220, 267 beta values, 259 between-group see independent design between-subject see independent design BIC, 304, 307, 782 Biggest Liar, 180–2 bimodal distribution, 21, 782 binary variables, 8, 10, 782 biserial and point-biserial, 182–5, 782, 791 bivariate correlation, 175, 782 black Americans (categorical data), 701 Blesbois, E., 43, 60 blockwise regression see hierarchical regression Board, B.J., 337, 346 Bock, R.D., 605 Boik, R.J., 472 Bonferroni, Carlo, 373 Bonferroni test, 373, 374, 402, 472, 473, 565–6, 782 bootstrap, 163, 782 boredom effects, 17, 782 Bowerman, B.L., 224, 263, 300 boxplots (box-whisker diagrams), 99–103, 782 1-D, 99 clustered, 99 outliers, 102–3 simple, 99 Box’s test, 604, 605, 782 Bozdogan’s criterion (CAIC), 737, 782 Brashers, D.E., 431 Bray, J.H., 588, 605, 620, 626 Brown-Forsythe F, 379, 380 Bryk, A.S., 737 Budescu, D.V., 360 Burch, R.L., 388, 394 bushtuckers (repeated-measures design), 463–79 CAIC, 737, 782 calculating the power of a test, 58 calculating sample size, 58 Caryl, P.G., 300, 315 Castellan, N.J., 567, 578, 583 categorical data (2 variables), 687–701, 782 chi-square test on SPSS assumptions, 691–2 breaking down with standardized residuals, 698–9 effect size, 699–700 raw scores, 692 reporting results, 700 running the analysis, 694–5 weight cases, 692–3 chi-square test on SPSS, output, 696–8 contingency coefficient, 698 Cramer’s V, 698 phi, 698 817 Index contingency table, 688 Fisher’s exact test, 690 likelihood ratio, 690–1 Pearson’s chi-square test, 688–9 Yates’ continuity correction, 691 see also loglinear analysis categorical variables, 8, 9, 10 cats dancing (categorical data), 687–701 cats and dogs dancing (loglinear analysis), 708–22 Cattell, R.B., 629, 639 causality, 173–4 cause and effect, 13 central limit theorem, 42, 156, 782 centring variables, 740–1, 782 Çetinkaya, H., 572, 583 Chamorro-Premuzic, T., 194, 196, 263 Chapman, J.P., 398, 420 Chart Builder, 91–3, 782 chartjunk, 88, 782 chat-up lines (logistic regression), 300–14 Chen, P.Y., 195 chi-square distribution, 269, 308, 782 chi-square test, 688–9, 783 as regression, 702–8 on SPSS, 692–700 chick flicks, 105–8 Christopher, A.N., 194, 196, 263 Claes, M., 299, 315 Clarke, S., 730 Cliff, N., 638 Cochran’s Q, 576, 783 Cohen, J., 33, 53, 56, 57, 58, 60, 342, 349, 404 Cole, D.A., 586 Collier, R.O., 461 column vector, 589 common variance, 637, 783 communality, 637, 661, 662, 783 complete separation, 274–5, 783 component matrix, 633, 665, 783 compound symmetry, 459, 783 compute function, 156–9 Comrey, A.L., 647 confidence intervals, 43–8, 783 shown visually, 47–8 in small samples, 46 confirmatory factor analysis, 636, 783 confounds, 397, 783 content validity, 12, 783 contingency table, 688, 783 continuous variables, 9–10, 93, 783 Cook, R.D., 217 Cook, S.A., 730, 731, 778 Cook’s distance, 217, 783 Cooper, M., 300 correlation coefficient, 57, 783 correlation matrix, 647–8, 656–7 correlation research, 12–13, 15, 783 correlation techniques, 65 correlations, 167–96 biserial and point-biserial, 182–5 causality, 173–4 comparing correlations, 191–2 confidence intervals for r, 172–3 covariance, 167–9 effect sizes, 192–3 part and partial, 186–90 using SPSS, 188–90 reporting correlation coefficients, 193–4 semi-partial, 190 significance of correlation coefficient, 171–2 standardization, 169–71 using SPSS data entry, 174 Kendall’s tau, 181–2, 193 Pearson’s r, 170, 177–9, 192 Spearman’s correlation coefficient, 179–81, 192 Cortina, J.M., 685 cosmetic surgery (multilevel linear models), 730–60, 775–6 covariance, 167–9, 783 standardization, 169–71 covariance ratio (CVR), 219, 783–4 covariance structures, 737–8 covariates, 784 covariates in ANOVA, 396–7 Cox, D.R., 269 Cox and Snell’s R² , 269, 784 Crain, B.R., 461 Cramer’s V, 695, 784 Crews, D., 559, 583 criterion validity, 11–12, 784 Cronbach, L.J., 33, 349 Cronbach’s α, 674, 675–6, 677 cross-product deviations, 169, 784 cross-products, 590 cross-sectional research, 784 cross-validation, 784 cubic trends, 372, 373, 784 currency variables, 71, 784 Dalgaard, P., 164 data analysis, 18–27, 372 like Internet dating, 91 see also statistical models data collection, 27 how to measure, 12–18 what to measure, 7–12 Data Editor, 62, 