Basic Statistics and Pharmaceutical Statistical Applications

Building on its best-selling predecessors, Basic Statistics and Pharmaceutical Statistical Applications, Third Edition covers statistical topics most relevant to those in the pharmaceutical industry and pharmacy practice. It focuses on the fundamentals required to understand descriptive and inferential statistics for problem solving. Incorporating new material in virtually every chapter, this third edition now provides information on software applications to assist with evaluating data. New to the Third Edition Use of Excel® and Minitab® for performing statistical analysis Discussions of nonprobability sampling procedures, determining if data is normally distributed, evaluation of covariances, and testing for precision equivalence Expanded sections on regression analysis, chi square tests, tests for trends with ordinal data, and tests related to survival statistics Additional nonparametric procedures, including the one-sided sign test, Wilcoxon signed-ranks test, and Mood’s median test With the help of flow charts and tables, the author dispels some of the anxiety associated with using basic statistical tests in the pharmacy profession and helps readers correctly interpret their results using statistical software. Through the text’s worked-out examples, readers better understand how the mathematics works, the logic behind many of the equations, and the tests’ outcomes.

INTRODUCTION Types of StatisticsParameters and Statistics Sampling and Independent Observations Types of VariablesIndependent and Dependent Variables Selection of the Appropriate Statistical Test Procedures for Inferential Statistical TestsApplications of Computer Software PROBABILITYClassic ProbabilityProbability Involving Two Variables Conditional Probability Probability Distribution Counting TechniquesBinomial Distribution Poisson Distribution SAMPLING Random Sampling Using Minitab or Excel to Generate a Random SampleOther Probability Sampling Procedures Nonprobability Sampling Procedure Random Assignment to Two or More Experimental LevelsPrecision, Accuracy, and Bias Reliability and Validity PRESENTATION MODESTabulation of DataVisual Displays for Discrete VariablesVisual Displays for Continuous Variables Visual Displays for Two or More Continuous Variables Using Excel or Minitab for Visual Displays MEASURES OF CENTRAL TENDENCY Centers of a Continuous Distribution Dispersion Within a Continuous Distribution Population versus Sample Measures of Central TendencyMeasurements Related to the Sample Standard Deviation Trimmed MeanUsing Excel or Minitab for Measures of Central TendencyAlternative Computational Methods for Calculating Central Tendency THE NORMAL DISTRIBUTION AND DATA TRANSFORMATION The Normal Distribution Determining if the Distribution is NormalData Transformations: An Overview Lognormal Transformation and the Geometric Mean Other Types of TransformationsUsing Excel or Minitab to Evaluate Normality CONFIDENCE INTERVALS AND TOLERANCE LIMITSSampling Distribution Standard Error of the Mean versus the Standard Deviation Confidence IntervalsStatistical Control ChartsProcess Capability Tolerance Limits Using Excel or Minitab for Applications Discussed HYPOTHESIS TESTING Hypothesis Testing Types of Errors Type I Error Type II Error and PowerExperimental Errors and Propagation of Errors t-TESTS Parametric Procedures The t-distribution One-tailed vs. Two-tailed TestsOne-Sample t-testsTwo-Sample t-tests Computer Generated p-valuesCorrected Degrees of Freedom for Unequal VariancesOne-sample t-test Revisited for Critical ValueMatched Pair t-Test (Difference t-Test) Using Excel or Minitab for Student t-tests ONE-WAY ANALYSIS OF VARIANCE (ANOVA)Hypothesis Testing with the One-way ANOVA The F-distributionTest Statistic ANOVA Definitional FormulaANOVA Computational Formula Randomized Block Design Homogeniety of VarianceUsing Excel or Minitab for One-Way ANOVAs MULTIPLE COMPARISON TESTSError Associated with Multiple t-testsOverview of Multiple Comparison Tests The q-statisticPlanned Multiple Comparisons Bonferroni AdjustmentSidák test Dunn's Multiple Comparisons Dunnett's Test Post Hoc ProceduresTukey HSD Test Student Newman-Keuls Test Fisher LSD TestScheffé ProcedureScheffé Procedure for Complex Comparisons Unbalanced Designs Lack of Homogeneity Other Post Hoc Tests