Fundamentals of Biostatistics for Public Health Students

Fundamentals of Biostatistics for Public Health Students

Copyright © 2020 by S. Mantravadi. All rights reserved.

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Brief Table of Contents (Optional Clickable Chapter numbers and Chapter titles)

Chapter 1

Jump Right in - A Sample of Biostatistics

Chapter 2

Levels of Measurement

Chapter 3

Concept of Probability

Chapter 4

Descriptive Statistics and Probability Distributions

Chapter 5

Hypothesis Testing and z Distribution

Chapter 6

The t-Tests

Chapter 7

Chi square Test

Chapter 8

Odds Ratio and Relative Risks

Chapter 9

Analysis of Variance (ANOVA)

Chapter 10

Regression

Chapter 11

Nonparametric Statistical Analysis and Survival Analysis

Appendix

Table of Contents (Optional Clickable Chapter Numbers, Chapter Titles and Sub-titles)

Chapter 1

Jump Right in - A Sample of Biostatistics

Terminologies

Table 1.1

Sampling Unit

Diagram 1.1

Schematics of Selection

Types of Sampling

Probability Sampling

Table 1.2

Periodicity

Nonprobability Sampling

Is a Sample Representative?

Summary of Probability Sampling Techniques

Summary of Nonprobability Sampling Techniques

Resources 1-21

Chapter 2

Classification of Variables

Diagram 2.1

Variable and Attributes

Types of Variables

Classifications of Variables are Essential to:

Levels of Measurement

Diagram 2.2

Levels of Measurement Hierarchy

Diagram 2.3

Quantitative Variables

Diagram 2.4

Qualitative and Quantitative Variables

Resources 22-24

Chapter 3

Concept of Probability

Terminologies

Overview of Salient Probability Rules

Table 3.1

Diabetes and Cardiovascular Disease (CVD)

Inclusion-Exclusion Rule

Probability Tree Diagrams

Diagram 3.1

Tree Diagram

Conditional Probability and Bayes’ Theorem

Probability of At Least One Event

Resources 25 - 38

Chapter 4

Probability Distributions and Descriptive Statistics

Numerical Measures of Descriptive Statistics

Relationships between Measures of Central Tendency

Diagram 4.1

Positively Skewed Distribution

Measures of Central Tendency

Diagram 4.2

Negatively Skewed Distribution

Measures of Central Tendency

Table 4.1

Summary of Measures of Central Tendency

Diagram 4.3

Variance/Dispersion

Graphical Analyses

Diagram 4.4

Scatterplot

Diagram 4.5

Line Graph

Diagram 4.6

Bar Graph

Table 4.2

Frequency Table

Table 4.3

Relative Frequency Table

Table 4.4

Cumulative Frequency and Cumulative Relative Table

Diagram 4.7

Frequency Histogram

Diagram 4.8

Relative Frequency Histogram

Diagram 4.9

Cumulative Relative Frequency Histogram

Diagram 4.10 Frequency Polygon

Diagram 4.11

Relative Frequency Polygon

Solution

Diagram 4.12

Cumulative Relative Frequency Polygon

Quartiles

Box and Whisker Plot

Diagram 4.13

Box and Whisker Plot

Diagram 4.14

Box and Whisker Plot

Theoretical Data

Stem-and-Leaf Plot

Table 4.5

Determining the Stem and Leaf

Steps to Create Stem

Table 4.6

Probability Distributions

Gaussian Distribution

Empirical Rule

Diagram 4.15

Empirical Rule

Tchebysheff’s Rule

Z Score

Central Limit Theorem

Student’s t-Distribution

Bernoulli Distribution

Binomial Distribution

Poisson Distribution

Chi Square Distribution

F Distribution

Resources 39 - 73

Chapter 5

Univariate Inferential Statistical Analysis

Hypothesis Testing and z Distribution

Table 5.1

Hypothesis Testing of One-tailed vs. Two-tailed tests

Steps to Determine Critical Value (CV) and Critical Region

Overview of Steps in Hypothesis Testing

Hypothesis Testing for Z Distribution

Z-test of Means

Steps for One-sample Z-Test of the Mean

Confidence Intervals for One-Sample Z-test of the Mean

Steps for Two-samples Z-Test of Means

Confidence Interval (CI) for Two-Sample Z-test of Means

Z-test of Proportions

Steps for One-sample Z-test of the Proportion

Confidence Interval for One-sample Z-test of the Proportion

Steps for Two-samples Z-test of Proportions

Confidence Intervals for Two-Samples Z-test of Proportions

Table 5.2 Summary of Z-tests

Resources 74 - 109

Chapter 6

Univariate Inferential Statistic Analysis

t-tests

Outcome and Predictor variables for t-test

Overview of Steps in t-test

One-Sample t-test of the Mean

Steps for One-sample t-test of the Mean

Confidence Interval for One-sample t-test of the Mean

Two-samples t-test of Means

Steps to Perform Two-samples Independent Heteroscedastic t-test of Means

Confidence Interval (CI) for Two-samples Independent Heteroscedastic t-test of Means

Steps to Perform Two-samples Independent Homoscedastic t-test of Means

Confidence Interval (CI) for Two-samples Independent Homoscedastic t-test of Means

