Solution Manual
Fundamentals Of Biostatistics
By Bernard Rosner
8th Edition
,CONTENTS
Preface, Vii
Chapter 1 General Overview 1
There Are No Problems/Solutions In Chapter 1 Of The Textbook.
Chapter 2 Descriptive Statistics 2
Review Of Key Concepts, 2 2.2.2 Quasi-Range, 6
2.1 Measures Of Location, 2 2.2.3 Standard Deviation, Variance, 7
2.1.1 Arithmetic Mean, 2 2.2.4 Coefficient Of Variation (Cv), 8
2.1.2 Median, 3 2.3 Some Other Methods For Describing Data, 8
2.1.3 Stem-And-Leaf Plots, 3 2.3.1 Frequency Distribution, 8
2.1.4 Percentiles, 4 2.3.2 Box Plot, 8
2.1.5 Geometric Mean, 5 Problems, 9
2.2 Measures Of Spread, 6 Solutions, 10
2.2.1 Range, 6 Reference, 11
Chapter 3 Probability 12
Review Of Key Concepts, 12 3.6 Sensitivity, Specificity, Predictive Values
3.1 Frequency Definition Of Probability, 12 Of Screening Tests, 15
3.2 Multiplication Law Of Probability, 13 3.6.1 Roc Curves, 16
3.3 Addition Law Of Probability, 13 3.7 Bayes’ Theorem, 17
3.4 Conditional Probability, 13 Problems, 18
3.4.1 Relative Risk, 14 Solutions, 21
3.5 Total Probability Rule, 14 References, 26
Chapter 4 Discrete Probability Distributions 28
Review Of Key Concepts, 28 4.4 Methods For Using The Binomial Distribution, 30
4.1 Random Variable, 28 4.5 Using Electronic Tables, 30
4.2 Combinations, Permutations, And Factorial, 4.6 Expected Value Of The Binomial Distribution, 31
28 4.7 Variance Of The Binomial Distribution, 31
4.3 Binomial Probability Distribution, 29
Iii
,Iv Contents
4.8 Poisson Distribution, 32 4.11 Poisson Approximation To The
4.9 Use Of Electronic Tables For Binomial Distribution, 33
Poisson Probabilities, 32 Problems, 33
4.10 Expected Value And Variance Of The Solutions, 38
Poisson Distribution, 33 References, 43
Chapter 5 Continuous Probability Distributions 44
Review Of Key Concepts, 44 5.7 Inverse Normal Distribution, 47
5.1 Probability Density Function, 44 5.8 Use Of Electronic Tables For The
5.2 Expected Value And Variance Of A Normal Distribution, 47
Continuous Random Variable, 45 5.9 Normal Approximation To The
5.3 Normal Probability Density Function, 45 Binomial Distribution, 48
5.4 Empirical And Symmetry Properties Of 5.10 Normal Approximation To The
The Normal Distribution, 45 Poisson Distribution, 50
5.5 Calculation Of Probabilities For A Problems, 50
Standard Normal Distribution, 46 Solutions, 54
5.6 Calculation Of Probabilities For A General References, 65
Normal Distribution, 47
Chapter 6 Estimation 66
Review Of Key Concepts, 66 6.8.2 Factors Influencing The Length Of
6.1 Relationship Of Population To Sample, 66 A Confidence Interval, 69
6.2 Random-Number Tables, 66 6.9 Estimation Of The Variance Of A Distribution, 69
6.3 Randomized Clinical Trials, 67 6.10 Estimation For The Binomial Distribution, 70
6.3.1 Techniques Of Study Design In 6.10.1 Large-Sample Method, 70
Randomized Clinical Trials, 67 6.10.2 Small-Sample Method, 71
6.4 Sampling Distribution, 67 6.11 Estimation For The Poisson Distribution, 71
6.5 Estimation Of The Mean Of A Distribution, 6.12 One-Sided Confidence Limits, 72
67 Problems, 73
6.6 Standard Error Of The Mean, 68 Solutions, 76
6.7 The Central-Limit Theorem, 68 Reference, 79
6.8 Interval Estimation For The Mean, 68
6.8.1 Use Of Confidence Intervals
For Decision-Making Purposes,
69