63–78, 784 data mining, 372 data splitting, 222 date variables, 71, 784 Davenport, J.M., 360 Davey, G.C.L., 449, 456, 626 Davidson, M.L., 462 Davies, J.A., 388, 394 De Leeuw, J., 739, 740, 741, 778 DeCarlo, L.T., 19 degrees of freedom (df), 37, 46, 784 Delaney, H.D., 461, 462 deleted residuals, 217, 229, 784 density plots, 117, 125, 784 dependent t-test, 325, 326–33, 784 dependent/independent variables, 7, 14, 784 deviance, 35, 276, 784 DFBeta, 218–19, 784 DFFit, 219, 784 diagonal variance structure, 738, 784 direct oblimin rotation, 644 direction of causality, 174 discrete values, 78, 785 discriminant function analysis, 585, 605, 615–25, 784 discriminant function variates, 599–601, 785 discriminant scores, 617 Domjan, M., 43, 60, 559, 572, 583 Donaldson, T.S., 360 Download Festival, 93–102, 93–103, 134–8, 154–64, 254 drugs: depressant effects (nonparametric tests), 540–58 dummy variables, 254, 351, 785 Dunlap, W.P., 155 Dunnett’s T3 test, 374, 375 Dunteman, G.E., 638, 685 Durbin, J., 221 Durbin-Watson test, 220–1, 228, 785 ecological validity, 12, 785 eel up anus (logistic regression), 277–94 effect size, 785 Efron, B., 163 eigenvalues, 243, 601, 640, 641 eigenvectors, 243 elimination of confounds, 397 Engle, R.W., 482 equamax rotation, 644 Eriksson, S.-G., 295 Erlebacher, A., 342 error bar graphs, 317–24, 785 adjusted values for each variable, 323–4 adjustment factor, 322 grand mean, 320–1 mean for each participant, 320 error sum of squares and crossproducts matrix (error SSCP), 590, 785 eta squared, 389, 415, 785 Exam Anxiety Questionnaire, 117–29, 175–7, 186–90 Exp(B), 270–1, 785 experimental research, 12, 13–17 experimentwise error rate, 348 external variables, 220 Eysenck, H.J., 629 F Max test, 150, 151, 787 F-ratio, 203, 204, 349, 350, 354–5, 358–9, 429–30, 785–6 repeated-measures design, 467–8 under violations of sphericity, 460–1 F-test, 155, 202 in MANOVA, 590 factor analysis, 66, 627–82, 786 discovering factors, 636–45 choosing a method, 636–7 communality, 637, 661, 662 eigenvalues and scree plots, 639–42 factor analysis and principal component analysis, 638–9, 641 how many to retain, 641 Kaiser’s criterion, 640–1 rotation, 631, 642–5 factor loadings, 644–5 oblique, 631, 642–3, 666–8 orthogonal, 631, 642–3, 664–6 factors, 78, 628–36 determinant of a matrix, 649, 657 factor scores, 633–6 methods, 634–5 uses of, 635–6 graphical representation, 630–1 mathematical representation, 631–3 R-matrix, 628, 629 reliability analysis, 673–81 Cronbach’s α 674, 675–6, 677 measures of reliability, 673–5 reporting, 681 using SPSS, 676–8 using SPSS: output, 678–81 reporting factor analysis, 671–2 research example, 645–72 correlations between variables, 647–50 distribution of data, 650 questionnaire, 645, 646 sample size, 645, 647 use of factor analysis in social sciences, 629 using SPSS, 650–5 factor extraction, 651–2 ‘non positive definite matrix, 656 options, 654–5 rotation, 653 scores, 654 using SPSS: output, 655–71 factor extraction, 660–4 factor scores, 669–70 preliminary analysis, 656–60 factor loading, 631, 786 factor matrix, 633, 786 factor scores, 633–6, 669–70, 786 factor transformation matrix, 643 factorial ANOVA, 422–55 effect sizes, 446–8 F-ratios, 429–30 factorial designs, 422–3 interaction graphs, 443–6 model sum of squares, 426–8 as regression, 450–4 reporting results, 448–9 residual sum of squares, 428–9 total sums of squares (SST), 424–5 using SPSS, 430–5 contrasts, 432–3, 439–40 entering data, 430–1 graphing interactions, 432 options, 434–5 post hoc tests, 434, 441 using SPSS: output, 435–43 contrasts, 439–40 Levene’s test, 436 818 main AOVA table, 436–9 post hoc analysis, 441 preliminary analysis, 435–6 simple effects analysis, 440, 442–3 violation of assumptions, 454 see also mixed design ANOVA; repeated measures design factors (independent variables), 375 falsification, 6, 786 familywise error rate, 348, 786 Feldman, S., 267 Feldt, L.S., 461 fertility of quails, 559, 572 Fesmire, F.M., 130 Fidell, L.S., 165, 222, 267, 586, 604, 635, 644, 647, 685, 710, 724, 741, 778 Field, A.P., 29, 52, 57, 60, 171, 324, 346, 449, 456, 482, 505, 538 Finlay, B., 272 Fisher, R.A., 49, 50, 51, 56, 171, 688, 690, 786 fixed effects, 732, 786 fixed variables, 