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1 | (18) |
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1 | (1) |
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The Aims of Medicine, Science, and Engineering |
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2 | (2) |
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The Roles of Models and Data |
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4 | (2) |
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Deterministic and Statistical Models |
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6 | (2) |
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6 | (1) |
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7 | (1) |
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Probability Theory and Computer Simulation |
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8 | (11) |
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9 | (10) |
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Classes of Models and Statistical Inference |
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19 | (28) |
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Statistical Models --- the Frequency Interpretation |
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19 | (4) |
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The frequency interpretation |
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19 | (4) |
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Some Useful Statistical Models |
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23 | (12) |
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Normal (Gaussian) distributions |
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24 | (6) |
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30 | (1) |
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31 | (1) |
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31 | (1) |
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Exponential distributions |
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32 | (1) |
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32 | (1) |
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32 | (1) |
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Negative binomial distributions |
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33 | (1) |
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Hypergeometric distributions |
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33 | (2) |
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Narrowing Down the Class of Potential Models |
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35 | (12) |
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Distinguishing characteristics of statistics |
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37 | (10) |
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Sampling and Descriptive Statistics |
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47 | (42) |
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Representative and Random Samples |
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47 | (13) |
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47 | (1) |
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Random sampling from a finite population without replacement |
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48 | (1) |
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Random sampling from a finite population with replacement |
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49 | (1) |
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Assertion The importance of random sampling |
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50 | (1) |
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Sampling from a theoretical population |
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50 | (1) |
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Random sampling from a finite population |
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51 | (9) |
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Descriptive Statistics of Location |
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60 | (6) |
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Long-run usual (and unusual) behavior of successive means |
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63 | (3) |
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Descriptive Statistics of Variability |
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66 | (4) |
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Population and sample standard deviations |
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67 | (1) |
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The two-sigma rule-of-thumb |
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68 | (2) |
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Other Descriptive Statistics |
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70 | (19) |
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72 | (2) |
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74 | (2) |
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The Correlation Coefficient |
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76 | (1) |
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Sample Correlation Coefficient |
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76 | (4) |
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The empirical cumulative distribution function (EDF) |
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80 | (9) |
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Survey of Basic Probability |
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89 | (54) |
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89 | (3) |
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Probability and its Basic Rules |
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92 | (13) |
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94 | (1) |
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Event, occurrence of a given event |
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94 | (1) |
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Formation of events from other events |
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95 | (2) |
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Definitions Formation of events from other events |
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97 | (3) |
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100 | (3) |
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103 | (2) |
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Discrete Uniform Models and Counting |
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105 | (8) |
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Systematic counting methods |
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106 | (1) |
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107 | (1) |
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Corollary to Theorem 4.11, ordered sampling |
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107 | (1) |
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Symbols for j-factorial and the binomial coefficient |
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108 | (1) |
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Corollary to Theorems 4.11 and 4.12 |
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108 | (5) |
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113 | (7) |
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Conditional probability of A given B |
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114 | (2) |
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The stratified sampling theorem |
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116 | (3) |
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Relation between random sample and random sampling one at a time without replacement |
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119 | (1) |
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Probability of intersection and conditional probability |
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119 | (1) |
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120 | (3) |
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Statistical independence of events A and B |
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121 | (1) |
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Mutual statistical independence |
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121 | (2) |
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Systematic Approach to Probability Problems |
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123 | (2) |
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Random Variables, Expectation and Variance |
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125 | (8) |
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125 | (1) |
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Probability function of a discrete RV |
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126 | (1) |
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Probability density of an RV |
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127 | (1) |
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Statistically independent random variables |
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127 | (1) |
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Population mean, mathematical expectation |
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128 | (3) |
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Variance and standard deviation |
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131 | (1) |
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132 | (1) |
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The Central Limit Theorem and its applications |
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133 | (10) |
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133 | (1) |
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Expectation and variance of sums |
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134 | (1) |
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135 | (6) |
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Distribution of independent normal sums |
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141 | (2) |
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Introduction to Statistical Estimation |
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143 | (38) |
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143 | (3) |
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Maximum likelihood estimators |
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144 | (1) |
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145 | (1) |
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Distribution of Sample Percentiles |
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146 | (3) |
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146 | (1) |
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Sample percentiles (quantiles) |
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147 | (1) |
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Distribution of order statistics |
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147 | (2) |
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149 | (3) |
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Confidence Limits and Confidence Intervals |
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152 | (10) |
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1- a level confidence limits and intervals |
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152 | (3) |
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Elementary confidence interval construction |
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155 | (1) |
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Standard normal distribution upper 1- point |
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155 | (1) |
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Summary of normal mean confidence results when standard deviation is known |
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156 | (4) |
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Confidence limits and intervals for percentiles |
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160 | (2) |
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Confidence Limits and Interval for Binomial p |
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162 | (7) |
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Binomial confidence limits and intervals |
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166 | (3) |
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169 | (4) |
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173 | (8) |
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Summary of bootstrap for binomial standard deviation |
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174 | (7) |
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181 | (36) |
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181 | (6) |
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182 | (5) |
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Some Commonly Used Statistical Tests |
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187 | (19) |
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187 | (3) |
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190 | (2) |
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Nonparametric alternative to the one-sample t test |
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192 | (1) |
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Independent two-sample Z tests |
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193 | (2) |
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Independent two-sample student t tests |
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195 | (3) |
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The independent two-sample Wilcoxon test (aka the Mann-Whitney test) |
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198 | (3) |
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The chi-square tests of homogeneity and independence |
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201 | (3) |
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204 | (1) |
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204 | (1) |
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Significance level of a test, p-value of test statistic |
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205 | (1) |
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Setting up tests of hypotheses |
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205 | (1) |
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Types I and II Errors and (Discriminating) Power |
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206 | (3) |
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Power function, type I and type II errors |
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206 | (3) |
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The Simulation Approach to Estimating Power |
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209 | (4) |
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Some Final Issues and Comments |
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213 | (4) |
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Basic Regression and Analysis of Variance |
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217 | (16) |
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217 | (1) |
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217 | (4) |
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Least squares curve fit to data Simple linear regression |
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218 | (3) |
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Multiple Linear Regression |
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221 | (1) |
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222 | (11) |
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223 | (4) |
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The additive two-way layout |
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227 | (3) |
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The general two way-layout |
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230 | (3) |
Epilogue |
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233 | (2) |
Bibliography |
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235 | (2) |
Selected Answers and Solutions |
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237 | (36) |
Index |
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273 | |