Steps to Perform Two-samples Paired t-test of Means

Confidence Interval (CI) for Paired t-test

Table 6.1

Summary of t-tests

Resources 110 - 122

Chapter 7

Inferential Statistical Analysis

Chi Square Test

Types of Chi Square Tests

Chi Square Test Basics

Table 7.1

Categorical Variables of Age and Arthritis

Observed Values

Table 7.2

Set Up of Chi Square Contingency Table

Chi Square Formula

Calculation of Expected Frequency

Overview of Steps for Chi Square Test

Chi Square Test of Independence

Table 7.3

Chi Square Test of Independence

Observed Values

Table 7.4 Chi Square Test of Independence Contingency Table

Chi Square Test of Goodness of Fit

Table 7.5

Chi Square Test of Goodness of Fit

Observed Frequencies of Crossing Genes Gg with Gg

Table 7.6

Chi Square Test of Goodness of Fit Contingency Table

Chi Square Test of Homogeneity

Table 7.7

Chi Square Test of Homogeneity

Table 7.8

Chi Square Test of Homogeneity Contingency Table

Simpson’s Paradox

Table 7.9

Summary of Chi Square Tests

Resources 123 - 136

Chapter 8

Salient Epidemiological Measures

Table 8.1

Epidemiological 2 x 2 Contingency Table

Odds Ratio

Table 8.2

Odds Ratio Epidemiological 2 x 2 Contingency Table

Example

Example

Relative Risk

Table 8.3

Relative Risk Epidemiological 2 x 2 Contingency Table

Prevalence and Incidence

Screening: Sensitivity, Specificity, Positive Predictive Value and Negative Predictive Value

Table 8.4

Screening Test

Measures of Validity and Reliability

Table 8.5

Summary of Epidemiological and Screening Measures

Resources 137 - 143

Chapter 9

Inferential Statistical Analysis

Analysis of Variance (ANOVA)

Terminologies

Table 9.1

One Way ANOVA Set Up

Post hoc Tests

Steps for One-way ANOVA

Table 9.2

One-Way ANOVA

Table 9.3

Summary of ANOVA

Resources 144 – 157

Chapter 10

Inferential Statistical Analysis – Regression Analysis

Types of Regression

Overview of Linear Regression

Pearson’s Product Moment Correlation (r)

Table 10.1

Pearson’s Correlation Coefficient Set Up

Steps for Linear Regression

Table 10.2

Performing Linear Regression

Diagram 10.1

Scatterplot

Diagram 10.2

Scatterplot with Regression Line and Equation

Diagram 10.3

Scatterplot with Regression Line, Equation and Correlation Coefficient

Table 10.3

Summary of Regression Analyses

Resources 158 - 175

Chapter 11

Nonparametric Tests and Survival Analyses

Data Rearrangement

Nonparametric Tests

Table 11.1

Comparison of Parametric and Nonparametric Tests

Types of Nonparametric Tests

How to Confirm if a Relationship is Linear or Nonlinear?

Table 11.2

Summary of Nonparametric Analyses

Survival Analysis

Techniques for Survival Analysis: Life Tables

Table 11.3

Survival Analysis Using a Life Table

Table 11.4

Survival Analysis Using a Life Table with Censoring

Techniques for Survival Analysis: Kaplan-Meier Analysis

Table 11.5

Survival Analysis Using Kaplan-Meier Analysis

Resources 176 - 190

Appendix

Summary of Statistical Tests

Chapter 5

Summary of z-tests

Chapter 6

Summary of t-tests

Chapter 7

Summary of Chi Square tests

Chapter 8

Summary of Epidemiological and Screening Measures

Chapter 9

Summary of ANOVA

Chapter 10

Summary of Regression Analyses

Abbreviations and Symbols Used in Statistics

Formulas Used in Statistics

Additional Resources 191 - 217

Preface

Congratulations on the decision to purchase this comprehensive, invaluable biostatistics book. When overwhelmed with myriad concepts or during midterm and final exams, this book will come to one’s rescue. No more of the hide and seek in this unknown landscape, whether one is preparing for exams, interviews, or just brushing up the cobwebs for refreshing concepts to work on projects. This all-inclusive book wards off the unpleasant task of fishing in the unknown terrain of lost books, scratch pages, and sticky notes. Feel free to turn off searchlights to locate the dust-laden books/notes hibernating in the shelves.

Dr. Mantravadi, a Certified Health Education Specialist (CHES), with certification in Public Health (CPH) has doctorate and master’s degree in public health. The book addresses pertinent and enriching practical applications of statistical analysis in the field of public health. The easy to grasp tables and graphs visually capture the essentials of biostatistics. This reader friendly book on biostatistics includes essential resources available with an easy click of the computer mouse. This work adds to the valued public health related collection  in the Statistical Journey.

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Chapter 1

Jump Right in - A Sample of Biostatistics

Biostatistics is often perceived as monotonous, endless calculations that follow data collection.

" Biostatistics is the development and application of statistical reasoning and methods in addressing, analyzing and solving problems in public health, health care, biomedical, clinical, and population-based research"¹⁴.

What does Biostatistics really do?

Biostatistics harnesses the power of patterns, and recognizes characteristics of a population. This field leverages a better grasp on data, and optimizes the inference process. Statistics quantitatively facilitates the why and accuracy of a phenomenon.

Examples: What does a vast spreadsheet of food safety in a restaurant mean?

What does the refrigerator reading of 41.8 degrees mean?

What does incidence data on the epidemic of Listeria monocytogenes in cantaloupe mean?

What was the reason for data collection? This often is a universal and important question

Planning data collection and selecting variables based on focus