732 frequencies, 137 frequency distributions, 18–26, 786 central tendency, 20–3 mean, 22–3 median, 21–2 mode, 21 dispersion, 23–4 kurtosis, 19–20 normal distribution, 18–19 and probability, 24–6 skewed, 19–20 and standard deviation, 39 see also histograms Friedman’s ANOVA, 573–80, 786 effect size, 579–80 inputting data, 575 post hoc tests, 577–9 using SPSS, 575–6 using SPSS, output, 576–7 writing results, 580 Fritzon, K., 337, 346 Furnham, A., 194, 196, 263 G*Power, 58, 404 Gabriel’s test, 374, 375 Gallup, G.G.J., 388, 394 Games, P.A., 155, 156, 472 Games-Howell test, 374, 375 factorial ANOVA, 441 Garwood, J., 194, 196, 263 Geisser, S., 461 General Linear Model see ANCOVA (analysis of covariance); ANOVA (analysis of variance); factorial ANOVA; mixed design ANOVA; repeated measures design generalization (regression), 214, 786 generalized least-squares factor analysis, 642 Glass, G.V., 150, 155 Glass, G.V et al, 359, 360 Glastonbury Festival, 254–60 D I S C O VE R I N G STAT I ST I C S US I N G S PSS Goodman and Kruskal’s lambda, 695, 786 goodness-of-fit, 201–4, 308, 786 gradients, 199–200 Graham, J.M., 631, 667 Granath, F., 14 grand mean, 320, 786 grand mean centring, 740, 786 graphs and charts editing, 126–9 factorial ANOVA, 443–6 good and bad, 88–91 see also bar charts; boxplots; histograms; line charts; scatterplots; SPSS, Chart Builder Grayson, D., 156 Green, S.B., 222 Greenhouse, S.W., 461 Greenhouse-Geisser correction, 461, 474, 475, 476, 786 Grobbee, D.E., 14 group mean centring, 740, 786 growth curves, 761, 762, 786 growth models, 761–74 Guadagnoli, E., 638, 647 Guthrie, A.C., 631 H statistic, 564, 572 Haitovsky, Y., 648–9, 657–8 Halekoh, U., 276 Hameetman, M., 420 Hardy, M.A., 263 Harman, B.H., 637 Harris, R.J., 605 Hartley, H.O., 150 Hartley’s F Max test, 150, 151, 787 Hayes, T.F., 461 HE - 598, 787 heavy metal and suicide, 299 Helmert contrasts, 433, 787 heterogeneity of variance see homomgeneity of variance heteroscedasticity, 220, 787 hiccups, 109–11 hierarchical data, 726 hierarchical regression, 212, 782, 787 histograms, 93–8, 94–8, 787 frequency polygons, 95 outliers, 97, 98 population pyramids, 95 simple, 94 stacked, 94 Højsgaard, S., 276 Hoaglin, D., 217 Hochberg’s GT2 test, 374, 375 Hoddle, G., 295 Hole, G.J., 29, 52, 60, 324, 346 homoescedasticity, 220 homogeneity of covariance matrices, 603, 787 homogeneity of regression slopes, 399, 413–15, 729, 734, 787 homogeneity of variance, 133, 139–52, 360, 787 Levene’s test, 150–2 homoscedasticity, 220 honeymoon period (growth models), 761–74 Horn, J.L., 641 Hosmer-Lemeshow, 269, 281, 282, 296, 787 Hotelling, Harold, 602 Hotelling-Lawley trace, 462, 602, 787 Howell, D.C., 56, 196, 263, 335, 394, 404, 420, 446, 456, 505, 538, 691, 692 Huberty, C.J., 586, 626 Huijding, J., 420 Hume, David, 13 Hurvich and Tsai’s criterion (AICC), 737, 781 Hutcheson, G., 224, 315, 647, 724 Huynh, H., 461 Huynh-Feldt correction, 461, 476, 482 hypotheses, 787 alternative (experimental) hypotheses, 27, 49, 51 non/directional hypotheses, 27 null hypotheses, 27, 49, 51, 53, 54 testing by data, 4–5, 5–6, 48–58 hypothesis sum of squares and cross-products matrix (hypotheis SSCP), 590, 787 identity matrix, 589, 787 I’m a celebrity, get me out of here (repeated-measures design), 463–79 image covariance analysis, 636 Ince, P., 295 independence, 133, 221, 603, 730, 787 independent ANOVA see ANOVA (analysis of variance) independent design, 15, 16, 18, 787 independent errors, 220–1, 787 independent factorial design see factorial ANOVA independent t-test, 334–41, 787 independent variables see predictor variables inferential statistics, 49 infidelity and jealousy (mixeddesign ANOVA), 535 inflated error rates, 348–9 interaction effects, 279, 787 Internet addiction, 673 interquartile range, 23, 788 interval data, 9, 788 intraclass correlation (ICC), 677, 728–9, 788 iterative processes, 274 Iverson, G.R., 394 Jackson, S., 431 James, M.I., 731 Joliffe, I.T., 640–1 Jonckheere-Terpstra test, 563, 564, 568–71, 788 effect size, 570–1 Jordan, B.D., 778 K-S test, 546 Kahneman, D., 761–2 Kaiser, H.F., 640–1 Kaiser, M.K., 462, 477 Kaiser-Meyer-Olkin measure of sampling adequacy (KMO), 647, 658, 659, 788 Kass, R.A., 647 Kellett, S., 