Chapter 7 Hypothesis Testing: One-Sample Inference 80
Review Of Key Concepts, 80 7.7.1 Relative Advantages Of
7.1 Fundamentals Of Hypothesis Testing, 80 Hypothesis- Testing Versus
7.2 One-Sample T Test, 80 Confidence-Interval Approaches,
7.3 Guidelines For Assessing 85
Statistical Significance, 81 7.8 One-Sample 2 Test, 85
7.4 Two-Sided Alternatives, 82 7.9 One-Sample Inference For The
7.5 The Power Of A Test, 83 Binomial Distribution, 86
7.6 Sample Size, 84 7.10 One-Sample Inference For The
7.7 Relationship Between Hypothesis Testing Poisson Distribution, 87
And Confidence Intervals, 85 Problems, 88
Solutions, 92
References, 98
, Study Guide/Fundamentals Of Biostatistics V
Chapter 8 Hypothesis Testing: Two-Sample Inference 99
Review Of Key Concepts, 99 8.4 T Test For Independent Samples—
8.1 Paired T Test, 99 Unequal Variances, 102
8.2 Two-Sample T Test For Independent 8.5 Sample-Size Determination For Comparing
Samples— Equal Variances, 100 Two Means From Independent Samples, 104
8.3 F Test For The Equality Of Two Variances, Problems, 105
101 Solutions, 111
8.3.1 Characteristics Of The F References, 122
Distribution, 102
Chapter 9 Nonparametric Methods 123
Review Of Key Concepts, 123 9.3 The Wilcoxon Signed-Rank Test, 124
9.1 Types Of Data, 123 9.4 The Wilcoxon Rank-Sum Test, 126
9.2 The Sign Test, 123 Problems, 127
9.2.1 Large-Sample Test, 123 Solutions, 128
9.2.2 Small-Sample Test, 124 Reference, 131
Chapter 10 Hypothesis Testing: Categorical Data 132
Review Of Key Concepts, 132 10.3.1 Computation Of P-Values With
10.1 Comparison Of Two Binomial Proportions, 132 Fisher’s Exact Test, 136
10.1.1 Two-Sample Test For 10.4 Mcnemar’s Test For Correlated Proportions, 136
Binomial Proportions 10.5 Sample Size For Comparing Two
(Normal-Theory Version), 132 Binomial Proportions, 138
10.2 The 2 2 Contingency-Table Approach, 133 10.6 R C Contingency Tables, 139
10.2.1 Relationship Between The Chi- 10.7 Chi-Square Goodness-Of-Fit Test, 141
Square Test And The Two-Sample 10.8 The Kappa Statistic, 143
Test For Binomial Proportions, 135 Problems, 144
10.3 Fisher’s Exact Test, 135 Solutions, 148
References, 158
Chapter 11 Regression And Correlation Methods 159
Review Of Key Concepts, 159 11.8.1 One-Sample Inference, 166
11.1 The Linear-Regression Model, 159 11.8.2 Two-Sample Inference, 167
11.2 Fitting Regression Lines—The Method Of 11.8.3 Sample Size Estimation For
Least Squares, 160 Correlation Coefficients, 168
11.3 Testing For The Statistical Significance Of 11.9 Multiple Regression, 168
A Regression Line, 161 11.9.1 Multiple Regression Model, 168
11.3.1 Short Computational Form For The F 11.9.2 Interpretation Of
Test, 162 Regression Coefficients,
11.4 The T Test Approach To Significance Testing 169
For Linear Regression, 163 11.9.3 Hypothesis Testing, 169
11.5 Interval Estimation For Linear Regression, 164 11.9.4 Several Types Of Correlation
11.6 R2, 165 Associated With Multiple Regression,
11.7 Assessing The Goodness Of Fit Of 170
Regression Lines, 165 11.10 Rank Correlation, 170
11.8 The Correlation Coefficient, 166 Problems, 171
Solutions, 176
References, 185
Fundamentals Of Biostatistics
By Bernard Rosner
8th Edition
,CONTENTS
Preface, Vii
Chapter 1 General Overview 1
There Are No Problems/Solutions In Chapter 1 Of The Textbook.
