Statistical Tools for the Comprehensive Practice of Industrial Hygiene and Environmental Health Sciences

Reviews and reinforces concepts and techniques typical of a first statistics course with additional techniques useful to the IH/EHS practitioner

The occupational health, safety, and environmental science fields are data–intensive. Industrial hygiene and environmental health sciences (IH/EHS) professionals spend a lot of their time measuring things, and do so with the goal of answering a specific question. How they go about the measurements the what, when, where, who, and how of the measurements is driven by the why. That is, by the question they are trying to answer. However, the data always has some uncertainty because of measurement variability, and statistics helps the user see through the fog of uncertainty in order to draw accurate inferences about what is being measured.

Most undergraduate and graduate programs in industrial hygiene and environmental health sciences recognize the value of statistical tools, and require an introductory statistics course. Additional statistical tools and techniques beyond those usually covered in a basic course are typically needed. Statistical Tools for the Comprehensive Practice of Industrial Hygiene and Environmental Health Sciences reviews and reinforces the concepts and techniques typical of a first statistics course, and supplement them with additional graphical and non–parametric techniques that may be particularly useful to the IH/EHS practitioner.

Organized into nine chapters Statistical Tools for the Comprehensive Practice of Industrial Hygiene and Environmental Health Sciences features: 

Techniques for displaying data, descriptive statistics, and data frequency distributions in various tabular and graphical formats Reviews parametric two–sample comparison techniques and introduces their non–parametric equivalents Techniques for assessing the likelihood of exposures in the upper tail of the distribution of potential exposures One–way parametric analysis of variance (ANOVA) and presents the non–parametric equivalent one–way ANOVA Two–way ANOVA and presents the non–parametric equivalent two–way ANOVA Parametric correlation analysis and regression analysis, including multiple regression and model–building Applications of the Chi–square test to frequency data, and introduces Fisher s Exact Test Application of Poisson probability based techniques, including comparison of two Poisson variables

Students in industrial hygiene, safety, safety engineering, environmental engineering, environmental health, environmental sciences, and similar programs, and graduates of these programs who are already practicing professionals will benefit from the techniques covered in this text. Analysis using the readily available Excel® statistical functions is emphasized, so that special statistical software and programming expertise are not required.

David L. Johnson has over 40 years of experience in environmental engineering and occupational safety and health practice, research, and teaching. Dr. Johnson was a practicing environmental engineer and industrial hygienist with the United States Army for 20 years, serving in a variety of positions in the United States, Europe, and the Middle East. He joined the faculty of the University of Oklahoma s College of Public Health, Department of Occupational and Environmental Health in 1991.