730 Kendall’s tau, 181–2, 193, 695, 788 Kendall’s W, 576, 788 Keselman, H.J., 472 Kirk, R.E., 390 Klockars, A.J., 373, 394 Kolmogorov-Smirnov test, 144–8, 145–8, 548, 788 Koot, V.C.M., 14 Kreft, I.G.G., 739, 740, 741, 778 Krueger, A.B., 762 Kruskal, Joseph, 560 Kruskal-Wallis test, 391, 559–68, 572, 788 inputting data, 562 post hoc tests, 565–8 using SPSS, 562–3 using SPSS, output, 564–5 writing results, 571 Kuh, E., 219 kurtosis, 88, 138, 139 Lacourse, E., 299, 315 latent variables, 599, 628 Law, I.C., 277, 315 least significance difference (LSD), 374 Lee, H.B., 647 Lehmann, E.L., 51 Lemeshow, S., 269, 281, 282, 296 Lenth, R.V., 57 Lépine, D., 460 leptokurtic distributions, 19, 788 Leung, L.S., 277, 315 levels of measurement, 8, 10, 93, 788 Levene’s test, 79, 340, 404, 405, 434, 788 factorial ANOVA, 434, 436 leverage (hat values), 217, 788–9 Levine, D.W., 155 Lewis, T., 218 likelihood, 309, 690–1, 789 Lilliefor correction, 147 line charts, 115–16, 789 linear trends, 372, 373 linearity, 221 Lo, S.F., 277, 315 local sphericity (circularity), 460 log linear analysis, 65, 708–22, 789 assumptions, 710–11 effect sizes, 720 following up, 719–20 reporting results, 721 using SPSS, 711–14 using SPSS: output, 714–19 log transformations, 155, 159–60 log-likelihood, 267–8, 308, 789 logistic regression, 264–300, 789 assumptions, 273, 294–300 independence of errors, 273, 276 linearity, 273, 276, 296–7 multicollinearity, 273, 276, 297–300 example, 277–82 categorical predictors, 279–80 main analysis, 278–9 method of regression, 279 obtaining residuals, 280–1 options, 281–2 819 Index interpreting, 282–94 effect size, 294 initial model, 282–4 intervention, 284–900 listing predicted probabilities, 291–2 residuals, 292–3 log-likelihood statistic, 267–8 methods of logistic regression, 271–2 forced entry, 271–2 stepwise, 272 odds ratio: Exp(B), 270–1 principles, 265–7 problems complete separation, 274–5, 276 incomplete information, 273–4 overdispersion, 276 R and R², 268–9 reporting, 294 testing assumptions, 294–300 Wald statistic, 269–70 zero frequencies, 307 see also multinomial logistic regression London, K., 30, 60, 196, 346, 394 Looks or personality (mixed ANOVA), 507–37 Lord, F.M., 398 Lucas, P.A., 155 Lumney, G.H., 360 MacCallum, R.C., 339 MacCallum, R.C et al, 647 MacDonald, C.B., 449, 456 McGill, P., 730 McGrath, R.E., 57 McNemar’s test, 555, 789 Mahalanobis distances, 217–18, 789 Mandeville, G.K., 461 Mann-Whitney test, 345, 540–51, 572, 789 effect size, 550 inputting data, 545–6 output, 548–9 as post hoc test for KruskalWallis test, 565, 566, 567 running the analysis, 546–7 writing the results, 550 MANOVA (multivariate analysis of variance), 65, 461, 462, 477, 585–625 assumptions, 603–4 violation of, 624 calculating MANOVA by hand, 591–8 model SSCP matrix (H), 597–8 relationship between DVs: cross-products, 593–5 residual SSCP matrix (E), 597 total SSCP matrix (T), 595–7 univariate ANOVA for DV1, 591–2 univariate ANOVA for DV2, 592–3 choosing a test statistic, 604–5 compared with ANOVA, 585–6 discriminant function analysis, 585, 605, 615–25 output, 618–21 reporting results, 621–2 final interpretation, 622–4 follow-up analysis, 605 matrices, 588–90 OCD data, 588 power of, 586 and principal component analysis, 638–9 principle of test statistic, 598–603 discriminant function variates, 599–601 Hotelling’s T², 602 Pillai-Bartlett trace, 601–2, 604, 605 Roy’s largest root, 602–3, 605 Wilks’s lambda, 602 reporting results, 614–15 using SPSS, 605–8 additional options, 607–8 main analysis, 606 multiple comparisons, 607 using SPSS: output, 608–14 contrasts, 613–14 MANOVA test statistics, 608–9 priliminary analysis and assumptions, 608 SSCP matrices, 611–12 univariate test statistics, 609–11 marginal homogeneity, 555 Martin, N., 194, 196, 263 Marziller, S.L., 615, 626 Mather, K., 51 matrices, 588–90 Matthews, R.C., 559, 583 Mauchly’s test, 460 maximum-likelihood method, 267, 637, 642, 789 Maxwell, S.E., 461, 462, 472, 586, 588, 605, 620, 626 Mayer, B., 420 mean, 22–3, 789 as statistical models, 35–40 mean squares (MS), 203, 467, 789 measurement error, 10–11, 789 validity and reliability, 11–12 median, 21–2, 789–90 median splits, 339 median test, 564, 790 Menard, S., 