Chapter 2 Descriptive Statistics 2
Review Of Key Concepts, 2 2.2.2 Quasi-Range, 6
2.1 Measures Of Location, 2 2.2.3 Standard Deviation, Variance, 7
2.1.1 Arithmetic Mean, 2 2.2.4 Coefficient Of Variation (Cv), 8
2.1.2 Median, 3 2.3 Some Other Methods For Describing Data, 8
2.1.3 Stem-And-Leaf Plots, 3 2.3.1 Frequency Distribution, 8
2.1.4 Percentiles, 4 2.3.2 Box Plot, 8
2.1.5 Geometric Mean, 5 Problems, 9
2.2 Measures Of Spread, 6 Solutions, 10
2.2.1 Range, 6 Reference, 11
Chapter 3 Probability 12
Review Of Key Concepts, 12 3.6 Sensitivity, Specificity, Predictive Values
3.1 Frequency Definition Of Probability, 12 Of Screening Tests, 15
3.2 Multiplication Law Of Probability, 13 3.6.1 Roc Curves, 16
3.3 Addition Law Of Probability, 13 3.7 Bayes’ Theorem, 17
3.4 Conditional Probability, 13 Problems, 18
3.4.1 Relative Risk, 14 Solutions, 21
3.5 Total Probability Rule, 14 References, 26
Chapter 4 Discrete Probability Distributions 28
Review Of Key Concepts, 28 4.4 Methods For Using The Binomial Distribution, 30
4.1 Random Variable, 28 4.5 Using Electronic Tables, 30
4.2 Combinations, Permutations, And Factorial, 4.6 Expected Value Of The Binomial Distribution, 31
28 4.7 Variance Of The Binomial Distribution, 31
4.3 Binomial Probability Distribution, 29
Iii
,Iv Contents
4.8 Poisson Distribution, 32 4.11 Poisson Approximation To The
4.9 Use Of Electronic Tables For Binomial Distribution, 33
Poisson Probabilities, 32 Problems, 33
4.10 Expected Value And Variance Of The Solutions, 38
Poisson Distribution, 33 References, 43
Chapter 5 Continuous Probability Distributions 44
Review Of Key Concepts, 44 5.7 Inverse Normal Distribution, 47
5.1 Probability Density Function, 44 5.8 Use Of Electronic Tables For The
5.2 Expected Value And Variance Of A Normal Distribution, 47
Continuous Random Variable, 45 5.9 Normal Approximation To The
5.3 Normal Probability Density Function, 45 Binomial Distribution, 48
5.4 Empirical And Symmetry Properties Of 5.10 Normal Approximation To The
The Normal Distribution, 45 Poisson Distribution, 50
5.5 Calculation Of Probabilities For A Problems, 50
Standard Normal Distribution, 46 Solutions, 54
5.6 Calculation Of Probabilities For A General References, 65
Normal Distribution, 47
Chapter 6 Estimation 66
Review Of Key Concepts, 66 6.8.2 Factors Influencing The Length Of
6.1 Relationship Of Population To Sample, 66 A Confidence Interval, 69
6.2 Random-Number Tables, 66 6.9 Estimation Of The Variance Of A Distribution, 69
6.3 Randomized Clinical Trials, 67 6.10 Estimation For The Binomial Distribution, 70
6.3.1 Techniques Of Study Design In 6.10.1 Large-Sample Method, 70
Randomized Clinical Trials, 67 6.10.2 Small-Sample Method, 71
6.4 Sampling Distribution, 67 6.11 Estimation For The Poisson Distribution, 71
6.5 Estimation Of The Mean Of A Distribution, 6.12 One-Sided Confidence Limits, 72
67 Problems, 73
6.6 Standard Error Of The Mean, 68 Solutions, 76
6.7 The Central-Limit Theorem, 68 Reference, 79
6.8 Interval Estimation For The Mean, 68
6.8.1 Use Of Confidence Intervals
For Decision-Making Purposes,
69
