Applied Statistics in Occupational Safety and Health

Christopher A. Janicak, Ph.D., CSP, ARM, is a Professor of Safety and Graduate Program Coordinator at Indiana University of Pennsylvania, Department of Safety Sciences. Dr. Janicak has over 20 years of professional experience in safety as a loss control consultant, safety manager, and university professor. He has presented at many national and international conferences, and has published books, book chapters, and journal articles in the field of occupational safety.

Contents
List of Figures and Tables
Preface
About the Author
1
Fundamentals of Statistics
Statistics and Their Use in Safety
Statistics Defined
Common Terms and Notations
Quantitative and Qualitative Data
Statistical Notations
Research Questions and Hypotheses
Types of Studies
 Retrospective Studies
 Prospective Studies
 Experiments
Statistical Samples versus Statistical Populations
Bias
Probability Sample Selection Procedures
Sampling Techniques  
Random Samples
 Simple Random Samples
 Cluster Samples
 Stratified Random Samples
Nonprobability Sample Selection Procedures
 Chunk Sampling
 Volunteer Samples
Variables
 Dependent and Independent Variables
Chapter Summary
Chapter Review Exercises

2
Probability and Chance

Probability
Marginal Probabilities
 Joint Event Probabilities
Union Probabilities
 Conditional Probabilities
Factorials, Permutations, Ordered Combinations, and Combinations
Factorials
 Permutations
 Combinations
Binomial Probabilities
Poisson Probability
Chapter Summary
Chapter Review Exercises


3
Distributions
Statistical Distributions and Populations
Frequencies
Histograms
Frequency Polygons
Percentages, Cumulative Percentages, and Percentiles
Normal Distribution
Binomial Distribution
t Distribution
Chi-square Distribution
F Distribution
Chapter Summary
Chapter Review Exercises


4
Descriptive Statistics
Data Formats
 Categorical Data
 Ordinal Data
 Interval Data
 Ratio Data
Strength of the Data Formats
Measures of Central Tendency
 Mean
 Median
 Mode
Measures of Variability
 Range
 Variance
 Standard Deviation
 Interquartile Range
z Scores
  z Scores and Percentages of the Population
Confidence Intervals for Means
 95% Confidence Intervals
 99% Confidence Intervals
 Interpreting Confidence Intervals
Chapter Summary
Chapter Review Exercises


5
Statistical Tests

Statistical Hypotheses
Inferential Statistical Testing
Type I and Type II Errors
Alpha Levels
Statistical Power of a Test
Inferential Statistics Test Procedure
 Developing a Statistical Hypothesis
 Choosing the Appropriate Statistical Test or Procedure
 Determining the Statistical Distribution
 Determining Significance Levels
 Formulating a Decision Rule
 Running the Test
 Formulating a Conclusion and Making a Decision
Chapter Summary
Chapter Review Exercises


6
Inferential Statistics for Means

z-Test Comparing a Sample Mean to a Known Population Mean
 Test Assumptions
 Hypothesis Construction
 Determine Significance Levels
 Using a z Table
 Formulate a Decision Rule
 z Test Formula
 Conclusions
 Example z Test Problem
Independent Samples z-Test
 Test Assumptions
 Independent Samples z-Test Formula
 Example Independent Samples z-test Problem
 Hypothesis Construction
 Conclusions
 Example z Test Problem
t –Test for a Single Mean
 Test Assumptions
 Hypothesis Construction
 t Test Hypotheses
 Determine Significance Levels
 Formulate a Decision Rule
 t-Test Formula for a Single Mean
 Conclusions
 Example t-Test Problem
t-Test for Independent Samples
Paired Samples t-Tests
  Test Assumptions
 Hypothesis Construction
 Determine Significance Levels
 Formulate a Decision Rule
 Test Formula
 Conclusions
 Example Paired Samples t-Test Problem
One-way Analysis of Variance
 Procedure Assumptions
 Hypothesis Construction
 Procedure Formulas
 Hypothesis Construction
 Formulate a Decision Rule
 Calculate F Ratio
 Conclusions
Post Hoc Procedures
Tukey’s HSD
 Calculate Tukey’s HSD
 Formulate a Decision Rule
 Example ANOVA Problem
 Formulate a Decision Rule
 Calculate F ratio
 Conclusions
 Run Post Hoc Tests
Chapter Summary
Chapter Review Exercises


