From: Medical Biostatistics, Fourth Edition by Abhaya Indrayan and Rajeev Kumar Malhotra

(Chapman & Hall/CRC Press, New York), 2018

Guide to Statistical Methods

Last two columns refer to the equation/para/section and page of the book

Although this book covers statistical methods for a large variety of datasets and problems but there are some setups that are not covered and not mentioned in the following tables. Several others for which name and applicability are mentioned in the book without details such as Breslow–Day, Tarone–Ware and Brown–Forsythe tests are also not mentioned in the following tables.

 Table S.1 Methods to Compute Some Confidence Intervals Parameter of Interest Conditions 95% CI Page Number Proportion (π) Large n, 0

 Table S.2 Statistical Procedures for Test of Hypothesis on Proportions Parameter of Interest and Setup Conditions Main Criterion Equation/ Section Page Number One-way and 2×2 Tables One dichotomous variable Independent trials Any n Binomial Use Equation 13.1 308 Large n Gaussian Z Equation 13.3 309 One polytomous variable Independent trials Large n Goodness-of-fit chi-square Equation 13.5 312 Small n Multinomial Use Equation 13.6 316 Two dichotomous variables (2 × 2) Two independent samples Large n Chi-square or Gaussian Z Equation 13.8 or 13.9 319/320 Small n Fisher exact Equation 13.11 326 Detecting a medically important difference – Large n Gaussian Z Equation 13.10 321 Equivalence, superiority and noninferiority tests TOSTs and others Table 13.10 325 Matched pairs Large n McNemar Equation 13.12 328 Small n Binomial Equation 13.13 329 Crossover design Large n Chi-square Section 13.2.2.5 322 Small n Fisher exact Equation 13.11 326 Bigger Tables, No Matching Large n Required The Case of Smalln Not Discussed in This Book Association (nominal) 2×C tables Chi-square Equation 13.15 332 Trend in proportions (ordinal) 2×C tables Chi-square for trend Equation 13.16 333 Dichotomy in repeated measures Many related 2×2 tables Cochran Q Equation 13.18 324 Association R×C tables Chi-square Equation 13.15 332 Association Three-way tables Test of full independence Chi-square Equation 13.19 340 Test of other types of independence (log–linear models) G2 Three-way extension of Equation 13.22 341 I × Itable Matched pairs McNemar–Bowker Section 13.3.2.2 337 Stratified Stratified into many 2×2 tables Mantel–Haenszel chi-square Equation 14.26 365

 Table S.3 Procedures for Test of Hypothesis on Relative Risk (RR) and Odds Ratio (OR) Parameter of Interest and Setup Conditions Main Criterion Equation/ Section Page Number Relative and Attributable Risks Large n Required The Case of Small n Not Discussed in This Book ln(RR) Two independent samples Gaussian Z or chi-square Equation 14.5 or 13.8 353/320 RR Matched pairs As for OR (Gaussian Z or McNemar) Equation 14.22 or 14.23 362 AR Two independent samples Chi-square or Gaussian Z Equation 13.8 or 13.9 319/320 Matched pairs McNemar Equation 13.12 328 Odds Ratio Large n Required The Case of Small n Not Discussed in This Book ln(OR) Two independent samples Chi-square Equation 13.8 319 OR Matched pairs Gaussian Z or McNemar Equation 14.22 or 14.23 363/363 Stratified Mantel–Haenszel chi-square Equation 14.26 365

 Table S.4 Statistical Procedures for Test of Hypothesis on Means or Locations Setu Conditions Main Criterion Equation/Section Page Number One sample Comparison with prespecified – Gaussian σ known Gaussian Z Section 15.1.1.1 378 σ not known Student t Equation 15.1 378 Comparison of two groups Paired – Gaussian Student t Equation 15.3 380 Paired – NonGaussian Any n Sign test Equation 15.17a–c 402 5 ≤n≤ 19 Wilcoxon signed-ranks WS Equation 15.18a 402 20 ≤n≤ 29 Standardized WS referred to Gaussian Z Equation 15.18b 403 n≥ 30 Student t Equation 15.1 378 Unpaired – Gaussian Equal variances Student t Equation 15.6a 381 Unequal variances Welch Equation 15.6b 381 Unpaired – NonGaussian n1, n2 between (4, 9) Wilcoxon rank-sum WR Equation 15.19 404 n1, n2 between (10, 29) Standardized WR referred to Gaussian Z Equation 15.20 405 n1, n2≥ 30 Student t Equation 15.6a or 15.6b 381 Crossover design – Gaussian conditions Student t Section 15.1.3 383 Detecting medically important difference – Gaussian conditions Student t Equation 15.23 414 Equivalence tests – Gaussian conditions Student t Section 15.4.2.2 415 Comparison of three or more groups One-way layout – Gaussian ANOVA F Equation 15.8 389 One-way layout – NonGaussian n≤ 5 Kruskal–Wallis H Equation 15.21 406 n≥ 6 H referred to chi-square Equation 15.21 406 Two-way layout – Gaussian ANOVA F Section 15.2.2 392 Two-way layout – NonGaussian (one observation per cell – repeated measures) J≤ 13 and K = 3 Friedman S Equation 15.22a or 15.22b 408 J≤ 8 and K = 4 Friedman S Equation 15.22a or 15.22b 408 J≤ 5 and K = 5 Friedman S Equation 15.22a or 15.22b 408 Larger J, K S referred to chi-square Equation 15.22a or 15.22b 408 Multiple comparisons Gaussian conditions All pairwise Tukey D Equation 15.15 399 With control group Dunnett Equation 15.16 400 Few comparisons Bonferroni Section 15.2.4.1 399 Repeated measures Gaussian conditions F-test with Hyunh–Feldt correction Section 15.2.3 399