Dedication 

Preface 

Acknowledgments 

About the Author 

Chapter 1.  Some Basic Concepts 

1.0  Objectives 

1.1  Introduction 

1.2 Physical vs. statistical sampling 

1.3 Representative measures 

1.4 Strategies for representative sampling 

1.5 Measurement precision 

1.6 Probability concepts 

1.6.1 The relative frequency approach 

1.6.2 The classical approach – probability based on deductive reasoning 

1.6.3 Subjective probability 

1.6.4 Complement of a probability 

1.6.5 Mutually exclusive events 

1.6.6 Independent events 

1.6.7 Events that are not mutually exclusive 

1.6.8 Marginal and conditional probabilities 

1.6.9 Testing for independence

1.7 Permutations and combinations 

1.7.1 Permutations for sampling without replacement 

1.7.2 Permutations for sampling with replacement 

1.7.3 Combinations 

1.8 Introduction to frequency distributions 

1.8.1 The Binomial distribution

1.8.2 The Normal distribution 

1.8.3 The Chi–square distribution 

1.9 Confidence intervals and hypothesis testing 

1.10 Summary 

1.11 Addendum: Glossary of Some Useful Excel Functions 

1.12 Exercises 

References 

Chapter 2.  Descriptive Statistics and Methods of Presenting Data

2.0 Objectives 

2.1 Introduction 

2.2 Quantitative descriptors of data and data distributions 

2.3 Displaying data with frequency tables

2.4 Displaying data with histograms and frequency polygons 

2.5 Displaying data frequency distributions with cumulative probability plots 

2.6 Displaying data with NED and Q–Q plots 

2.7 Displaying data with Box and Whisker plots 

2.8 Data transformations to achieve normality 

2.9 Identifying outliers 

2.10 What to do with censored values? 

2.11 Summary 

2.12 Exercises 

References 

Chapter 3.  Analysis of Frequency Data 

3.0 Objectives 

3.1 Introduction 

3.2 Tests for association and goodness–of–fit 

3.2.1 r×c contingency tables and the Chi–Square Test 

3.2.2 Fisher s Exact Test 

3.3 Binomial proportions 

3.4 Rare events and the Poisson distribution 

3.4.1 Poisson probabilities 

3.4.2 Confidence interval on a Poisson count 

3.4.3 Testing for fit with the Poisson distribution 

3.4.4 Comparing two Poisson rates 

3.4.5 Type I error, Type II error, and power 

3.4.6 Power and sample size in comparing two Poisson rates 

3.5 Summary 

3.6 Exercises 

References 

Chapter 4.  Comparing Two Conditions 

4.0 Objectives 

4.1 Introduction 

4.2 Standard error of the mean 

4.3 Confidence interval on a mean 

4.4 The t–distribution 

4.5 Parametric one–sample test – Student s t–test 

4.6 Two–tailed vs. one–tailed hypothesis tests 

4.7 Confidence interval on a variance 

4.8 Other applications of the confidence interval concept in IH/EHS work 

4.8.1 OSHA compliance determinations 

4.8.2 Laboratory analyses LOB, LOD, and LOQ 

4.9 Precision, power, and sample size for one mean 

4.9.1 Sample size required to estimate a mean with a stated precision 

4.9.2 Sample size required to detect a specified difference in Student s t–test 

4.10 Iterative solutions using the Excel Goal Seek utility 

4.11 Parametric two–sample tests 

4.11.1 Confidence interval for a difference in means: the two–sample t–test 

4.11.2 Two–sample t–test when variances are equal 

4.11.3 Verifying the assumptions of the two–sample t–test 

Lilliefors test for normality 

Shapiro–Wilk W Test for normality 

Testing for homogeneity of variance 

Transformations to stabilize variance 

4.11.4 Two–sample t–test with unequal variances Welch s Test 

4.11.5 Paired sample t–test 

4.11.6 Precision, power, and sample size for comparing two means 

4.12 Testing for difference in two Binomial proportions 

4.12.1 Testing a binomial proportion for difference from a known value 

4.12.2 Testing two binomial proportions for difference 

4.13 Nonparametric two–sample tests 

4.13.1 Mann–Whitney U Test 

4.13.2 Wilcoxon Matched Pairs Test 

