Basic Statistics and Pharmaceutical Statistical Applications

INTRODUCTION Types of Statistics Parameters and Statistics Sampling and Independent Observations Types of Variables Independent and Dependent Variables Selection of the Appropriate Statistical Test Procedures for Inferential Statistical Tests Example Problems Answers to Problems PROBABILITY Classic Probability Probability Involving Two Variables Conditional Probability Probability Distribution Counting Techniques Binomial Distribution Poisson Distribution Example Problems Answers to Problems SAMPLING Random Sampling Other Probability Sampling Procedures Precision, Accuracy and Bias Reliability and Validity Example Problems Answers to Problems PRESENTATION MODES Tabulation of Data Visual Displays for Discrete Variables Visual Displays for Continuous Variables Visual Displays for Two or More Continuous Variables Example Problems Answers to Problems MEASURES OF CENTRAL TENDENCY Centers of a Continuous Distribution Dispersion Within a Continuous Distribution Population versus Sample Measures of Central Tendency Measurements Related to the Sample Standard Deviation Trimmed Mean Alternative Computational Methods for Calculating Central Tendency Example Problems Answers to Problems THE NORMAL DISTRIBUTION AND DATA TRANSFORMATION The Normal Distribution Determining if the Distribution is Normal New! Data Transformations: An Overview New! Lognormal Transformation and the Geometric Mean New! Other Types of Transformations Example Problems Answers to Problems CONFIDENCE INTERVALS AND TOLERANCE LIMITS Sampling Distribution Standard Error of the Mean versus the Standard Deviation Confidence Intervals Statistical Control Charts New! Process Capability New! Tolerance Limits Example Problems Answers to Problems HYPOTHESIS TESTING Hypothesis Testing Types of Errors Type I Error Type II Error and Power New! Experimental Errors and Propagation of Errors Example Problems Answers to Problems T-TESTS Parametric Procedures The t-distribution One-tailed vs. Two-tailed Tests One-Sample t-tests Two-Sample t-tests New! Corrected Degrees of Freedom for Unequal Variances One-sample t-test Revisited for Critical Value Matched Pair t-Test (Difference t-Test) Example Problems Answers to Problems ONE-WAY ANALYSIS OF VARIANCE (ANOVA) Hypothesis Testing with the One-way ANOVA The F-distribution Test Statistic ANOVA Definitional Formula ANOVA Computational Formula Randomized Block Design Homogeniety of Variance Example Problems Answers to Problems MULTIPLE COMPARISON TESTS Error Associated with Multiple t-tests Overview of Multiple Comparison Tests New! The q-statistic New! Planned Multiple Comparisons Bonferroni Adjustment New! Sidak test Dunn's Multiple Comparisons New! Dunnett's Test Post hoc Procedures New! Tukey HSD Test Student Newman-Keuls Test New! Fisher LSD Test Scheffe Procedure Scheffe Procedure for Complex Comparisons New! Unbalanced Designs Lack of Homogeneity New! Other Post hoc Tests Example Problems Answers to Problems FACTORIAL DESIGNS: AN INTRODUCTION Factorial Designs Two-way Analysis of Variance Computational Formula with Unequal Cell Size Post Hoc Procedures New! Repeated Measures Design New! Repeatability and Reproducibility New! Latin Square Designs Other Designs New! Fixed, Random and Mixed Effect Models Beyond a Two-way Factorial Design Example Problems Answers to Problems CORRELATION Graphic Representation of Two Continuous Variables Pearson Product Moment Correlation Coefficient Correlation Line Statistical Significance of a Correlation Coefficient Correlation and Causality In vivo - In vitro Correlation New! Other Types of Bivariate Correlations Pair-wise Correlations Involving More Than Two Variables Multiple Correlations Partial Correlations Non-linear Correlations New! Assessing Independence and Randomness Example Problems Answers to Problems LINEAR REGRESSION The Regression Line Coefficient of Determination ANOVA Table Confidence Intervals and Hypothesis Testing for the Population Slope (b) Confidence Intervals for the Regression Line New! Inverse Prediction New! Multiple Data at Various Points on the Independent Variable New! Assessing Parallelism of the Slopes of Two Sample Multiple Linear Regression Models Example Problems Answers to Problems Z-TESTS OF PROPORTIONS z-test of Proportions - One-sample Case z-test of Proportions - Two-sample Case New! Estimating