Applied statistics in occupational safety and health

1 Fundamentals of Statistics 1 Statistics and Their Use in Safety 1 Statistics Defined 2 Common Terms and Notations 2 Quantitative Data and Qualitative Data 3 Statistical Notations 3 Research Questions and Hypotheses 4 Types of Studies 4 Retrospective Studies 4 Prospective Studies 5 Experiments 5 Statistical Samples versus Statistical Populations 5 Bias 6 Probability Sample Selection Procedures 6 Random Samples 7 Sampling Techniques 7 Simple Random Samples 7 Cluster Samples 8 Stratified Random Samples 10 Nonprobability Sample Selection Procedures 10 Chunk Sampling 10 Volunteer Samples 10 Variables 10 Dependent and Independent Variables 11 Chapter Summary 11 Chapter Review Exercises 12 2 Probability and Chance 15 Probability 15 Probability Rules 15 iv CONTENTS Simple Event Probabilities 16 Joint Event Probabilities 16 Compound Event Probabilities 17 Conditional Probabilities 18 Permutations, Ordered Combinations, and Combinations 19 Permutations 19 Ordered Combinations 20 Combinations 21 Binomial Probabilities 22 Binomial Probability Formula 22 Binomial Probability Example 22 Poisson Probability 23 Poisson Probability Formula 23 Poisson Probability Example 23 Chapter Summary 23 Chapter Review Exercises 24 3 Distributions 27 Statistical Distributions and Populations 27 Frequencies 27 Frequency Distribution Example 27 Histograms 28 Frequency Polygons 29 Percentages, Cumulative Percentages, and Percentiles 30 Normal Distribution 31 Binomial Distribution 32 Binomial Distribution Example 32 t Distribution 35 Chi-square Distribution 37 F Distribution 37 Chapter Summary 38 Chapter Review Exercises 38 4 Descriptive Statistics 39 Data Formats 39 Categorical Data 39 Ordinal Data 39 Interval Data 40 Ratio Data 40 Strength of the Data Formats 40 Measures of Central Tendency 41 Mean 41 Median 41 Mode 42 Measures of Variability 42 Range 42 Variance 43 Standard Deviation 44 Interquartile Range 44 z Scores 45 z Score Formula 45 z Score Problem 45 z Scores and Percentages of the Population 46 Confidence Intervals for Means 49 95% Confidence Intervals 49 99% Confidence Intervals 51 Interpreting Confidence Intervals 51 Chapter Summary 51 Chapter Review Exercises 52 5 Statistical Tests 53 Statistical Hypotheses 53 Inferential Statistical Testing 54 Type I and Type II Errors 54  Levels 55 Statistical Power of a Test 55 Inferential Statistics Test Procedure 56 Developing a Statistical Hypothesis 56 Choosing the Appropriate Statistical Test or Procedure 56 Determining the Statistical Distribution 56 Determining Significance Levels 57 Formulating a Decision Rule 57 Running the Test 57 Formulating a Conclusion and Making a Decision 57 Chapter Summary 57 Chapter Review Exercises 58 6 Inferential Statistics for Means 59 z Tests 59 Test Assumptions 59 Hypothesis Construction 59 Determine Significance Levels 60 Using a z Table 60 Formulate a Decision Rule 61 z Test Formula 61 Conclusions 61 Example z Test Problem 61 t Tests 62 Test Assumptions 63 Hypothesis Construction 63 Determine Significance Levels 63 Formulate a Decision Rule 64 t Test Formula for a Single Mean 64 t Test Formula for Independent Groups 64 CONTENTS v Conclusions 65 Example t Test Problem 65 Paired t Tests 66 Test Assumptions 66 Hypothesis Construction 67 Determine Significance Levels 67 Formulate a Decision Rule 67 Test Formula 67 Conclusions 68 Example Paired t Test Problem 68 One-way Analysis of Variance 69 Procedure Assumptions 70 Hypothesis Construction 70 Procedure Formulas 70 Hypothesis Construction 73 