270, 272, 287, 298, 315 Mendoza, J.L., 461, 462 meta-analysis, 57, 790 Meyer, G.J., 57 Miles, J., 30, 60, 170, 196, 223, 263, 315, 346 Mill, J.S., 14 Miller, G.A., 398, 420 Miller, G.A et al, 775, 778 missing data, 730 Mitzel, H.C., 472 mixed design ANOVA, 422, 507–37, 790 effect sizes, 531–3 main analysis, 508–12 options, 513–14 output, 514–31 interaction between attractiveness and charisma, 524–7 interaction between gender and charisma, 523–4 interaction between gender and looks, 521–3 interaction between looks, charisma and gender, 527–30 main effect of charisma, 520–1 main effect of gender, 517–18 main effect of looks, 518–20 Maulchy’s test, 514, 515 reporting results, 533–5 violation of assumptions, 536 mode, 21, 790 model sum of squares, 202, 203, 426–8, 466 Monte Carlo method, 547, 554, 563, 790 Morris, J.D., 586, 626 Morrison, R., 300, 315 Moses Extreme Reactions, 548, 790 multicollinearity, 220, 223–4, 790 factor analysis, 648–50 multilevel linear models, 65, 726–77, 790 assumptions, 739 benefits of, 729–30 centring variables, 740–1 fixed and random coefficients, 732–4 random intercept model, 734, 739 random intercept and slope model, 734 random slope model, 734 growth models, 761–74 example ‘honeymoon period’, 761–3 further analysis, 774 growth curves (polynomials), 761, 762 restructuring the data, 763–7 uses, 761 using SSPS, 767–74 hierarchical data, 726 intraclass correlation, 728–9 the multilevel model, 734–8 assessing the fit, 737 comparing models, 737 types of covariance structures, 737–8 reporting, 775–6 sample size and power, 740 using SPSS, 741–60 adding and interaction, 756–60 entering the data, 742 factoring in the data structure: random intercepts, 749–52 factoring in the data structure: random intercepts and slopes, 752–6 ignoring the data structure: ANCOVA, 746–9 ignoring the data structure: ANOVA, 742–6 multimodal distribution, 21, 790 multinomial logistic regression, 265, 300–14, 790 interpreting output, 306–12 goodness-of-fit, 308 likelihood ratio tests, 309 model fitting information, 308 parameter esimates, 311 pseudo R-square, 308 step summary, 308 options, 305–6 save options, 306 reporting results, 312–13 running in SPSS, 301–3 custom model, 302–3 statistics, 304–5 asymptotic correlations and covariances, 304 cell probabilities, 304 classification table, 304 estimates, 304 goodness-of-fit, 304 information criteria, 304 likelihood ratio tests, 304, 309 model fitting information, 304 monotinicity measures, 304 pseudo R-square, 304 step summary, 304 multiple R, 211–12 multiple regression, 209–61, 790 assessing the model: diagnostics, 214–19 DFFit, 217, 219 influential cases, 217–19 outliers, 215–16 residuals, 216–17 assessing the model: generalization, 220–4 checking assumptions, 220–1 cross-validation, 221–2 multicollinearity, 223–4 sample size, 222–3 categorical predictors, 253–60 dummy coding, 253–6 SPSS output for dummy variables, 256–60 example of model, 210–11 methods of regression, 212–14 forced entry, 212 hierarchical regression, 212 stepwise regression, 212–13, 213 reporting, 252 sums of squares, 211–12 using SPSS, 225–33 casewise diagnostics, 244–7 checking assumptions, 247–51 options, 225–7, 231–3 regression plots, 229–30 820 saving diagnostics, 230–1 statistics, 227–9 using SPSS: output assessing assumption of no multicollinearity, 241–2 descriptives, 233–4 excluded variables, 241 model parameters, 237–41 summary of model, 234–7 violations of assumptions, 251 multiple regression, factorial ANOVA as, 450–4 multivariate analysis of variance see MANOVA (multivariate analysis of variance) multivariate normality, 603–4, 790 multivariate tests, 585 Muris, Peter et al, 409, 420 Myers, R., 224, 298 Nagelkerke, N.J.D., 269, 790 Namboodiri, K., 588, 598 Neyman, J., 51, 171 Nicewander, W.A., 462 Nichols, L., 673, 685 Nicki, R., 673, 685 no affiliation group, 259 nominal variables, 8, 93, 790 non-orthogonal contrasts, 369–70, 784, 785 non-parametric statistics, 66, 790 non-parametric tests, 540–81 Friedman’s ANOVA, 573–81 Jonckheere-Terpstra test, 568–72 Kruskal-Wallis test, 560–7 and statistical power, 551 Wilcoxon rank-sum test and Mann-Whitney test, 540–51 Wilcoxon signed-rank test, 552–8 non-significant results, 53 