Chapter 7 Hypothesis Testing: One-Sample Inference 80
Review Of Key Concepts, 80 7.7.1 Relative Advantages Of
7.1 Fundamentals Of Hypothesis Testing, 80 Hypothesis- Testing Versus
7.2 One-Sample T Test, 80 Confidence-Interval Approaches,
7.3 Guidelines For Assessing 85
Statistical Significance, 81 7.8 One-Sample 2 Test, 85
7.4 Two-Sided Alternatives, 82 7.9 One-Sample Inference For The
7.5 The Power Of A Test, 83 Binomial Distribution, 86
7.6 Sample Size, 84 7.10 One-Sample Inference For The
7.7 Relationship Between Hypothesis Testing Poisson Distribution, 87
And Confidence Intervals, 85 Problems, 88
Solutions, 92
References, 98
, Study Guide/Fundamentals Of Biostatistics V
Chapter 8 Hypothesis Testing: Two-Sample Inference 99
Review Of Key Concepts, 99 8.4 T Test For Independent Samples—
8.1 Paired T Test, 99 Unequal Variances, 102
8.2 Two-Sample T Test For Independent 8.5 Sample-Size Determination For Comparing
Samples— Equal Variances, 100 Two Means From Independent Samples, 104
8.3 F Test For The Equality Of Two Variances, Problems, 105
101 Solutions, 111
8.3.1 Characteristics Of The F References, 122
Distribution, 102
Chapter 9 Nonparametric Methods 123
Review Of Key Concepts, 123 9.3 The Wilcoxon Signed-Rank Test, 124
9.1 Types Of Data, 123 9.4 The Wilcoxon Rank-Sum Test, 126
9.2 The Sign Test, 123 Problems, 127
9.2.1 Large-Sample Test, 123 Solutions, 128
9.2.2 Small-Sample Test, 124 Reference, 131
Chapter 10 Hypothesis Testing: Categorical Data 132
Review Of Key Concepts, 132 10.3.1 Computation Of P-Values With
10.1 Comparison Of Two Binomial Proportions, 132 Fisher’s Exact Test, 136
10.1.1 Two-Sample Test For 10.4 Mcnemar’s Test For Correlated Proportions, 136
Binomial Proportions 10.5 Sample Size For Comparing Two
(Normal-Theory Version), 132 Binomial Proportions, 138
10.2 The 2 2 Contingency-Table Approach, 133 10.6 R C Contingency Tables, 139
10.2.1 Relationship Between The Chi- 10.7 Chi-Square Goodness-Of-Fit Test, 141
Square Test And The Two-Sample 10.8 The Kappa Statistic, 143
Test For Binomial Proportions, 135 Problems, 144
10.3 Fisher’s Exact Test, 135 Solutions, 148
References, 158
Chapter 11 Regression And Correlation Methods 159
Review Of Key Concepts, 159 11.8.1 One-Sample Inference, 166
11.1 The Linear-Regression Model, 159 11.8.2 Two-Sample Inference, 167
11.2 Fitting Regression Lines—The Method Of 11.8.3 Sample Size Estimation For
Least Squares, 160 Correlation Coefficients, 168
11.3 Testing For The Statistical Significance Of 11.9 Multiple Regression, 168
A Regression Line, 161 11.9.1 Multiple Regression Model, 168
11.3.1 Short Computational Form For The F 11.9.2 Interpretation Of
Test, 162 Regression Coefficients,
11.4 The T Test Approach To Significance Testing 169
For Linear Regression, 163 11.9.3 Hypothesis Testing, 169
11.5 Interval Estimation For Linear Regression, 164 11.9.4 Several Types Of Correlation
11.6 R2, 165 Associated With Multiple Regression,
11.7 Assessing The Goodness Of Fit Of 170
Regression Lines, 165 11.10 Rank Correlation, 170
11.8 The Correlation Coefficient, 166 Problems, 171
Solutions, 176
References, 185
