Table of contents : Preface Author 1First steps 1.1What shall we do? Example 1 1.2The setting 1.2.1Losses and gains 1.2.2States, spaces and parameters 1.2.3Estimation. Fixed and random. 1.3Study design 1.4Exercises 2Statistical paradigms 2.1Frequentist paradigm 2.1.1Bias and variance 2.1.2Distributions 2.1.3Sampling from finite populations 2.2Bayesian paradigm 2.3Computer-based replications 2.4Design and estimation 2.5Likelihood and fiducial distribution 2.5.1Example. Variance estimation. 2.6From estimate to decision 2.7Hypothesis testing 2.8Hypothesis test and decision 2.9Combining values and probabilities—Additivity 2.10Further reading 2.11Exercises 3Positive or negative? 3.1Constant loss 3.1.1Equilibrium and critical value 3.2The margin of error 3.3Quadratic loss 3.4Combining loss functions 3.5Equilibrium function Example 2 Example 3 3.6Plausible values and impasse 3.7Elicitation 3.7.1Post-analysis elicitation 3.8Plausible rectangles Example 4 3.8.1Summary 3.9Further reading 3.10Exercises 4Non-normally distributed estimators 4.1Student t distribution 4.1.1Fiducial distribution for the t ratio Example 5 Example 6 4.2Verdicts for variances 4.2.1Linear loss for variances 4.2.2Verdicts for standard deviations 4.3Comparing two variances Example 7 4.4Statistics with binomial and Poisson distributions 4.4.1Poisson distribution Example 8 4.5Further reading 4.6Exercises Appendix 5Small or large? 5.1Piecewise constant loss 5.1.1Asymmetric loss 5.2Piecewise linear loss Example 9 5.3Piecewise quadratic loss Example 10 Example 11 5.4Ordinal categories 5.4.1Piecewise linear and quadratic losses 5.5Multitude of options 5.5.1Discrete options 5.5.2Continuum of options 5.6Further reading 5.7Exercises Appendix A. Expected loss Ql in equation (5.3) B. Continuation of Example 9 C. Continuation of Example 10 6Study design 6.1Design and analysis 6.2How big a study? 6.3Planning for impasse 6.3.1Probability of impasse Example 12 6.4Further reading 6.5Exercises Appendix. Sample size calculation for hypothesis testing. 7Medical screening 7.1Separating positives and negatives Example 13 7.2Cutpoints specific to subpopulations 7.3Distributions other than normal 7.3.1Normal and t distributions 7.4A nearly perfect but expensive test Example 14 7.5Further reading 7.6Exercises 8Many decisions 8.1Ordinary and exceptional units Example 15 8.2Extreme selections Example 16 8.3Grey zone 8.4Actions in a sequence 8.5Further reading 8.6Exercises Appendix A. Moment-matching estimator B. The potential outcomes framework 9Performance of institutions 9.1The setting and the task 9.1.1Evidence of poor performance 9.1.2Assessment as a classification 9.2Outliers 9.3As good as the best 9.4Empirical Bayes estimation 9.5Assessment based on rare events 9.6Further reading 9.7Exercises Appendix A. Estimation of θ and ν2 B. Adjustment and matching on background 10Clinical trials 10.1Randomisation 10.2Analysis by hypothesis testing 10.3Electing a course of action—approve or reject? 10.4Decision about superiority 10.4.1More complex loss functions 10.4.2Trials for non-inferiority 10.5Trials for bioequivalence 10.6Crossover design 10.6.1Composition of within-period estimators 10.7Further reading 10.8Exercises 11Model uncertainty 11.1Ordinary regression 11.1.1Ordinary regression and model uncertainty 11.1.2Some related approaches 11.1.3Bounded bias 11.2Composition 11.3Composition of a complete set of candidate models 11.3.1Summary 11.4Further reading 11.5Exercises Appendix A. Inverse of a partitioned matrix B. Mixtures EM algorithm C. Linear loss 12Postscript References Solutions to exercises Index
Statistics for Making Decisions places decision making at the centre of statistical inference, proposing its theory as a new paradigm for statistical practice