noniles, 145, 790 normal distribution, 133–48, 790 checking visually, 134–6 exploring groups of data, 140–4 analysis for all data, 140–1 analysis for different groups, 141–4 quantifying with numbers, 136–9 tests for, 144–8 normally distributed errors, 221 nQuery Advisor, 58 null hypotheses, 27, 49, 51, 53, 54, 790 numeric variables, 71, 74, 790 Nunnally, J.C., 641, 647 Nyren, O., 14 oblique rotation, 631, 642–3, 790 O’Brien, M.G., 462, 477 obsessive compulsive disorder (OCD) (MANOVA), 449, 587–624 O’Connell, R.T., 224, 263, 300 O’Connor, B.P., 641 odds ratio, 270–1, 699–700, 790 O’Donnell, D., 300 Olejnik, S.F., 454 Olson, C.L., 604, 605 omega squared, 389, 416, 790 D I S C O VE R I N G STAT I ST I C S US I N G S PSS one and two-tailed tests, 384, 791 ordinal data, 8, 9, 93, 791 orthogonal contrasts, 367–8 orthogonal rotation, 631, 642–3, 791 outcome variables, 7, 791 outliers, 153, 791 overdispersion, 276 p-p plots (probability-probability plots), 134–5, 134–6, 792 pairwise comparisons, 372–3, 791 pairwise/listwise analyses, 177 parametric tests, 132, 791 partial eta squared, 404, 415, 791 partial out, 396, 791 Parvez, R., 388, 394 pattern matrix, 631, 666, 667, 791 Pearson, E.S., 51, 57, 150 Pearson, K., 170, 171, 178, 547, 688, 791 Peckham, P.D., 155 see also Glass, G.V et al Pedhazur, E., 636, 643, 644, 685 Peeters, P.H.M., 14 Penn State Worry Questionnaire (PSWQ), 295–300 percentiles, 145, 791 perfect collinearity, 223–4, 791 Phi (categorical data), 695, 791 Pillai-Bartlett trace, 481, 601–2, 791 planned contrasts, 360–72, 791 platykurtic distributions, 19, 791 polychotomous logistic regression see multinomial logistic regression polynomial trends, 372, 791 polynomials, 761, 762 Popper, Karl, Poppvich, P.M., 195 populations and samples, 34–5, 40–2, 58, 791 and confidence intervals, 43–8 post hoc tests, 361, 372–5, 791–2 practice effects, 17, 792 Preacher, K.J., 339 predictor variables, 7, 198, 199, 200, 220, 792 principal component analysis, 633, 636–7, 638–9, 641, 792 principal factors analysis, 636 probability, 24–6, 50, 51, 792 probability distributions, 25 promax rotation, 644 pseudo R-square, 304 pubs, 214–15 Q-Q plots, 145, 147–8, 792 quadratic trends, 372, 373, 792 qualitative methods, 2, 792 quantiles, 145, 792 quantitative methods, 2, 792 quartic trends, 372, 373, 792 quartiles, 23–4, 792 quartimax rotation, 644, 792 R (statistics program), 163, 164 R-matrix, 628, 629 R-statistic, 268–9 Ramsey, M., 559, 583, 586 random coefficients, 732, 792 random effects, 732, 792 random intercepts, 749–52, 792 random sampling, 603 random slopes, 752–6, 792 random variables, 732, 792 randomization, 17–18, 792 range, 23, 24, 792 ranking data, 542, 792 ratio variables, 9, 792 Raudenbush, S.W., 737 ‘real-world’ phenomena, 32 reciprocal transformation, 155 record sales 2, 225–7 regression, 33, 198–209 assessing goodness of fit, 201–4 sums of squares, 202–4 assessing individual predictors, 204–5 method of least squares, 200–1 straight lines, 199–200 using the model, 208–9 using SPSS, 205–6 using SPSS: output model parameters, 207–8 overall fit, 206–7 using the model, 208–9 see also multiple regression regression coefficients, 199 regression lines, 119, 792 regression method of calculating factor scores, 634–5 reliability, 11, 12, 66, 793 repeated contrasts, 433, 793 repeated-measures design, 15, 16, 17, 133, 422, 458–82, 793 between-participant sum of squares, 468 effect sizes, 479–81 F-ratio, 467–8 mean squares, 467 model sum of squares, 466 reporting, 481–2 residual sum of squares, 467 sphericity, 459–61 deviation from, 460 Mauchly’s test, 474–5, 481, 482 measuring sphericity, 459–60 violations of assumption, 460–1, 462, 472 total sum of squares, 464–5 using SPSS, 468–73 defining contrasts, 471 main analysis, 468–71 options, 472–3 post hoc tests, 471–3, 478–9 using SPSS: output, 374–9 contrasts, 477–8 descriptives, 474 main ANOVA, 475–7 Mauchly’s test, 474–5, 481, 482 post hoc tests, 478–9 within-participant, 465–6 repeated-measures with several independent variables, 482–504 contrasts, 488, 498–501 effect sizes, 501–2 graphing interactions, 490–1 main analysis, 484–8 output, 492–501 contrasts, 498–501 descriptives and main analysis, 492–3 effect of drink, 