 Table S.5 Procedures for Test of Hypothesis on Some Other Parameters Parameter of Interest and Setup Conditions Main Criterion Equation/ Section Page Number One sample Product–moment correlation Gaussian conditions Student t Equation 16.20 455 Serial correlation Gaussian conditions Durbin–Watson Section 16.3.4 442 Intraclass correlation Gaussian conditions F Section 16.5.3.2 459 Spherecity (repeated measures) Gaussian conditions Mauchly Section 15.2.3.2 459 Goodness of fit of whole model Large n Hosmer–Lemeshow Section 17.1.2.3 474 Two-sample Comparison Two independent samples Comparison of two distributions Very large n(mean and SD known) Kolmogorov-Smirnov Section 12.4.2.1 285 Large n Shapiro–Wilk Section 12.4.2.1 285 Moderate n Anderson–Darling Section 12.4.2.1 285 Comparison of two correlations Gaussian  conditions Fisher z-transformation Section 16.5.1.3 456 Comparison of two survival curves Any distribution Log-rank Section 18.3.1.2 519 Comparison of two variances Gaussian conditions F or Levene Section 15.1.2.2 381

 Table S.6 Methods for Studying the Nature of Relationship Dependent Variable (y) Independent Variables (xs) Method Equation/ Section Page Number Quantitativea Qualitative ANOVA Section 15.2 387 Quantitative Quantitative Quantitative regression Chapter 16 423 Quantitativea Mixture of qualitative and quantitative ANCOVA Section 16.4.2.4 452 Qualitative (dichotomous) Qualitative or quantitative or mixture Logistic Sections 17.1 469 Qualitative (polytomous) Qualitative or quantitative or mixture Logistic – any two categories at a time Section 17.3.2 483 Quantitative Discriminant Section 19.2.3 539 Survival probability Groups – duration in time intervals Life table Equation 18.8 511 Groups – duration in continuous time Kaplan–Meier Equation 18.10 513 Hazard ratio Mixture of qualitative and quantitative Cox model Section 18.3.2 521 Note:  Large n required, particularly for tests of significance. Exact methods for small n not discussed in this book. a  Quantitative are variables on metric scale without any broad categories. Fine categories are admissible.

 Table S.7 Main Methods of Measurement of Strength of Relationship between Two Variables Types of Variables Measure Equation/Section Page Number Both qualitative Binary categories OR, Jaccard, Yule, and several others Section 17.5.1.1 488 Polytomous categories – nominal Phi-coefficient Equation 17.7a 490 Tschuprow coefficient Equation 17.7b 490 Contingency coefficient Equation 17.7c 490 Cramer V Equation 17.7d 490 Proportional reduction in error Equation 17.8 492 Polytomous categories – ordinal Kendall tau, Goodman–Kruskal gamma, Somerd Section 17.5.1.4 492 Dependent qualitative and independent quantitative Odds ratio Section 17.1 469 Dependent quantitative and independent qualitative R2 from ANOVA or η2 from regression Equation 17.9 or Equation 16.11 17.9/440 Both quantitative For multiple linear (more than 2 variables) R2 from regression Use Equation 16.12 441 For simple linear Product–moment correlation (r) Equation 16.19 452 For monotonic relation Spearman (rank) correlation (rS) Equation 16.22 457 For intraclass Intraclass correlation (rI) Equation 16.23 459 With previous value Serial (auto) correlation Section 16.5.1.4 456 Keeping other variables fixed Partial correlation Equation 16.21 456 Two sets of quantitative variables Canonical correlation Section 19.2.1.1 531 One quantitative and the other dichotomous Biserial Section 17.5.2.2 495 Agreement Qualitative Cohen kappa Equation 17.10 496 Quantitative Limits of disagreement Section 16.6.1.2 461 Alternative methods Section 16.6.2.1 463 Intraclass correlation Equation 16.23 459

 Table S.8 Multivariate Methods in Different Situations (Large n Required) Nature of the Variables Objective Types of Variables Statistical Method Section Page Number A dependent set and an independent set Relationship Both quantitative Multivariate multiple regression Section 19.2.1.2 532 Equality of means of dependents Dependent quantitative and independent qualitative MANOVA Section 19.2.2.1 537 Dependent is one (many groups) Classify subjects into known groups Independent quantitative Discriminant analysis Section 19.2.3.1 539 All variables interrelated (none is dependent) Discover natural clusters of subjects Qualitative or quantitative or mixed Cluster analysis Section 19.3.1 543

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