1. INTRODUCTION

1.1 What is Biostatistics?
1.2 Data – The Key Component of a Study
1.3 Design – The Road to Relevant Data
1.4 Replication – Part of the Scientific Method
1.5 Applying Statistical Methods
Concluding Remarks
Exercises
References


2. DATA AND NUMBERS

2.1 Data: Numerical Representation
2.2 Observations and Variables
2.3 Scales Used with Variables
2.4 Reliability and Validity
2.5 Randomized Response Technique
2.6 Common Data Problems
Concluding Remarks
Exercises
References


3. DESCRIPTIVE METHODS

3.1 Introduction to Descriptive Methods
3.2 Tabular and Graphic Presentation of Data
3.2.1 Frequency Tables
3.2.2 Line Graphs
3.2.3 Bar Charts
3.2.4 Histograms
3.2.5 Stem-and-Leaf Plots
3.2.6 Dot Plots
3.2.7 Scatter Plots
3.3 Measures of Central Tendency
3.3.1 Mean, Median, and Mode
3.3.2 Use of the Measures of Central Tendency
3.3.3 The Geometric Mean
3.4 Measures of Variability
3.4.1 Ranges and Percentiles
3.4.2 Box Plots
3.4.3 Variance and Standard Deviation
3.5 Rates and Ratios
3.5.1 Crude and Specific Rates
3.5.2 Adjusted Rates
3.6 Measures of Change Over Time
3.6.1 Linear Growth
3.6.2 Geometric Growth
3.6.3 Exponential Growth
3.7 Correlation Coefficients
3.7.1 Pearson Correlation Coefficient
3.7.2 Spearman Rank Correlation Coefficient
Concluding Remarks
Exercises
References


4. PROBABILITY AND LIFE TABLES

4.1 A Definition of Probability
4.2 Rules for Calculating Probabilities
4.2.1 Addition Rule for Probabilities
4.2.2 Conditional Probabilities
4.2.3 Independent Events
4.3 Definitions from Epidemiology
4.3.1 Rates and Probabilities
4.3.2 Sensitivity, Specificity, and Predicted Value Positive and Negative
4.3.3 Receiver Operating Characteristic Plot
4.4 Bayes’ Theorem
4.5 Probability in Sampling
4.5.1 Sampling With Replacement
4.5.2 Sampling Without Replacement
4.6 Estimating Probabilities by Simulation
4.7 Probability and the Life Table
4.7.1 The First Four Columns of the Life Table
4.7.2 Some Uses of the Life Table
4.7.3 Expected Values in the Life Table
4.7.4 Other Expected Values in the Life Table
Concluding Remarks
Exercises
References


5. PROBABILITY DISTRIBUTIONS

5.1 The Binomial Distribution
5.1.1 Binomial Probabilities
5.1.2 Mean and Variance of the Binomial Distribution
5.1.3. Shapes of the Binomial Distribution
5.2 The Poisson Distribution
5.2.1 Poisson Probabilities
5.2.2 Mean and Variance of the Poisson Distribution
5.2.3 Finding Poisson Probabilities
5.3 The Normal Distribution
5.3.1 Normal Probabilities
5.3.2 Transforming to the Standard Normal Distribution
5.3.3 Calculation of Normal Probabilities
5.3.4 Normal Probability Plot
5.4 The Central Limit Theorem
5.5 Approximations to the Binomial and Poisson Distributions
5.5.1 Normal Approximation to the Binomial Distribution
5.5.2 Normal Approximation to the Poisson Distribution
Concluding Remarks
Exercises
References

6. STUDY DESIGNS

6.1 Design: Putting Chance to Work
6.2 Sample Surveys and Experiments
6.3 Sampling and Sample Designs
6.3.1 Sampling Frame
6.3.2 Importance of Probability Sampling
6.3.3 Simple Random Sampling
6.3.4 Systematic Sampling
6.3.5 Stratified Random Sampling
6.3.6 Cluster Sampling
6.3.7 Problems Due to Unintended Sampling
6.4 Designed Experiments
6.4.1 Comparison Groups and Randomization
6.4.2 Random Assignment
6.4.3 Sample Size
6.4.4 Single and Double Blind Experiments
6.4.5 Blocking and Extraneous Variables
6.4.6 Limitations of Experiments
6.5 Variations in Study Designs
6.5.1 The Cross-Over Design
6.5.2 The Case Control Design
6.5.3 The Cohort Study Design
Concluding Remarks
Exercises
References