Using Minitab for Multiple Comparisons FACTORIAL DESIGNS: AN INTRODUCTIONFactorial Designs Two-Way Analysis of Variance Computational Formula with Unequal Cell SizePost Hoc ProceduresRepeated Measures Design Repeatability and Reproducibility Latin Square Designs Other Designs Fixed, Random, and Mixed Effect ModelsBeyond a Two-way Factorial DesignUsing Excel or Minitab for Two-Way ANOVAs CORRELATION Graphic Representation of Two Continuous Variables CovariancePearson Product-Moment Correlation Coefficient Correlation LineStatistical Significance of a Correlation Coefficient Correlation and Causality In vivoand In vitro Correlation Other Types of Bivariate Correlations Pair-wise Correlations Involving More Than Two Variables Multiple CorrelationsPartial Correlations Nonlinear Correlations Assessing Independence and Randomness Using Excel or Minitab for Correlation REGRESSION ANALYSISThe Regression LineCoefficient of DeterminationANOVA Table Confidence Intervals and Hypothesis Testing for the Population Slope (b)Confidence Intervals and Hypothesis Testing for the PopulationIntercept (a)Confidence Intervals for the Regression LineInverse Prediction Multiple Data at Various Points on the Independent Variable Lack-of-Fit TestAssessing Parallelism of the Slopes of Two SampleCurvilinear and Nonlinear RegressionMultiple Linear Regression Models Stepwise Regression Using Excel or Minitab for Regression Z-TESTS OF PROPORTIONS z-test of Proportions - One-sample Case z-test of Proportions - Two-sample Case Estimating Power and Desired Sample size for two-sample Z-test of Proportionsz-tests for Proportions - Yates' Correction for Continuity Proportion Testing for More Than Two Levels of a DiscreteIndependent Variable CHI SQUARE TESTS Chi Square Statistic Chi Square for One Discrete Independent Variable Chi Square Goodness-of-fit Test Chi Square Test of IndependenceYates' Correction for 2x2 Contingency Table Comparison of Chi Square to the Z-test of Proportions Fisher's Exact Test McNemar's TestCochran's Q Test Mantel-Haenszel Test MEASURES OF ASSOCIATION Introduction Dichotomous Associations Nominal AssociationsOrdinal Associations Nominal-by-interval Associations Reliability Measurements 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 EVIDENCE-BASED PRACTICE: AN INTRODUCTION Sensitivity and Specificity Two-by-Two Contingency Table Defining Evidence Based Practice Frequentist versus Bayesian Approaches to Probability Predictive ValuesLikelihood Ratios SURVIVAL STATISTICS Censored Survival DataLife Table Analysis Survival CurveKaplan-Meier Procedure Visually Comparison of Two Survival CurvesTests to Compare Two Levels of an Independent VariableHazard RatioMultiple Regression with Survival Data:Proportional Hazards Regression Other Measures and Tests of Survival NONPARAMETRIC TESTSUse of Nonparametric Tests Ranking of Information Mann-Whitney U TestMedian Test Wilcoxon Matched-Pairs Test Sign TestKruskal-Wallis TestPost hoc Comparisons using Kruskal-Wallis Friedman Two-Way Analysis of Variance Spearman Rank-Order CorrelationTheil's Incomplete Method Kolmogorov-Smirnov Goodness-of-Fit Test Anderson-Darling TestRuns Tests Range Tests STATISTICAL TESTS FOR EQUIVALENCE Bioequivalence Testing Experimental Designs for Bioequivalence StudiesTwo-sample t-test Example Power in Bioequivalence TestsRules for Bioequivalence Creating Confidence Intervals Comparison Using Two One-sided t-testsClinical Equivalence and Non-inferiority Dissolution TestingSUPAC-IR GuidanceOUTLIER TESTS Regulatory Considerations Outliers on a Single Continuum Plotting and Number of Standard Deviations from the CenterThe "Huge" Rule Grubbs' Test for Outlying ObservationsDixon Q Test Hampel's Rule Multiple Outliers Bivariate Outliers in Correlation and Regression Analysis STATISTICAL ERRORS IN THE LITERATURE Errors and the Peer Review Process Problems with Experimental Design Standard Deviations versus Standard Error of the MeanProblems with Hypothesis Testing Problems with Parametric Statistics Errors with the Chi Square Test of IndependenceAppendix A: Flow Chart for the Selection of Appropriate Tests Appendix B: Statistical TablesAppendix C: Summary of Commands for Excel and MinitabAppendix D: Answers to Example Problems Index References, Supplemental Readings, and Example Problems appear at the end of each chapter.

James E. De Muth