Foundations Of Applied Statistical Methods

Preface
Contents
Chapter 1: Description of Data and Essential Probability Models
1.1 Types of Data
1.2 Description of Data
1.2.1 Distribution
1.2.2 Description of Categorical Data
1.2.3 Description of Continuous Data
1.2.4 Stem-and-Leaf Plot
1.2.5 Box-and-Whisker Plot
1.3 Descriptive Statistics
1.3.1 Statistic
1.3.2 Central Tendency Descriptive Statistics for Quantitative Outcomes
1.3.3 Dispersion Descriptive Statistics for Quantitative Outcomes
1.3.4 Variance
1.3.5 Standard Deviation
1.3.6 Property of Standard Deviation After Data Transformations
1.3.7 Other Descriptive Statistics for Dispersion
1.3.8 Dispersions Among Multiple Data Sets
1.3.9 Caution to CV Interpretation
1.4 Statistics for Describing Relationships Between Two Outcomes
1.4.1 Linear Correlation Between Two Continuous Outcomes
1.4.2 Contingency Table to Describe an Association Between Two Categorical Outcomes
1.4.3 Odds Ratio
1.5 Two Essential Probability Distribution
1.5.1 Gaussian Distribution
1.5.2 Probability Density Function of Gaussian Distribution
1.5.3 Application of Gaussian Distribution
1.5.4 Standard Normal Distribution
1.5.5 Binomial Distribution
Bibliography
Chapter 2: Statistical Inference Concentrating on a Single Mean
2.1 Population and Sample
2.1.1 Sampling and Non-sampling Errors
2.1.2 Sample Distribution and Sampling Distribution
2.1.3 Standard Error
2.1.4 Sampling Methods and Sampling Variability of the Sample Means
2.2 Statistical Inference
2.2.1 Data Reduction and Related Nomenclatures
2.2.2 Central Limit Theorem
2.2.3 The t-Distribution
2.2.4 Hypothesis Testing
2.2.4.1 Frame of Hypothesis Testing
2.2.4.2 Step-by-Step Overview of Hypothesis Testing
2.2.4.3 Stating Null and Alternative Hypotheses
2.2.4.4 How to Phrase the Statistical Hypotheses
2.2.4.5 Significance of the Test
2.2.4.6 One-Sample t-Test
2.2.4.7 Comments on Statistically Significant Test Results
2.2.4.8 Types of Errors in Hypothesis Tests
2.2.5 Accuracy and Precision
2.2.6 Interval Estimation and Confidence Interval
2.2.6.1 Overview
2.2.6.2 Confidence Interval for a Mean
2.2.6.3 Confidence Interval for a Proportion
2.2.7 Bayesian Inference
2.2.8 Study Design and Its Impact to Accuracy and Precision
2.2.8.1 Sampling and Non-sampling Error Control
2.2.8.2 Study Types and Related Study Designs
2.2.8.3 Observational Study Designs
2.2.8.4 Experimental Study Designs
Bibliography
Chapter 3: t-Tests for Two-Mean Comparison
3.1 Independent Samples t-Test for Comparing Two Independent Means
3.1.1 Independent Samples t-Test When Variances Are Unequal
3.1.2 Denominator Formulae of the Test Statistic for Independent Samples t-Test
3.1.3 Connection to the Confidence Interval
3.2 Paired Sample t-Test for Comparing Paired Means
3.3 Use of Excel for t-Tests
Bibliography
Chapter 4: Inference Using Analysis of Variance (ANOVA) for Comparing Multiple Means
4.1 Sums of Squares and Variances
4.2 F-Test
4.3 Multiple Comparisons and Increased Chance of Type 1 Error
4.4 Beyond Single-Factor ANOVA
4.4.1 Multi-factor ANOVA
4.4.2 Interaction
4.4.3 Repeated Measures ANOVA
4.4.4 Use of Excel for ANOVA
Bibliography
Chapter 5: Inference of Correlation and Regression
5.1 Inference of Pearson´s Correlation Coefficient
5.2 Linear Regression Model with One Independent Variable: Simple Regression Model
5.3 Simple Linear Regression Analysis
5.4 Linear Regression Models with Multiple Independent Variables
5.5 Logistic Regression Model with One Independent Variable: Simple Logistic Regression Model
5.6 Consolidation of Regression Models
5.6.1 General and Generalized Linear Models
5.6.2 Multivariate Analysis Versus Multivariable Model
5.7 Application of Linear Models with Multiple Independent Variables
5.8 Worked Examples of General and Generalized Linear Models
5.8.1 Worked Example of a General Linear Model
5.8.2 Worked Example of a Generalized Linear Model (Logistic Model) Where All Multiple Independent Variables Are Dummy Variabl...
5.9 Measure of Agreement Between Outcome Pairs: Concordance Correlation Coefficient for Continuous Outcomes and Kappa (κ) for ...
5.10 Handling of Clustered Observations
Bibliography
Chapter 6: Normal Distribution Assumption-Free Nonparametric Inference
6.1 Comparing Two Proportions Using a 2 x 2 Contingency Table
6.1.1 Chi-Square Test for Comparing Two Independent Proportions
6.1.2 Fisher´s Exact Test
6.1.3 Comparing Two Proportions in Paired Samples
6.2 Normal Distribution Assumption-Free Rank-Based Methods for Comparing Distributions of Continuous Outcomes
6.2.1 Permutation Test
6.2.2 Wilcoxon´s Rank Sum Test
6.2.3 Kruskal-Wallis Test
6.2.4 Wilcoxon´s Signed Rank Test
6.3 Linear Correlation Based on Ranks
6.4 About Nonparametric Methods
Bibliography
Chapter 7: Methods for Censored Survival Time Data
7.1 Censored Observations
7.2 Probability of Surviving Longer Than Certain Duration
7.3 Statistical Comparison of Two Survival Distributions with Censoring
Bibliography
Chapter 8: Sample Size and Power
8.1 Sample Size for Single Mean Interval Estimation
8.2 Sample Size for Hypothesis Tests
8.2.1 Sample Size for Comparing Two Means Using Independent Samples z- and t-Tests
8.2.2 Sample Size for Comparing Two Proportions
Bibliography
Chapter 9: Review Exercise Problems
9.1 Review Exercise 1
9.1.1 Solutions for Review Exercise 1
9.2 Review Exercise 2
9.2.1 Solutions for Review Exercise 2
Chapter 10: Statistical Tables
Index