493–5 effect of imagery, 495–6 interaction effect, 496–7 reporting, 502–3 simple effects analysis, 488–90 on SPSS, 489–90 violation of assumptions, 503–4 research process, 3–29, 48–9 data analysis, 18–27 data collection, 7–18 initial observation, 3–4 theories and hypotheses, 4–6 residual sum of squares, 202, 203, 428–9, 467, 793 residuals, 229, 793 reverse score transformations, 155 Roa’s efficient score statistic, 284, 793 robust tests, 155, 163, 793 Rockwell, R.C., 648 Rosenthal, R., 88, 346, 394, 456, 505 Rosnow, R.L., 346, 394, 456, 505 Rosser, R., 730, 731, 778 rotation, 631, 642–5, 793 Rouanet, H., 460 row vector, 589 Roy-Bose simultaneous confidence interval, 472 Roy’s largest root, 602–3, 793 Rubin, D.B., 394, 456, 505 Rucker, D.D., 339 Rutherford A., 420 Ryan, Einot, Gabriel and Welsch Q (REGWQ) test, 374 factorial ANOVA, 441 S-Plus, 163 Salas, E., 586 Salmon, P., 730, 731, 778 Salsburg, David, 50 sample mean, 41, 42, 43 differences, 327–9, 333–4 samples, 34–5, 40–2, 134, 793 and confidence intervals, 43–8 size, 58, 645, 647 sampling distributions, 42, 53, 327, 793 sampling variation, 42, 44, 793 Sanders, J.R., 155 see also Glass, G.V et al saturated model, 705, 793 Savage, L.J., 171 Sax, G., 373, 394 Scariano, S.M., 360 scatterplots, 116–26, 793 drop line, 117, 126 grouped, 117, 119–20 grouped 3-D, 117, 121–2 matrix, 117, 123–5 regression lines, 119, 124 simple, 117–19 simple 3-D, 117, 121–2 simple dot (density) plot, 117, 125 summary point plot, 117 Schmelkin, L., 636, 643, 644, 685 Schützwohl, Achim, 535, 538 Schwarz’s Bayesian criterion (BIC), 737 821 Index scientific/non-scientific statements, 5, 27 score statistic, 272 scree plots, 639–42, 793 self-report data, 8, 11 Serlin, R., 380 Shapiro-Wilk test, 144, 147, 546, 793 Shee, J.C., 90 Shevlin, M., 223, 263, 315 Shimp, T.A., 482 shrinkage, 221, 793 Sidak correction, 402, 473, 793 Siegel, S., 567, 578, 583 sign test, 555, 793 simple effects analysis, 440, 442–3, 793 singularity, 648, 794 skewness, 138, 139, 794 SmartViewer, 81–2, 794 Snell, D.J., 269 Sofroniou, N., 224, 647 Spearman, C., 180 Spearman’s correlation coefficient, 179–81, 192, 794 sperm of Japanese quail, 43–4, 47 killed by Coca Cola, 7, 9, 11 sperm competition, 388 sperm count and soya (nonparametric tests), 559–72 sphericity (circularity), 459–61 lower bound estimate, 461 Mauchly’s test, 474–5 post hoc tests, 472 spiders, 317–41 split file, 140, 141, 142, 143 split-half reliability, 674, 794 SPSS Chart Builder, 91–3, 782 Basic Elememnts, 92, 93 Drop Zones, 92, 95 Gallery, 92 Variable List, 92 Chart Editor, 126–9, 782 compute function, 65 Data Editor, 62, 63–78 creating variables, 70–7 Data View, 64 entering data, 69–70 icons, 67–9 keyboard shortcuts, 64 menus, 64–6 Variable View, 64 dialog boxes, 63 ‘E’ in numbers, 81 Open Data, 84 printing, 80 recode function, 65 retrieving files, 84 Save Data, 83 SmartViewer, 81–2, 794 Start-up Window, 62, 63 Syntax Window, 62, 82, 795 versions of SPSS, 62 Viewer, 62, 78–81, 796 icons, 80–1 SPSS anxiety (factor analysis), 645–72 SPSS Exam data, 140–4, 151 square matrix, 589, 794 square root transformation, 155 SSCP matrices, 590, 638–9, 795 standard contrasts, 433 standard deviation, 37–8, 39–40, 42, 170, 794 standard error, 40–3, 204, 327, 794 standard error of differences, 327–9, 794 standard error of the mean (SE), 42, 794 standardized β values, 239 standardized DFBeta, 218–19, 794 standardized DFFit, 219, 794 standardized residuals, 216, 229, 794 Startup, H.M., 449, 456 statistical models fitting to data, 26–7, 31–4 going beyond the data, 40–8 confidence intervals, 43–8 standard error, 40–3 linear, 33–4 mean as, 35–40 to test research, 48–58 effect sizes, 51, 56–7, 58 one and two-tailed tests, 54–5 statistical power, 58 test statistics, 52–4 Type I and Type II errors, 55–6 statistical power and nonparametric tests, 551 statistically significant, 50, 53–4 Stein’s formula, 222 stepwise methods (logistic regression), 272, 794 Stevens, J.P., 217, 219, 263, 397, 461, 462, 476, 586, 588, 598, 604, 638, 641, 644, 645 Stockwell, M., 388, 394 straight lines, 199–200 string variables, 71, 794 structure matrix, 631, 666, 668, 794 Stuart, E.W., 482 Studentized deleted residuals, 217, 229, 794 