Formulate a Decision Rule 73 Calculate F Ratio 74 Conclusions 74 Post Hoc Procedures 74 Scheffe’s Test 74 Calculate Scheffe’s CD 75 Formulate a Decision Rule 75 Example ANOVA Problem 75 Formulate a Decision Rule 78 Calculate F ratio 78 Conclusions 78 Chapter Summary 78 Chapter Review Exercises 78 7 Correlation and Regression 81 Correlation 81 Pearson Correlation Coefficient 82 Spearman Rank-Order Correlation Coefficient 84 Phi Coefficient 85 Eta Coefficient 86 Point Biserial Correlation 87 Significance Testing for Correlation Coefficients 89 Regression 90 Assumptions 90 Formulas 90 Sample Problem 91 Chapter Summary 93 Chapter Review Exercises 93 8 Nonparametric Statistics 97 Underlying Assumptions Concerning Nonparametric Statistics 97 Chi-square Test for Goodness of Fit 97 vi CONTENTS Degrees of Freedom 97 Test Assumptions 98 Hypothesis Construction 98 Test Formula 98 Determine Critical Value 98 Sample Problem 98 2 Test of Association 100 Degrees of Freedom 100 Expected Number of Cases 100 Test Assumptions 100 Hypothesis Construction 101 Test Formula 101 Sample Problem 101 Wilcoxon Rank-Sum Test 102 Test Assumptions 102 Hypothesis Construction 103 Test Formula 103 Sample Problem 103 Cochran’s Q Test 105 Test Assumptions 105 Hypothesis Construction 105 Test Formula 106 Sample Problem 106 Chapter Summary 107 Chapter Review Exercises 108 9 Survey Research 109 Types of Survey Studies 109 Planning a Survey Study 109 Collection and Maintenance 109 Outline for Planning a Survey 110 Constructing the Instrument 113 Types of Survey Items 113 Forms of Questions 114 Unstructured Questions 114 Structured Questions 114 Rating Scales 115 Likert-type Scales 115 Semantic Differential Scales 116 Formatting Questionnaires for the Mail 116 Sound Survey Research Procedures 117 Measurable Objective 117 Representative Population 118 Match the Hypothesis to the Statistical Tests 118 Conduct Background Research 118 Instrument Validity and Reliability 118 CONTENTS vii Cover Letters and Instructions 119 Sampling for Surveys 119 Calculating Sample Sizes 120 Survey Research Limitations 120 Pilot Testing 120 Permission to Use Human Subjects 121 Chapter Summary 121 Chapter Review Exercises 121 10 Experimental Design 123 Experimental Design Uses 123 Research Hypotheses and Experimental Design 123 Dependent and Independent Variables 124 Types of Experimental Designs 124 One-way ANOVA 124 Completely Randomized Design 125 Randomized Block Design 125 Latin Square Design 125 Completely Randomized Factorial Design 126 Chapter Summary 126 Chapter Review Exercises 126 11 Presenting Research 129 Data Presentation for Safety Professionals 129 Displaying Descriptive Statistics 129 Displaying Tables 130 Bar Charts 130 Pie Charts 131 Presenting Inferential Statistics 132 z Tests and t Tests 132 One-way Analysis of Variance 132 Correlation Procedures 133 Regression Procedures 133 Nonparametric Procedures 133 Using Computer Software to Develop Presentations 133 Sample Data Analysis Using Microsoft Excel 134 Developing Presentations Using Microsoft Office 136 Chapter Summary 136 Chapter Review Exercises 136 Appendixes: Statistical Tables Appendix A: Cumulative Distribution Function for the Standard Normal Random Variable 138 Appendix B: Critical Values for the t Distribution 142 Appendix C: Critical Values for the Chi-square Distribution 144 viii CONTENTS Appendix D: Critical Values for the F Distribution 146 Appendix E: Table of Random Units 147 Glossary of Terms 149 References 155 Solutions to Selected Sample Problems 157 Index 181 About the Author 185