7. INTERVAL ESTIMATION

7.1 Prediction, Confidence, and Tolerance Intervals
7.2 Distribution-Free Intervals
7.2.1 Prediction Interval
7.2.2 Confidence Interval
7.2.3 Tolerance Interval
7.3 Confidence Intervals Based on the Normal Distribution
7.3.1 Confidence Interval for the Mean
7.3.2 Confidence Interval for a Proportion
7.3.3 Confidence Interval for Crude and Adjusted Rates
7.4 Confidence Interval for the Difference of Two Means and Proportions
Difference of Two Independent Means
7.4.1 Difference of Two Dependent Means
7.4.2 Difference of Two Independent Proportions
7.4.3 Difference of Two Dependent Proportions
7.5 Confidence Interval and Sample Size
7.6 Confidence Interval for Other Measures
7.6.1 Confidence Interval for the Variance
7.6.2 Confidence Interval for Pearson Correlation Coefficient
7.7 Prediction and Tolerance Intervals Based on the Normal Distribution
7.7.1 Prediction Interval
7.7.2 Tolerance Interval
Concluding Remarks
Exercises
References


8. TESTS OF HYPOTHESES

8.1 Preliminaries in Tests of Hyppotheses
8.1.1 Definitions of Terms Used in Hypothesis Testing
8.1.2 Determination of Decision Rule
8.1.3 Relationship of the Decision Rule, á and â
8.1.4 Conducting the Test
8.2 Testing Hypotheses about the Mean
8.2.1 Known Variance
8.2.2 Unknown Varinace
8.3 Testing Hypotheses about the Proportion and Rates
8.4 Testing Hypotheses about the Variance
8.5 Testing Hypotheses about the Pearson Correlation Coefficient
8.6 Testing Hypotheses about the Difference of Two Means
8.6.1 Difference of Two Independent Means
8.6.2 Difference of Two Dependent Means
8.7 Testing Hypotheses about the Difference of Two Proportions
8.7.1 Difference of Two Independent Proportions
8.7.2 Difference of Two Dependent Means
8.8 Tests of Hypotheses and Sample Size
8.9 Statistical and Practical Significance
Concluding Remarks
Exercises
References


9. NONPARAMETRIC TESTS

9.1 Why Nonparametric Tests?
9.2 The Sign Test
9.3 The Wilcoxon Signed Rank Test
9.4 The Wilcoxon Rank Sum Test
9.5 The Kruskal-Wallis Test
9.6 The Friedman Test
Concluding Remarks
Exercises
References


10. ANALYSIS OF CATEGORICAL DATA

10.1 Goodness-of-Fit Test
10.2 The 2 by 2 Contingency Table
10.2.1 Comparing Two Independent Binomial Proportions
10.2.2 Expected Cell Counts Assuming No Association
10.2.3 The Odds Ratio – a Measure of Association
10.2.4 The Fisher’s Exact Test
10.2.5 Analysis of Paired Data: The McNemar Test
10.3 The r by c Contingency Table
10.3.1 Testing Hypothesis of Non Association: The Chi-Square Test
10.3.2 Testing Hypothesis of No Trend
10.4 Multiple 2 by 2 Tables
10.4.1 Analyzing the Tables Separately
10.4.2 The Cochran-Mantel-Haenszel Test
104.3 The Mantel-Haenszel Common Odds Ratio
Concluding Remarks
Exercises
References


11. ANALYSIS OF SURVIVAL DATA

11.1 Data Collection in Follow-Up Studies
11.2 The Life Table Method
11.3 The Product-Limit Method
11.4 Comparison of Two Survival Distributions
11.4.1 The Cochran-Mantel-Haenszel Test
11.4.2 The Log-Rank Test
Concluding Remarks
Exercises
References


12. ANALYSIS OF VARIANCE

12.1 Assumptions for the Use of the ANOVA
12.2 One-Way ANOVA
12.2.1 Sums of Squares and Mean Squares
12.2.2 The F Statistics
12.2.3 The ANOVA Table
12.3 Multiple Comparisons
12.3.1 Error Rates: Individual and Family
12.3.2 Tukey-Kramer Method
12.3.3 Fisher’s Least Significant Difference Method
12.3.4 Dunnett’s Method
12.4 Two-Way ANOVA for the Randomized Block Design with m Replicates
12.5 Two-Way ANOVA with Interaction
12.6 Linear Model Representation of the ANOVA
12.6.1 The Completely Randomized Design
12.6.2 The Randomized Block Design with m Replicates
12.6.3 Two-Way ANOVA with Interaction
12.7 ANOVA with Unequal Numbers of Observations in Subgroups
Concluding Remarks
Exercises
References


13. LINEAR REGRESSION

13.1 Simple Linear Regression
13.1.1 Estimation of Coefficients
13.1.2 The Variance of Y