Statistical Methods in the Biological and Health Sciences

1 Descriptive Methods1.1 Distribution Tables: Discrete DataBar GraphsBivariate Data: Two-Way Tables1.2 A Quick Look at Distribution: Stem and LeafConstructing a Simple Stem-and-Leaf Diagram1.3 Frequency Distributions: HistogramsRules for Breaking Data into ClassesCumulative Distribution1.4 Measures of Location or Central TendencySample MeanSample Median1.5 Measures of Variability or DispersionSample VarianceSample Standard DeviationSample RangeInterquartile RangeFinding the Sample Interquartile RangeMultiple Data Sets 1.6 Box Plots Constructing a Box Plot1.7 Handling Grouped Data 2 Introduction to Probability and Counting2.1 Interpreting Probablilities2.2 Tree Diagrams and Elementary GeneticsElementary Genetics 2.3 Permutations and Combinations 2.4 Multiplication Principle Guidelines for Using the Multiplication Principle2.5 Permutations of Indistinguishable Objects 2.6 Combinations 3 Probability and Problem Solving 3.1 Venn Diagrams and the Axioms of ProbabilityVenn DiagramsAxioms of Probability3.2 General Addition Rule3.3 Conditional Probability3.4 Diagnostic Tests and Relative RiskRelative Risk3.5 Independence3.6 The Multiplication Rule3.7 Bayes' Theorem4 Discrete Random Variables4.1 Discrete and Continuous Variables4.2 Discrete Density Functions and ExpectationExpectation4.3 Cumulative Distribution Function4.4 Binomial DistributionExpected Value and Variance: BinomialCalculating Binomial Probabilities: Cumulative Distribution4.5 Poisson Distribution 5 Continuous Random Variables5.1 Continuous Random Variables Expectation 5.2 Cumulative Distribution Function 5.3 Normal Distribution Properties of Normal Curves Standard Normal Distribution Standardization 5.4 Normal Probability Rule and Medical Tables 6 Inferences on the Mean6.1 Random Sampling and Randomization Simple Random Sampling Randomization 6.2 Point Estimation of the Mean and Introduction to Interval Estimation:Central Limit Theorem Interval Estimation Central Limit Theorem 6.3 Confidence Interval on the Population Mean and the T Distribution Properties of T Random Variables 6.4 Introduction to Hypothesis Testing 6.5 Testing Hypotheses on the PopulationMean: T Test Preset Alpha Values 6.6 Sample Size: Confidence Intervals and Power Sample Size: Hypothesis Testing 7 Chi-Squared Distribution and Inferences on the Variance 7.1 Chi-Squared Distribution and Interval Estimation of the Population Variance Confidence Interval on s2 7.2 Testing Hypotheses on the Population Variance 8 Inferences on Proportions 8.1 Point Estimation 8.2 Interval Estimation of p 8.3 Sample Size for Estimating p 8.4 Hypothesis Testing on p 8.5 Comparing Two Proportions: Estimation Confidence Interval on the Difference in Two Proportions 8.6 Comparing Two Proportions: Hypothesis Testing Testing That the Null Value Is Zero:Pooled Test 9 Comparing Two Means and Two Variances 9.1 Comparing Two Means and Two Variances 9.2 Comparing Variances: F Distribution Rule of Thumb Variance ComparisonF Test for Comparing Variances: F Distribution 9.3 Inferences on m1 - m2: Pooled T Interval Estimation of m1 - m2 Pooled T Tests 9.4 Inferences on m1 - m2: Unequal Variances 9.5 Inferences on m1 - m2: Paired T Paired T Test 10 k-Sample Procedures: Introduction to Design 10.1 One-Way Classification, Completely Random Design with Fixed Effects Data Format and Notation 10.2 Paired and Multiple Comparisons Bonferroni T Tests: Paired Comparisons Duncan's Multiple Range Test A Note on Computing 10.3 Random Effects 10.4 Randomized Complete Blocks Data Format and Notation Testing HO: m1. = m2. = @ @ @ = mk. Effectiveness of Blocking Paired and Multiple Comparisons A Note on Computing 10.5 Factorial Experiments Data Format and Notation Testing Main Effects and Interaction Multiple and Paired Comparisons A Note on Computing 11 Regression and Correlation 11.1 Introduction To Simple Linear Regression 11.2 Method of Least Squares Estimating an Individual Response A Note on Computing 11.3 Introduction to Correlation Estimating r 11.4 Evaluating the Strength of the Linear Relationship Coefficient of Determination Analysis of Variance A Note on Computing 11.5 Confidence Interval Estimation 11.6 Multiple Regression 12 Categorical Data 12.1 2 A' 2 Contingency Tables Test of Independence Test of Homogeneity 12.2 r A' c Contingency Tables 13 Some Additional Procedures and Distribution-Free Alternatives 13.1 Testing for Normality: The Lilliefors Test 13.2 Tests of Location: One Sample Sign Test for Median Wilcoxon Signed-Rank Test 13.3 Tests of Location: Paired Data Sign Test for Median Difference Wilcoxon Signed-Rank Test: Paired Data 13.4 Tests of Location: Unmatched Data Wilcoxon Rank-Sum Test 13.5 Kruskal-Wallis k-Sample Test forLocation: Unmatched Data Kruskal-Wallis k-Sample Test 13.6 Friedman k-Sample Test for Location: Matched Data Friedman Test 13.7 Correlation Spearman's Rank Correlation Coefficient 13.8 Bartlett's Test for Equality of Variances 13.9 Normal Approximations 13.10 A Small Sample Test on Proportions Appendix ASummation Notation and Rules for Expectation and Variance Summation Notation Rules for Expectation and Variance Appendix BStatistical Tables ReferencesAnswers to Odd-Numbered ProblemsIndex