Fundamentals of Biostatistics for Public Health Students
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An all-inclusive look at Biostatistics in the field of Public Health, with enriching examples! This is a must have study guide for Biostatistics, from a student's perspective.
This book includes pertinent and practical applications of statistical analysis with easy to grasp tables and graphs that visually captures the attention of the reader.
This reader friendly book comes to your rescue, and wards off the unpleasant task of fishing in the unknown terrain of lost books, scratch pages, and sticky notes.
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Fundamentals of Biostatistics for Public Health Students - S. Mantravadi, PhD
Fundamentals of Biostatistics for Public Health Students
Copyright © 2020 by S. Mantravadi. All rights reserved.
All rights reserved. This product is protected by copyright. No part of it may be reproduced, stored in an information retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, digitizing, web distributions, taping, information networks, or otherwise, without a written permission from the author.
Readers should be aware that Internet Websites offered as citations and/or sources for further information may have changed or disappeared between the time this was written and when it is read.
Limit of Liability/Disclaimer of Warranty: While the author has used the best efforts in preparing this book, the author makes no representations or warranties with respect to the accuracy or completeness of the content in this book, and specifically disclaim any implied warranty of merchantability or fitness for a particular purpose. The author has done everything possible to make this book accurate, up to date, and in accord with accepted standards at the time of publication. The author is not responsible for errors or omissions or for consequences from application of the book, and makes no warranty, expressed or implied, in regards to the contents of the book. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Any practice described in this book, should be applied by the reader in accordance with professional standards of care used in regard to the unique circumstances that may apply in each situation. The author is not liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.
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.
Note to the Reader
To get an entire view of a table in this book, use the landscape format or change font size
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