Power and Desired Sample size for two-sample Z-test of Proportions z-tests for Proportions - Yates' Correction for Continuity Proportion Testing for More Than Two Levels of a Discrete Independent Variable Example Problems Answers to Problems CHI SQUARE TESTS Chi Square Statistic Chi Square for One Discrete Independent Variable Chi Square Goodness-of-fit Test Chi Square Test of Independence Yates' Correction for 2x2 Contingency Table New! Comparison of Chi Square to the Z-test of Proportions Fisher's Exact Test McNemar's Test Cochran's Q Test Mantel-Haenszel Test Example Problems Answers to Problems NEW! MEASURES OF ASSOCIATION Introduction Dichotomous Associations Nominal Associations Ordinal Associations Nominal-by-interval Associations Reliability Measurements Summary Example Problems Answers to Problem NEW! ODDS RATIOS AND RELATIVE RISK RATIOS Probability, Odds, and Risk Odds Ratio Relative Risk Graphic Display for Odds Ratios and Relative Risk Ratios Mantel-Haenszel Estimate of Relative Risk Logistic Regression Example Problems Answers to Problems NEW! EVIDENCE-BASED PRACTICE: AN INTRODUCTION Sensitivity and Specificity Two-by-Two Contingency Table Defining Evidence Based Practice Frequentist versus Bayesian Approaches to Probability Predictive Values Likelihood Ratios Example Problems Answers to Problems NEW! SURVIVAL STATISTICS Censored Survival Data Life Table Analysis Survival Curve Kaplan-Meier Procedure Visually Comparison of Two Survival Curves Tests to Compare Two Levels of an Independent Variable Hazard Ratio Multiple Regression with Survival Data: Proportional Hazards Regression Other Measures and Tests of Survival Example Problems Answers to Problems NONPARAMETRIC TESTS New! Use of Nonparametric Tests Ranking of Information Mann-Whitney U Test Median Test Wilcoxon Matched-Pairs Test Sign Test Kruskal-Wallis Test New! Post hoc Comparisons using Kruskal-Wallis Friedman Two-Way Analysis of Variance Spearman Rank-Order Correlation Theil's Incomplete Method New! Kolmogorov-Smirnov Goodness-of-Fit Test New! Anderson-Darling Test New! Runs Tests New! Range Tests Example Problems Answers to Problems STATISTICAL TESTS FOR EQUIVALENCE Bioequivalence Testing Experimental Designs for Bioequivalence Studies Two-sample t-test Example Power in Bioequivalence Tests Rules for Bioequivalence Creating Confidence Intervals Comparison Using Two One-sided t-tests New! Clinical Equivalence and Non-inferiority Dissolution Testing SUPAC-IR Guidance Example Problems Answers to Problems OUTLIER TESTS New! Regulatory Considerations Outliers on a Single Continuum Plotting and Number of Standard Deviations from the Center The "Huge" Rule Grubbs' Test for Outlying Observations Dixon Q Test New! Hampel's Rule Multiple Outliers Bivariate Outliers in Correlation and Regression Analysis Example Problems Answers to Problems STATISTICAL ERRORS IN THE LITERATURE Errors and the Peer Review Process Problems with Experimental Design Standard Deviations versus Standard Error of the Mean Problems with Hypothesis Testing Problems with Parametric Statistics Errors with the Chi Square Test of Independence Summary Appendix A: Flow Chart for the Selection of Appropriate Tests Appendix B: Statistical Tables B1 Random Numbers Table B2 Normal Standardized Distribution New! B3 K-Values for Calculating Tolerance Limits (two-tailed) New! B4 K-Values for Calculating Tolerance Limits (one-tailed) B5 Student t-Distribution (1-a/2) B6 Comparison of One-tailed vs. Two-tailed t-Distributions B7 Analysis of Variance F-Distribution B8 Upper Percentage Points of the Fmax Statistic B9 Upper Percentage Points of the Cochran C Test for Homogeneity of Variance B10 Percentage Points of the Standardized Range (q) New! B11 Percentage Points of the Dunn Multiple Comparisons New! B12 Critical Values of q for the Two-Tailed Dunnett's Test New! B13 Critical Values of q for the One-Tailed Dunnett's Test B14 Values of r at Different Levels of Significance B15 Chi Square Distribution New! B16 Critical Values for Kolmogorov Goodness-of-fit Test (a =0.05) New! B17 Critical Values for Smirnov Test Statistic (a =0.05) New! B18 Critical Values for the Runs Test (a = 0.05) New! B19 Critical Values for TI Range Test (a = 0.05) New! B20 Critical Values for the FR Test for Dispersion B21 Values for Use in Grubbs Test for Outlier (a ) B22 Values for Use in Dixon Test for Outlier (a ) Index