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An Adventure in Statistics

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Table of Contents

Prologue: The Dying Stars 1 Why You Need Science: The Beginning and The End 1.1. Will you love me now? 1.2. How science works 1.2.1. The research process 1.2.2. Science as a life skill 1.3. Research methods 1.3.1. Correlational research methods 1.3.2. Experimental research methods 1.3.3. Practice, order and randomization 1.4. Why we need science 2 Reporting Research, Variables and Measurement: Breaking the Law 2.1. Writing up research 2.2. Maths and statistical notation 2.3. Variables and measurement 2.3.1. The conspiracy unfolds 2.3.2. Qualitative and quantitative data 2.3.3. Levels of measurement 2.3.4. Measurement error 2.3.5. Validity and reliability 3 Summarizing Data: She Loves Me Not? 3.1. Frequency distributions 3.1.1. Tabulated frequency distributions 3.1.2. Grouped frequency distributions 3.1.3. Graphical frequency distributions 3.1.4. Idealized distributions 3.1.5. Histograms for nominal and ordinal data 3.2. Throwing Shapes 4 Fitting Models (Central Tendency): Somewhere In The Middle 4.1. Statistical Models 4.1.1. From the dead 4.1.2. Why do we need statistical models? 4.1.3. Sample size 4.1.4. The one and only statistical model 4.2. Central Tendency 4.2.1. The mode 4.2.2. The median 4.2.3. The mean 4.3. The 'fit' of the mean: variance 4.3.1. The fit of the mean 4.3.2. Estimating the fit of the mean from a sample 4.3.3. Outliers and variance 4..4. Dispersion 4.4.1. The standard deviation as an indication of dispersion 4.4.2. The range and interquartile range 5 Presenting Data: Aggressive Perfector 5.1. Types of graphs 5.2. Another perfect day 5.3. The art of presenting data 5.3.1. What makes a good graph? 5.3.2. Bar graphs 5.3.3. Line graphs 5.3.4. Boxplots (box-whisker diagrams) 5.3.5. Graphing relationships: the scatterplot 5.3.6. Pie charts 6 Z-Scores: The wolf is loose 6.1. Interpreting raw scores 6.2. Standardizing a score 6.3. Using z-scores to compare distributions 6.4. Using z-scores to compare scores 6.5. Z-scores for samples 7 Probability: The Bridge of Death 7.1. Probability 7.1.1. Classical probability 7.1.2. Empirical probability 7.2. Probability and frequency distributions 7.2.1. The discs of death 7.2.2. Probability density functions 7.2.3. Probability and the normal distribution 7.2.4. The probability of a score greater than x 7.2.5. The probability of a score less than x: The tunnels of death 7.2.6. The probability of a score between two values: The catapults of death 7.3. Conditional probability: Deathscotch Inferential Statistics: Going Beyond the Data 8.1. Estimating parameters 8.2. How well does a sample represent the population? 8.2.1. Sampling distributions 8.2.2. The standard error 8.2.3. The central limit theorem 8.3. Confidence Intervals 8.3.1. Calculating confidence intervals 8.3.2. Calculating other confidence intervals 8.3.3. Confidence intervals in small samples 8.4. Inferential statistics 9 Robust Estimation: Man Without Faith or Trust 9.1. Sources of bias 9.1.1. Extreme scores and non-normal distributions 9.1.2. The mixed normal distribution 9.2. A great mistake 9.3. Reducing bias 9.3.1. Transforming data 9.3.2. Trimming data 9.3.3. M-estimators 9.3.4. Winsorizing 9.3.5. The bootstrap 9.4. A final point about extreme scores 10 Hypothesis Testing: In Reality All is Void 10.1. Null hypothesis significance testing 10.1.1. Types of hypothesis 10.1.2. Fisher's p-value 10.1.3. The principles of NHST 10.1.4. Test statistics 10.1.5. One- and two-tailed tests 10.1.6. Type I and Type II errors 10.1.7. Inflated error rates 10.1.8. Statistical power 10.1.9. Confidence intervals and statistical significance 10.1.10. Sample size and statistical significance 11 Modern Approaches to Theory Testing: A Careworn Heart 11.1. Problems with NHST 11.1.1. What can you conclude from a 'significance' test? 11.1.2. All-or-nothing thinking 11.1.3. NHST is influenced by the intentions of the scientist 11.2. Effect sizes 11.2.1. Cohen's d 11.2.2. Pearson's correlation coefficient,r 11.2.3. The odds ratio 11.3. Meta-analysis 11.4. Bayesian approaches 11.4.1. Asking a different question 11.4.2. Bayes' theorem revisited 11.4.3. Comparing hypothesis 11.4.4. Benefits of bayesian approaches 12 Assumptions: Starblind 12.1. Fitting models: bringing it all together 12.2. Assumptions 12.2.1. Additivity and linearity 12.2.2. Independent errors 12.2.3. Homoscedasticity/ homogeneity of variance 12.2.4. Normally distributed something or other 12.2.5. External variables 12.2.6. Variable types 12.2.7. Multicollinearity 12.2.8. Non-zero variance 12.3. Turning ever towards the sun 13 Relationships: A Stranger's Grave 13.1. Finding relationships in categorical data 13.1.1. Pearson's chi-square test 13.1.2. Assumptions 13.1.3. Fisher's exact test 13.1.4. Yates's correction 13.1.5. The likelihood ratio (G-test) 13.1.6. Standardized residuals 13.1.7. Calculating an effect size 13.1.8. Using a computer 13.1.9. Bayes factors for contingency tables 13.1.10. Summary 13.2. What evil lay dormant 13.3. Modelling relationships 13.3.1. Covariance 13.3.2. Pearson's correlation coefficient 13.3.3. The significance of the correlation coefficient 13.3.4. Confidence intervals for r 13.3.5. Using a computer 13.3.6. Robust estimation of the correlation 13.3.7. Bayesian approaches to relationships between two variables 13.3.8. Correlation and causation 13.3.9. Calculating the effect size 13.4. Silent sorrow in empty boats 14 The General Linear Model: Red Fire Coming Out From His Gills 14.1. The linear model with one predictor 14.1.1. Estimating parameters 14.1.2. Interpreting regression coefficients 14.1.3. Standardized regression coefficients 14.1.4. The standard error of b 14.1.5. Confidence intervals for b 14.1.6. Test statistic for b 14.1.7. Assessing the goodness of fit 14.1.8. Fitting a linear model using a computer 14.1.9. When this fails 14.2. Bias in the linear model 14.3. A general procedure for fitting linear models 14.4. Models with several predictors 14.4.1. The expanded linear model 14.4.2. Methods for entering predictors 14.4.3. Estimating parameters 14.4.4. Using a computer to build more complex models 14.5. Robust regression 14.5.1. Bayes factors for linear models 15 Comparing Two Means: Rock or Bust 15.1. Testing differences between means: The rationale 15.2. Means and the linear model 15.2.1. Estimating the model parameters 15.2.2. How the model works 15.2.3. Testing the model parameters 15.2.4. The independent t-test on a computer 15.2.5. Assumptions of the model 15.3. Everything you believe is wrong 15.4. The paired-samples t-test 15.4.1. The paired-samples t-test on a computer 15.5. Alternative approaches 15.5.1. Effect sizes 15.5.2. Robust tests of two means 15.5.3. Bayes factors for comparing two means 16 Comparing Several Means: Faith in Others 16.1. General procedure for comparing means 16.2. Comparing several means with the linear model 16.2.1. Dummy coding 16.2.2. The F-ratio as a test of means 16.2.3. The total sum of squares (SSt) 16.2.4. The model sum of squares (SSm) 16.2.5. The residual sum of squares (SSr) 16.2.6. Partitioning variance 16.2.7. Mean squares 16.2.8. The F-ratio 16.2.9. Comparing several means using a computer 16.3. Contrast coding 16.3.1. Generating contrasts 16.3.2. Devising weights 16.3.3. Contrasts and the linear model 16.3.4. Post hoc procedures 16.3.5. Contrasts and post hoc tests using a computer 16.4. Storm of memories 16.5. Repeated-measures designs 16.5.1. The total sum of squares, SSt 16.5.2. The within-participant variance, SSw 16.5.3. The model sum of squares, SSm 16.5.4. The residual sum of squares, SSr 16.5.5. Mean squares and the F-ratio 16.5.6. Repeated-measures designs using a computer 16.6. Alternative approaches 16.6.1. Effect sizes 16.6.2. Robust tests of several means 16.6.3. Bayesian analysis of several means 16.7. The invisible man Factorial Designs 17.1. Factorial designs 17.2. General procedure and assumptions 17.3. Analysing factorial designs 17.3.1. Factorial designs and the linear model 17.3.2. The fit of the model 17.3.3. Factorial designs on a computer 17.4. From the pinnacle to the pit 17.5. Alternative approaches 17.5.1. Calculating effect sizes 17.5.2. Robust analysis of factorial designs 17.5.3. Bayes factors for factorial designs 17.6. Interpreting interaction effects Epilogue: The Genial Night: SI Momentum Requiris, Circumspice


