Advanced Mathematics

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Advanced Mathematics




BIOSTATISTICS FOR THE HEALTH SCIENCES



Chapter 1: What is Statistics? How Is It Applied to the Health Sciences?


=> What is Statistics? How Is It Applied to the Health Sciences?
=> Definitions of Statistics and Statisticians
=> Why Study Statistics?
=> Types of Studies
=> Exercises

Chapter 2: Defining Populations and Selecting Samples


=> Defining Populations and Selecting Samples
=> What are Populations and Samples?
=> Why Select a Sample?
=> How Samples Can be Selected
=> How to Select a Simple Random Sample
=> How to Select a Bootstrap Sample
=> Why Does Random Sampling Work?
=> Exercises questions answers

Chapter 3: Systematic Organization and Display of Data


=> Systematic Organization and Display of Data
=> Types of Data
=> Frequency Tables and Histograms
=> Graphical Methods
=> Exercises questions answers

Chapter 4: Summary Statistics


=> Measures of Central Tendency
=> Measures of Dispersion
=> Coefficient of Variation (CV) and Coefficient of Dispersion (CD)
=> Exercises questions answers

Chapter 5: Basic Probability


=> What is Probability?
=> Elementary Sets as Events and Their Complements
=> Independent and Disjoint Events
=> Probability Rules
=> Permutations and Combinations
=> Probability Distributions
=> The Binomial Distribution
=> The Monty Hall Problem
=> A Quality Assurance Problem
=> Exercises questions answers

Chapter 6: The Normal Distribution


=> The Importance of the Normal Distribution in Statistics
=> Properties of Normal Distributions
=> Tabulating Areas under the Standard Normal Distribution
=> Exercises questions answers

Chapter 7: Sampling Distributions for Means


=> Population Distributions and the Distribution of Sample Averages from the Population
=> The Central Limit Theorem
=> Standard Error of the Mean
=> Z Distribution Obtained When Standard Deviation Is Known
=> Student’s t Distribution Obtained When Standard Deviation Is Unknown
=> Assumptions Required for t Distribution
=> Exercises questions answers

Chapter 8: Estimating Population Means


=> Estimation Versus Hypothesis Testing
=> Point Estimates
=> Confidence Intervals
=> Confidence Intervals for a Single Population Mean
=> Z and t Statistics for Two Independent Samples
=> Confidence Intervals for the Difference between Means from Two Independent Samples (Variance Known)
=> Confidence Intervals for the Difference between Means from Two Independent Samples (Variance Unknown)
=> Bootstrap Principle
=> Bootstrap Percentile Method Confidence Intervals
=> Sample Size Determination for Confidence Intervals
=> Exercises questions answers

Chapter 9: Tests of Hypotheses


=> Tests of Hypotheses: Terminology
=> Neyman-Pearson Test Formulation
=> Test of a Mean (Single Sample, Population Variance Known)
=> Test of a Mean (Single sample, Population Variance Unknown)
=> One-Tailed Versus Two-Tailed Tests
=> p-Values
=> Type I and Type II Errors
=> The Power Function
=> Two-Sample t Test (Independent Samples with a Common Variance)
=> Paired t Test
=> Relationship between Confidence Intervals and Hypothesis Tests
=> Bootstrap Percentile Method Test
=> Sample Size Determination for Hypothesis Tests
=> Sensitivity and Specificity in Medical Diagnosis
=> Meta-Analysis
=> Bayesian Methods
=> Group Sequential Methods
=> Missing Data and Imputation
=> Exercises questions answers

Chapter 10: Inferences Regarding Proportions


=> Why Are Proportions Important?
=> Mean and Standard Deviation for the Binomial Distribution
=> Normal Approximation to the Binomial
=> Hypothesis Test for a Single Binomial Proportion
=> Testing the Difference between Two Proportions
=> Confidence Intervals for Proportions
=> Sample Size Determination-Confidence Intervals and Hypothesis Tests
=> Exercises questions answers

Chapter 11: Categorical Data and Chi-Square Tests


=> Categorical Data and Chi-Square Tests
=> Understanding Chi-Square
=> Chi-Square Distributions and Tables
=> Testing Independence between Two Variables
=> Testing for Homogeneity
=> Testing for Differences between Two Proportions
=> The Special Case of 2 × 2 Contingency Table
=> Simpson’s Paradox in the 2 × 2 Table
=> McNemar’s Test for Correlated Proportions
=> Relative Risk and Odds Ratios
=> Goodness of Fit Tests-Fitting Hypothesized Probability Distributions
=> Limitations to Chi-Square and Exact Alternatives
=> Exercises questions answers

Chapter 12: Correlation, Linear Regression, and Logistic Regression


=> Correlation, Linear Regression, and Logistic Regression
=> Uses of Correlation and Regression
=> Uses of Correlation and Regression
=> The Scatter Diagram
=> Pearson’s Product Moment Correlation Coefficient and Its Sample Estimate
=> Testing Hypotheses about the Correlation Coefficient
=> The Correlation Matrix
=> Regression Analysis and Least Squares Inference Regarding the Slope and Intercept of a Regression Line
=> Sensitivity to Outliers, Outlier Rejection, and Robust Regression
=> Galton and Regression toward the Mean
=> Multiple Regression
=> Logistic Regression
=> Exercises questions answers

Chapter 13: One-Way Analysis of Variance


=> One-Way Analysis of Variance
=> Purpose of One-Way Analysis of Variance
=> Decomposing the Variance and Its Meaning
=> Necessary Assumptions
=> F Distribution and Applications
=> Multiple Comparisons
=> Exercises questions answers

Chapter 14: Nonparametric Methods


=> Advantages and Disadvantages of Nonparametric Versus Parametric Methods
=> Procedures for Ranking Data
=> Wilcoxon Rank-Sum Test
=> Wilcoxon Signed-Rank Test
=> Sign Test
=> Kruskal–Wallis Test: One-Way ANOVA by Ranks
=> Spearman’s Rank-Order Correlation Coefficient
=> Permutation Tests
=> Insensitivity of Rank Tests to Outliers
=> Exercises questions answers

Chapter 15: Analysis of Survival Times


=> Introduction to Survival Times
=> Survival Probabilities
=> Survival Probabilities: Life Tables
=> Survival Probabilities: The Kaplan–Meier Curve
=> Survival Probabilities: Parametric Survival Curves
=> Survival Probabilities: Cure Rate Models
=> Comparing Two or More Survival Curves-The Log Rank Test
=> Exercises questions answers

Chapter 16: Software Packages for Statistical Analysis


=> General-Purpose Packages
=> Exact Methods
=> Sample Size Determination
=> Why You Should Avoid Excel

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