Biostatistics for Oral Healthcare

Biostatistics for Oral Healthcare......Page 6
Contents......Page 8
Preface......Page 12
1.1 What Is Biostatistics?......Page 14
1.4 How Do I Study Statistics?......Page 15
1.5 Reference......Page 16
2.1 Raw Data and Basic Terminology......Page 18
2.2 The Levels of Measurements......Page 20
2.3.1 Frequency Tables......Page 22
2.3.2 Relative Frequency......Page 25
2.4.1 Bar Graphs......Page 26
2.4.3 Line Graph......Page 27
2.4.4 Histograms......Page 28
2.4.5 Stem and Leaf Plots......Page 32
2.5 Clinical Trials and Designs......Page 33
2.7 Exercises......Page 35
2.8 References......Page 37
3.2 Mean......Page 40
3.3 Weighted Mean......Page 43
3.4 Median......Page 44
3.5 Mode......Page 46
3.7 Harmonic Mean......Page 47
3.8 Mean and Median of Grouped Data......Page 48
3.9 Mean of Two or More Means......Page 50
3.10 Range......Page 51
3.11 Percentiles and Interquartile Range......Page 52
3.12 Box-Whisker Plot......Page 54
3.13 Variance and Standard Deviation......Page 56
3.14 Coefficient of Variation......Page 59
3.16 Skewness......Page 61
3.17 Exercises......Page 63
3.18 References......Page 66
4.2 Sample Space and Events......Page 68
4.3 Basic Properties of Probability......Page 69
4.4 Independence and Mutually Exclusive Events......Page 74
4.5 Conditional Probability......Page 75
4.6 Bayes Theorem......Page 78
4.7.1 Prevalence and Incidence......Page 82
4.7.2 Sensitivity and Specificity......Page 83
4.7.3 Relative Risk and Odds Ratio......Page 86
4.8 Exercises......Page 88
4.9 References......Page 92
5.2 Binomial Distribution......Page 94
5.3 Poisson Distribution......Page 99
5.4 Poisson Approximation to Binomial Distribution......Page 100
5.5.1 Properties of Normal......Page 101
5.5.2 Standard Normal Distribution......Page 103
5.5.3 Using Normal Probability Table......Page 104
5.5.4 Further Applications of Normal Probability......Page 107
5.5.5 Finding the (1—α) 100th Percentiles......Page 108
5.5.6 Normal Approximation to the Binomial Distribution......Page 109
5.6 Exercises......Page 112
5.7 References......Page 115
6.2 Sampling Distribution of the Mean......Page 116
6.2.1 Standard Error of the Sample Mean......Page 117
6.2.2 Central Limit Theorem......Page 119
6.3 Student t Distribution......Page 121
6.4 Exercises......Page 123
6.5 References......Page 124
7.2 Confidence Intervals for the Mean μ and Sample Size n When σ Is Known......Page 126
7.3 Confidence Intervals for the Mean μ and Sample Size n When σ Is Not Known......Page 130
7.4 Confidence Intervals for the Binomial Parameter ρ......Page 132
7.5 Confidence Intervals for the Variances and Standard Deviations......Page 134
7.6 Exercises......Page 137
7.7 References......Page 139
8.1 Introduction......Page 140
8.2 Concepts of Hypothesis Testing......Page 141
8.3 One-Tailed Z Test of the Mean of a Normal Distribution When σ2 Is Known......Page 144
8.4 Two-Tailed Z Test of the Mean of a Normal Distribution When σ2 Is Known......Page 150
8.5 t Test of the Mean of a Normal Distribution......Page 154
8.6 The Power of a Test and Sample Size......Page 157
8.7 One-Sample Test for a Binomial Proportion......Page 161
8.8 One-Sample χ2 Test for the Variance of a Normal Distribution......Page 163
8.9 Exercises......Page 166
8.10 References......Page 170
9.2 Two-Sample Z Test for Comparing Two Means......Page 172
9.3 Two-Sample t Test for Comparing Two Means with Equal Variances......Page 174
9.4 Two-Sample t Test for Comparing Two Means with Unequal Variances......Page 176
9.5 The Paired t Test......Page 178