7
Correlation and Regression

Correlation
 Pearson Correlation Coefficient
 Assumptions
 Pearson Correlation Coefficient Formula
 Sample Problem
 Significance Testing for Correlation Coefficients
 Test Hypotheses
 Test Formula
 Sample Problem

 Spearman Rank-Order Correlation Coefficient
 Assumptions
 Spearman Rank–Order Correlation Coefficient Formula
 Sample Problem
 Phi Coefficient
 Assumptions
 Phi Coefficient Formula
 Sample Problem
 Point Biserial Correlation
 Assumptions
 Point Biserial Correlation Formula
 Sample Problem
 Significance Testing for Correlation Coefficients
Linear Regression
 Procedure Assumptions
  Linear Regression Formulas
 Sample Problem
Chapter Summary
Chapter Review Exercises


8
Nonparametric Statistics
Underlying Assumptions Concerning Nonparametric Statistics
Chi-square Test for Goodness of Fit
 Degrees of Freedom
 Test Assumptions
 Hypothesis Construction
 Test Formula
  Determining the Critical Value
 Sample Problem
c2 Test of Independence
 Degrees of Freedom
 Expected Number of Cases
 Test Assumptions
 Hypothesis Construction
 Test Formula
 Sample Problem
Cochran’s Q Test
 Test Assumptions
 Hypothesis Construction
 Cochran’s Q Test Formula
 Sample Problem
Cochran's Q Test
 Test Assumptions
 Hypothesis Construction
 Test Formula
 Sample Problem
Chapter Summary
Chapter Review Exercises


9
Survey Research
Types of Survey Studies
Collecting and Maintaining Survey Data
Outline for Planning a Survey
Constructing the Instrument
Types of Survey Items
Forms of Questions
 Unstructured Questions
 Structured Questions
Rating Scales
Likert Scales
Semantic Differential Scales
Formatting Questionnaires for the Mail
Sound Survey Research Procedures
 Measurable Objective
 Representative Population
 Match the Hypothesis to the Statistical Tests
 Conduct Background Research
 Instrument Validity and Reliability
 Cover Letters and Instructions
 Sampling for Surveys
 Calculating Sample Sizes
 Survey Research Limitations
 Pilot Testing
 Permission to Use Human Subjects
Chapter Summary
Chapter Review Exercises

10
Experimental Design

Experimental Design Uses
Research Hypotheses and Experimental Design
Dependent and Independent Variables
Types of Experimental Designs
 One-way ANOVA
 Completely Randomized Design
 Randomized Block Design
 Latin Square Design
 Completely Randomized Factorial Design
Chapter Summary
Chapter Review Exercises

11
Presenting Research

Data Presentation for Safety Professionals
Displaying Descriptive Statistics
 Displaying Tables
 Column Charts
 Pie Charts
Presenting Inferential Statistics
 z-Tests and t-Tests
 Example Results from a Paired t-Test Procedure
 One-way Analysis of Variance
 Correlation Procedures
 Regression Procedures
 Nonparametric Procedures
Using Computer Software to Develop Presentations
 Sample Data Analysis Using Microsoft Excel
 Developing Presentations Using Microsoft Office
Chapter Summary
Chapter Review Exercises

Appendix
Statistical Tables
 Cumulative Distribution Function for the Standard Normal Random Variable
 Critical Values for the t Distribution
 Critical Values for the Chi-square Distribution
 Critical Values for the F Distribution
 Table of Random Units

 Critical Values of the Studentized Range

Glossary
References
Solutions to Selected Problems
Index