4.13.3 McNemar and Binomial tests for paired nominal data 

4.14 Summary 

4.15 Exercises 

References 

Chapter 5.  Characterizing the Upper Tail of the Exposure Distribution 

5.0 Objectives 

5.1 Introduction 

5.2 Upper Tolerance Limits 

5.3 Exceedance Fractions 

5.4 Distribution free tolerance limits 

5.5 Summary 

5.6 Exercises 

References 

Chapter 6.  One–Way Analysis of Variance 

6.0 Objectives 

6.1 Introduction 

6.2 Parametric one–way ANOVA 

6.2.1 How the parametric ANOVA works sums of squares and the F–test 

6.2.2 Post hoc multiple pairwise comparisons in parametric ANOVA 

Tukey s Test 

Tukey–Kramer Test 

Dunnett s test for comparing means to a control mean 

Planned contrasts using the Scheffé S test 

6.2.3 Checking the ANOVA model assumptions NED plots and variance tests 

Levene s Test 

Bartlett s Test 

6.3 Nonparametric Analysis of Variance 

6.3.1 Kruskal–Wallis nonparametric one–way ANOVA 

6.3.2 Post hoc multiple pairwise comparisons in nonparametric ANOVA 

Nemenyi s Test 

Bonferroni–Dunn Test 

6.4 ANOVA disconnects 

6.5 Summary 

6.6 Exercises 

References 

Chapter 7.  Two–Way Analysis of Variance 

7.0 Objectives 

7.1 Introduction 

7.2 Parametric two–way ANOVA 

7.2.1 Two–way ANOVA without interaction 

7.2.2 Checking for homogeneity of variance 

7.2.3 Multiple pairwise comparisons when there is no interaction term 

7.2.4 Two–way ANOVA with interaction 

7.2.5 Multiple pairwise comparisons with interaction 

7.2.6 Two–way ANOVA without replication 

7.2.7 Repeated measures ANOVA 

7.2.8 Two–way ANOVA with unequal sample sizes 

7.3 Nonparametric two–way ANOVA 

7.3.1 Rank tests 

The Rank test 

The Rank Transform test 

Other options Aligned Rank tests 

7.3.2 Repeated measures nonparametric ANOVA Friedman s test 

Friedman s Test without replication 

Multiple comparisons for Friedman s test without replication 

Friedman s Test with replication 

Multiple comparisons for Friedman s test with replication 

7.4 More powerful non–ANOVA approaches:  linear modeling 

7.5 Summary 

7.6 Exercises 

References

Chapter 8.  Correlation Analysis 

8.0 Objectives 

8.1 Introduction 

8.2 Simple parametric correlation analysis 

8.2.1 Testing the correlation coefficient for significance 

t–test for significance 

F test for significance 

8.2.2 Confidence limits on the correlation coefficient 

8.2.3 Power in simple correlation analysis 

8.2.4 Comparing two correlation coefficients for difference 

8.2.5 Comparing more than two correlation coefficients for difference 

8.2.6 Multiple pairwise comparisons of correlation coefficients 

8.3 Simple nonparametric correlation analysis 

8.3.1 Spearman rank correlation coefficient 

8.3.2 Testing Spearman s rank correlation coefficient for statistical significance 

8.3.3 Correction to Spearman s rank correlation coefficient when there are tied ranks 

8.4 Multiple correlation analysis 

8.4.1 Parametric multiple correlation 

8.4.2 Nonparametric multiple correlation:  Kendall s coefficient of concordance 

8.5 Determining causation 

8.6 Summary 

8.7 Exercises 

References 

Chapter 9.  Regression Analysis 

9.0 Objectives 

9.1 Introduction 

9.2 Linear regression 

9.2.1 Simple linear regression 

9.2.2 Non–constant variance transformations and weighted least squares regression 

9.2.3 Multiple linear regression 

Multiple regression in Excel 

Multiple regression using the Excel Solver utility 

Multiple regression using advanced software packages 

9.2.4 Using regression for factorial ANOVA with unequal sample sizes 

9.2.5 Multiple correlation analysis using multiple regression 

Assumptions of parametric multiple correlation 

Options when collinearity is a problem 

9.2.6 Polynomial regression 

9.2.7 Interpreting linear regression results 

9.2.8 Linear regression vs. ANOVA 

9.3 Logistic regression 

9.3.1 Odds and odds ratios 

9.3.2 The logit transformation 