9.6 Z Test for Comparing Two Binomial Proportions......Page 181
9.7.1 Estimation of Sample Size......Page 183
9.7.2 The Power of a Two-Sample Test......Page 185
9.8 The F Test for the Equality of Two Variances......Page 186
9.9 Exercises......Page 189
9.10 References......Page 192
10.2 2 × 2 Contingency Table......Page 194
10.3 r × c Contingency Table......Page 200
10.4 The Cochran-Mantel-Haenszel Test......Page 202
10.5 The McNemar Test......Page 204
10.6 The Kappa Statistic......Page 207
10.7 χ2 Goodness-of-Fit Test......Page 208
10.8 Exercises......Page 211
10.9 References......Page 214
11.2 Simple Linear Regression......Page 216
11.2.1 Description of Regression Model......Page 219
11.2.2 Estimation of Regression Function......Page 220
11.2.3 Aptness of a Model......Page 222
11.3 Correlation Coefficient......Page 225
11.3.1 Significance Test of Correlation Coefficient......Page 228
11.4 Coefficient of Determination......Page 230
11.5 Multiple Regression......Page 232
11.6.1 The Logistic Regression Model......Page 234
11.6.2 Fitting the Logistic Regression Model......Page 235
11.8 Exercises......Page 236
11.9 References......Page 238
12.2 Factors and Factor Levels......Page 240
12.4 Basic Concepts in ANOVA......Page 241
12.5 F Test for Comparison of k Population Means......Page 242
12.6.2 Bonferroni Approach......Page 247
12.6.3 Scheffé's Method......Page 249
12.6.4 Tukey's Procedure......Page 250
12.7 One-Way ANOVA Random Effects Model......Page 251
12.8.1 Bartlett's Test......Page 252
12.8.2 Hartley's Test......Page 254
12.9 Exercises......Page 255
12.10 References......Page 256
13.1 Introduction......Page 258
13.2 General Model......Page 259
13.3 Sum of Squares and Degrees of Freedom......Page 260
13.4 F Tests......Page 263
13.5 Repeated Measures Design......Page 266
13.5.1 Advantages and Disadvantages......Page 267
13.7 References......Page 268
14.1 Introduction......Page 270
14.2 The Sign Test......Page 271
14.3 The Wilcoxon Rank Sum Test......Page 272
14.4 The Wilcoxon Signed Rank Test......Page 275
14.5 The Median Test......Page 277
14.6 The Kruskal-Wallis Rank Tes......Page 279
14.7 The Friedman Test......Page 281
14.8 The Permutation Test......Page 282
14.9 The Cochran Test......Page 283
14.10 The Squared Rank Test for Variance......Page 285
14.11 Spearman's Rank Correlation Coefficient......Page 287
14.12 Exercises......Page 288
14.13 References......Page 290
15.2 Person-Time Method and Mortality Rate......Page 292
15.3 Life Table Analysis......Page 294
15.4 Hazard Function......Page 295
15.5 Kaplan-Meier Product Limit Estimator......Page 297
15.6 Comparing Survival Functions......Page 300
15.6.1 Gehan Generalized Wilcoxon Test......Page 301
15.6.2 The Log Rank Test......Page 302
15.6.3 The Mantel-Haenszel Test......Page 303
15.7.1 Small Sample Illustration......Page 304
15.7.2 General Description of PEXE......Page 305
15.7.3 An Example......Page 306
15.7.4 Properties of PEXE and Comparisons with Kaplan-Meier Estimator......Page 308
15.8 Exercises......Page 310
15.9 References......Page 311
Solutions to Selected Exercises......Page 312
Table A Table of Random Numbers......Page 322
Table B Binomial Probabilities......Page 323
Table C Poisson Probabilities......Page 329
Table D Standard Normal Probabilities......Page 332
Table E Percentiles of the t Distribution......Page 333
Table F Percentiles of the χ2 Distribution......Page 335
Table G Percentiles of the F Distribution......Page 336
Table H A Guide to Methods of Statistical Inference......Page 341
Index......Page 342