Studentized Newman-Keuls (SNK) procedure, 374 Studentized residuals, 217, 229, 794–5 sum of squared errors (SS), 36, 795 sum of squares, 432, 795 sum of squares and cross-products (SSCP) matrices, 590, 638–9, 795 suppressor effects, 213, 272, 795 Syntax Window, 62, 82, 795 systematic variation, 16, 17, 328, 795 t-distribution, 46 t-test, 65, 134, 204, 324–45 assumptions, 326 dependent, 325, 326–33, 784 assumption of normality, 329, 344–5 effect size, 332 equation, 327–9 one- and two-tailed significance, 332 reporting, 333 using SPSS, 329–33 using SPSS, output, 330–2 as general linear model, 342–4 independent, 334–41 effect size, 341 equation, 334–6 reporting, 341 using SPSS, 336–7, 337–41 using SPSS, output, 339–41 Tabachnick, B.G., 165, 222, 267, 586, 604, 635, 644, 647, 685, 710, 724, 741, 778 tertium quid, 14, 173, 795 test-retest reliability, 12, 795 theories, 795 generating and testing, 4–6 and hypotheses, 4–5 third-variable problem, 173 Thompson, B., 631 Tibshirani, R., 163 tied ranks (of data), 542, 543 Tinsley D.J., 636 Tinsley, H.E.A., 636, 647 tolerance, 224, 795 Tomarken, A.J., 380 Toone, H., 731 Toothaker, L.E., 373, 374, 394, 461, 462 total sum of squares, 202, 424–5, 464–5, 795 total sum of squares and cross products matrix (total SSCP), 590 transformations, 153–64 choosing, 154–6 effect of, 161–2 log transformations, 155, 159–60 reciprocal, 160 square root transformations, 160 trimmed mean, 163, 795 Tufte, E.R., 88, 130 Tukey’s test, 374, 402 sphericity, 472 Twisk, J.W.R., 737, 740, 741, 778 two-tailed tests, 384, 795 Tybur, J.M., 778 Type I and II errors, 55–6, 348, 374, 795 U statistic, 544, 572 Umpierre, S.A., 30 unbiased models, 221 unique variance, 637 univariate tests, 585, 795 unstandardized [beta] values, 260 unstandarized residuals, 216, 795 unstructured covariance, 738, 795 unsystematic variation, 15–16, 17, 795 validity of measurements, 11–12, 795 van der Ende, J., 647 variables, 4, 7–10, 93, 795 categorical, 8, continuous, 9–10 dependent/independent, 7, 14 graphing relationships see scatterplots predictor/outcome, variance, 36–8, 40, 637, 796 see also ANOVA (analysis of variance) variance components, 738, 796 variance inflation factor (VIF), 224, 796 variance ratio, 150 variance structures, 737–8 variance sum law, 335, 796 variation: systematic/unsystematic, 15–17, 52 varimax rotation, 644, 664–6, 796 Vassell, D., 295 Velicer, W.F., 638, 641, 647 Viagra (ANCOVA), 396–420, 732–3 Viagra (ANOVA), 350–72 Viewer, 62, 78–81, 796 Villeneuve, M., 299, 315 Wainer, H., 88, 130 Wald, Abraham, 270 Wald statistic, 268–9, 269–70, 272, 752, 796 Wald-Wolfowitz runs, 548, 796 Watson, G.S., 221 weighted average, 633 weights, 365, 796 Weisberg, S., 217 Welch’s F, 379, 380, 796 Welsch, R., 217, 219 Wherry’s equation, 221 Wilcox, R., 156, 163, 165, 251, 345, 360, 418, 454, 503, 583, 624 Wilcoxon, Frank, 541 Wilcoxon rank-sum test, 540–51, 796 effect size, 550 inputting data, 545–6 output, 548–9 writing the results, 550 Wilcoxon signed-rank test, 345, 552–8, 796 effect size, 558 output for alcohol group, 557 output for ecstasy group, 556 as post hoc test for Friedman’s ANOVA, 577–8 running the analysis, 554–5 writing the results, 558 Wildt, A.R., 397, 420 Wilks’s lambda, 602, 796 Williams, J., 43, 60 Williams, S., 130 within-group error variance, 396 within-subject design, 15, 796 Wong, S.H., 277, 315 Wright, D.B., 30, 60, 88, 130, 196, 346, 394, 727 Yates’s continuity correction, 691, 796 Yates, F., 51 Yip, A.W.C., 277, 315 z-scores, 26, 102, 134, 135, 138, 796 Zabell, S.L., 171 Zappieri, M.L., 388, 394 Zara, A., 449, 456 Zhang, S., 339 Zwick, W.R., 624, 641 ... means 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 316 What will this chapter tell me? Looking at differences 1 9.2 .1 A problem with error bar graphs of repeated-measures designs 9.2 .2... 9.4 .1 Sampling distributions and the standard error 9.4 .2 The dependent t-test equation explained 1 9.4 .3 The dependent t-test and the assumption of normality 9.4 .4 Dependent t-tests using spss. .. PSS 19.3 .2 An example 19.4 .1 19.4 .2 Fixed and random coefficients 19.4 The multilevel model 19.3 .1 Assessing the fit and comparing multilevel models Types of covariance structures 19.5