About the Author

Andy Field is Professor of Child Psychopathology at the University of Sussex. He has published over 80 research papers, 29 book chapters, and 17 books mostly on child emotional development and statistics. He is the founding editor of the Journal of Experimental Psychopathology and has been an associate editor and editorial board member for the British Journal of Mathematical and Statistical Psychology, Cognition and Emotion, Clinical Child and Family Psychology Review and Research Synthesis Methods. His ability to make statistics accessible and fun has been recognized with local and national teaching awards (University of Sussex, 2001, 2015, 2016; the British Psychological Society, 2007), a prestigious UK National Teaching Fellowship (2010), and the British Psychological Society book award (2006). He adores cats (and dogs), and loves to listen to and play very heavy music. He lives in Brighton with his wonderful wife Zoe, his son Zach, his crazy spaniel Ramsey and Fuzzy the cat.


See what students are saying! "PERFECT FOR EVERYONE that finds stats difficult, pointless or boring, this book proves them wrong! The way the concepts are explained is so easy to grasp and it makes it even entertaining to learn! I wish I had discovered this sooner!" -- Larissa Quiroga Escamilla "A MUST-HAVE FOR ANY STATISTICS STUDENT looking for a thorough understanding of statistical terminology and concepts. Students will come for the statistics and stay for the narrative." -- Tess Liddell "A UNIQUE, ENGAGING EXPERIENCE...The narrative helps to build a context for introducing concepts and allows for the characters to explain the concepts through their successive parts. This is a must-have for those studying statistics." -- Benjamin Schade "Funny and engaging book, YOU CANNOT STOP READING it because you cannot wait to know what happens to Zach and Alice." -- Eszter Stockl "This book is EXTREMELY HELPFUL IN UNDERSTANDING THE BASICS behind some of the more complex statistical procedures gone over in lectures." -- Rebecca, Payne

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