9.3.3 The likelihood function 

9.3.4 Logistic regression in Excel 

9.3.5 Likelihood Ratio test for significance of MLE coefficients 

9.3.6 Odds ratio confidence limits in multivariate models 

9.4 Poisson regression 

9.4.1 Poisson regression model 

9.4.2 Poisson regression in Excel 

9.5 Regression with Excel add–ons 

9.6 Summary 

9.7 Exercises 

References 

Chapter 10.  Analysis of Covariance 

10.0 Objectives 

10.1 Introduction 

10.2 The simple ANCOVA model and its assumptions 

10.2.1 Required regressions 

10.2.2 Checking the ANCOVA assumptions 

Linearity, independence, and normality 

Similar variances 

Equal regression slopes 

10.2.3 Testing and estimating the treatment effects 

10.3 The two–factor covariance model 

10.4 Summary 

10.5 Exercises 

References 

Chapter 11.  Experimental Design 

11.0 Objectives 

11.1 Introduction 

11.2 Randomization 

11.3 Simple randomized experiments 

11.4 Experimental designs blocking on categorical factors 

11.5 Randomized full factorial experimental design 

11.6  Randomized full factorial design with blocking 

11.7 Split plot experimental designs 

11.8 Balanced experimental designs Latin Square 

11.9 Two–level factorial experimental designs with quantitative factors 

11.9.1 Two–level factorial designs for exploratory studies 

11.9.2 The Standard Order 

11.9.3 Calculating main effects 

11.9.4 Calculating interactions 

11.9.5 Estimating standard Errors 

11.9.6 Estimating effects with REGRESSION in Excel 

11.9.7 Interpretation 

11.9.8 Cube, surface, and NED plots as an aid to interpretation 

11.9.9 Fractional factorial two–level experiments 

11.10 Summary 

11.11 Exercises 

References .

Chapter 12.  Uncertainty and Sensitivity Analysis 

12.0 Objectives 

12.1 Introduction 

12.2 Simulation modeling 

12.2.1 Propagation of errors 

12.2.2 Simple bounding 

Sums and differences 

Products and ratios 

Powers 

12.2.3 Addition in Quadrature 

Sums and differences 

Products and ratios 

Powers 

12.2.4. LOD and LOQ revisited – dust sample gravimetric analysis 

12.3 Uncertainty analysis 

12.4 Sensitivity analysis 

12.4.1 One–at–a–time (OAT) analysis 

12.4.2 Variance–based analysis 

12.5 Further reading on uncertainty and sensitivity analysis 

12.6 Monte Carlo simulation 

12.7 Monte Carlo simulation in Excel 

12.7.1 Generating random numbers in Excel 

12.7.2 The populated spreadsheet approach 

12.7.3 Monte Carlo simulation using VBA macros 

12.8 Summary 

12.9 Exercises 

References 

Chapter 13.  Bayes Theorem and Bayesian Decision Analysis 

13.0 Objectives 

13.1 Introduction 

13.2 Bayes Theorem 

13.3  Sensitivity, specificity, and positive and negative predictive value in screening tests 

13.4 Bayesian Decision Analysis in Exposure Control Banding 

13.4.1 Introduction to BDA 

13.4.2 The prior distribution and the parameter space 

13.4.3 The posterior distribution and likelihood function 

13.4.4 Relative influences of the prior and the data 

13.4.5 Frequentist vs. Bayesian perspectives 

13.5 Exercises 

13.6 References 

Appendix A z–tables of the standard normal distribution 

Appendix B Critical values of the chi–square distribution 

Appendix C Critical values for the t–distribution 

Appendix D Critical values for Lilliefors test 

Appendix E Shapiro–Wilk W Test coefficients and critical values 

Appendix F Critical values of the F distribution for =0.05 

Appendix G Critical U values for the Mann–Whitney U test 

Appendix H Critical Wilcoxon matched pairs test T values 

Appendix I K values for Upper Tolerance Limits 

Appendix J Exceedance Fraction 95% Lower Confidence Limit vs Z 

Appendix K q values for Tukey s, Tukey–Kramer, & Nemenyi s MSD tests 

Appendix L q′ values for Dunnett s test 

Appendix M Q values for the Bonferroni–Dunn MSD test 

Appendix N Critical Spearman rank correlation test values 

Appendix O Critical values of Kendall s W 

Index