Evidence-Based Statistics. Peter M. B. Cahusac

More than Two Independent Samples 7.6 Permutation Analyses 7.7 Bootstrap Analyses for One Sample or Related Samples 7.8 R Code for Chapter 7 7.9 Exercises References

      13  8 Other Useful Techniques 8.1 Other Techniques 8.2 Critical Prior Interval 8.3 False Positive Risk 8.4 The Bayes Factor and the Probability of the Null Hypothesis 8.5 Bayesian t Tests 8.6 The Armitage Stopping Rule 8.7 Counternull Effect Size References Notes

      14  Appendix A: Orthogonal Polynomials

      15  Appendix B: Occam's Bonus Reference

      16  Appendix C: Problems with p Values C.1 The Misuse of p Values C.2 The Use of p Values References

      17  Index

      18  End User License Agreement

      List of Tables

      1 Chapter 2Table 2.1 Interpreting support.Table 2.2 Likelihood values used in British courts to aid the jury in decidin...Table 2.3S-likelihood interval values and their corresponding frequentist confid...

      2 Chapter 3Table 3.1 How sample size affectsS and p.Table 3.2 Values for strength of evidenceS are given in the left column and p...

      3 Chapter 4Table 4.1 Fitness data for 40 participants.Table 4.2 ANOVA summary table for an independent group's analysis.Table 4.3 Data and means for skill according to weeks of training.Table 4.4 ANOVA summary table for an independent group's analysis for the pra...Table 4.5 Contrast weights for linear and quadratic models, with calculated S...Table 4.6 As in the previous Table 4.5, showing weights and calculations for ...Table 4.7 Blood clotting times in haemophiliac patients and normal volunteers...Table 4.8 Summary table for blood clotting data in a two-way factorial ANOVA.Table 4.9 Blood clotting time means as plotted in Figure 4.4.Table 4.10 Data on additional sleep obtained following three different drugs^a...Table 4.11 ANOVA summary for a one-way repeated measures design.Table 4.12 The same data as in Table 4.10 with the patient's sex added in the...Table 4.13 ANOVA summary for within and between participants design of data s...Table 4.14 Means and weights used for the contrast.Table 4.15 Means and weights used for the second contrast.

      4 Chapter 5Table 5.1 Summary of a regression analysis given as SS in ANOVA format.Table 5.2 Summary of a polynomial regression fit given in ANOVA format.Table 5.3 Prescription errors made by doctors in a hospital.Table 5.4 Output obtained using R.Table 5.5 Calculation of the log likelihood for the full model.Table 5.6 The same as Table 5.5 but for a model consisting only of a constant...Table 5.7 Summary of logistic regression analysis when the variablescore is r...Table 5.8 The same as Table 5.5 but for a model without thescore variable.Table 5.9 Summary output obtained in R.

      5 Chapter 6Table 6.1 A week's data of butterfly sightings.Table 6.2 Two hundred patients assessed with a CT scan either show positive s...Table 6.3 The same data as Table 6.2 but with a prevalence of 0.1.Table 6.4 The effects of disease prevalence on statistics.Table 6.5 The results from using an ultrascan on the same 200 patients as bef...Table 6.6 Matched sample tables (a) and (b), representing diseased and health...Table 6.7 The numbers represent a total of 288 individuals who are either pos...Table 6.8 Table 6.7 data with extra rows incorporating the age variablex.

      6 Chapter 7Table 7.1 Calculations going from raw data on the left to normal scores, and ...Table 7.2 The same calculations as were performed in Table 7.1, except that t...Table 7.3 Subtracting 5 from just the group 1 scores (first column), calculat...Table 7.4 For the second hypothesis, calculated values of ranks, quantiles, v...Table 7.5 Outputs from running the R code to obtain bootstrap estimates.Table 7.6 Bootstrap estimate from running the R code for two independent samp...

      7 Chapter 8Table 8.1 Estimates obtained using the FPR calculator for different total sam...Table 8.2 Exchange rates betweenp values, likelihood ratios, and posterior pr...Table 8.3 Comparison between likelihood ratios obtained by JZS Bayes factor a...

      8 Appendix CTable C.1 Baseline characteristics of the 104 493 individuals from the Copenh...

      List of Illustrations

      1 Chapter 1Figure 1.1 From sampling distribution to likelihood function. The top curve ...Figure 1.2 Effect size versus sample size: which provides most evidence agai...Figure 1.3 A flow diagram illustrating the general procedure of calculating ...

      2 Chapter 2Figure 2.1 The scales for LR and support S. The ‘compressed’ LR scale is app...Figure 2.2 The Greek goddess Themis, personifying justice. She holds the Sca...Figure 2.3 The likelihood function (dark grey) and wider population distribu...Figure 2.4 The likelihood function for the extra sleeping time data. The mea...Figure 2.5 An alternative visualization for the likelihood that produces ide...Figure 2.6 This shows the likelihood function indicating the likelihood if t...Figure 2.7 Calculating the maximum likelihood ratio (LR _M ). The same likeliho...Figure 2.8 The likelihood function showing likelihood interval limits for S-...Figure 2.9 The support curve for data given in Section 2.1.3. The vertical a...Figure 2.10 (a) Support (log LR) curves for different effect sizes: −0.5, 0....Figure 2.10 (b) The same plot of support curves for effect sizes from −0.5 t...Figure 2.11 Misleading and weak evidence in relation to Type I and Type II e...Figure 2.12 Flowchart showing the steps necessary for the evidential analysi...

      3 Chapter 3Figure 3.1 The likelihood function for the difference in sleeping time. The ...Figure 3.2 The likelihood function for the independent samples analysis.