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Subject Index
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Efficient estimate, 195, 199 Elementary event, 4 Empirical probability, 5 Empirical probability distributions, 161 Envelope problem, 25 Equally likely outcomes, 6 Error: in regression, 266 variation due to, 319, 321, 322 Error function [erf(z)], 110 Event, 4, 10 certain or sure, 4 elementary, 4 impossible, 4 Expected frequency, 219 Expected value, 75, 85 some theorems on, 76 77, 85 Expected values of variations, 316 Experiment, random, 3, 10 Experimental design, 323 Explained variation, 270, 273, 289, 292 Exponential distribution, 118 F distribution, 116, 138, 233 F test for null hypothesis of equal means, 317 Fermi-Dirac statistics, 31 Finite population, 153, 156 Finite sample apace, 4 Fisher, R. A., 116, 198, 314 Fisher s transformation: in analysis of variance, 314 in correlation, 274 Fisher s Z transformation, 274 Fitting data by theoretical distributions, 239 241 Fourier series, 81, 97 Fourier transform, 81 Frequency: approach to probability, 5 classes, 160 distribution, 160, 175 histogram, 176 polygon, 160 Functions of random variables, 76 Fundamental principle of counting, 8 Gamma distribution, 114, 133, 147 Gamma function, 114, 411 Stirling s asymptotic formula for, 412 Gaussian distribution, 109 Generalized correlation coefficient, 271, 292 Geometric distribution, 117 Geometric probability, 44, 60 Goodness of fit, 219, 242, 246 Graeco-Latin squares, 324, 335 Grand mean, 314, 319 Group means, 314 H test corrected for ties, 350 Haldane s prior density, 379 Hypergeometric distribution, 113, 131 Hypothesis test (see Tests of hypotheses and significance) Impossible event, 4 Improper density, 373 Improper prior distributions, 378, 392 Independent: events, 7, 8, 14 random variables, 41, 47, 59 samples, 157, 169, 197 trials, 108 variable, 265 Infinite population, 153, 156 Interaction effects, 321 Interquartile range, 84 Interval estimate, 195 Interval probability, 36 Invariant under transformation, 268, 271 Inverse Fourier transform, 81 Jacobian, 42, 52, 54 Joint: density function, 40, 48 51 distribution function, 40, 47, 51 distributions, 39, 47 51 probability function, 39, 47, 48 probability table, 39 Kruskal-Wallis H test, 283, 350, 360 corrected for ties, 350 Kurtosis, 84, 85, 96 98 Large samples, 196, 216 Laplace s law of succession, 380, 386 Latin squares, 323, 334 Law of large numbers, 83, 94, 103 for Bernoulli trials, 109, 122 Least-squares: curve, 266 line, 266 268, 275 method, 266 parabola, 266, 268, 269, 284 regression curve, 266, 272 Level of significance, 214 Likelihood function, 373 374 Likelihood, 198 Linear: correlation coefficient, 270, 289 model for analysis of variance, 315 regression, 265, 266, 275 relationship, 265, 292 Mann-Whitney U test, 349, 354, 358 Marginal: density functions, 41, 58 distributions functions, 41, 48, 49, 61 frequency, 221 probability functions, 39 Mathematical expectation, 75 some theorems on, 76, 77 Maximum likelihood: estimate, 198, 206 likelihood estimator, 199, 206 likelihood method, 198 Maxwell distribution, 118 Mean: arithmetic, 75 deviation, 84 for group data, 161, 162 of functions of random variables, 76 Means: grand, 314 group, 314 overall, 314 row, 314 treatment, 314 Measurable subsets, 5 Measure of central tendency, 75, 94, 103 Measure of dispersion about the mean, 77, 96, 103 Median, 83, 94, 95, 103 Mendel s experiments, 243 Method of least squares, 266 Mode, 83, 94, 103 Moment generating function 79, 80, 88, 96, 100 of Binomial distribution, 121 of Cauchy distribution, 132
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of Poisson distribution, 129 of a sum of independent random variables, 89 Moments (See also rth moments), 78, 88, 93, 100, 177 Moments for grouped data, 161, 162 More efficient estimator, 195 Multinomial distribution, 112, 131, 146 Multinomial population, 220 Multiple correlation coefficients, 271, 293 Multiple regression, 269, 285 Mutually exclusive events, 4, 13 Negative binomial distribution, 117 Noninformative prior distribution, 373 Nonlinear equations reducible to linear form, 282 Nonlinear regression curve, 271 Nonlinear relationship, 265, 292 Nonparametric analysis of variance, 350 Nonparametric statistics, 184, 349 351 Nonparametric tests, 348 371 Normal curve graph paper, 219 Normal distribution, 109, 122 properties of, 110 Normal approximation to binomial, 126, 129 Normal equations, 267, 269 Normal population, 154 Normally distributed random variable, 109, 122 Null hypothesis, 213 Observed frequency, 219 OC curves, 219 Odds, 5 One-factor experiments, 314, 324 tables for, 317, 318 One-sided tests, 215 One-tailed tests, 215 One-way classification, 314 Operating characteristic curves, 219, 234, 251 Operating characteristic function, 235 Overall mean, 314, 319 P value, 215 Paired samples, sign test for, 348 Parabolic curve, 265 Pascal s distribution, 117 Percentage (relative) frequency distributions, 161 Percentiles, 84, 96, 103 Perfect linear correlation and regression, 268, 270 Permutations, 9, 18, 28 Point estimate, 195 Poisson distribution, 111, 128, 129, 146 Pooled variance, 218 Population, 153 correlation coefficient, 273 parameters, 154 size, 153 Posterior probability, 373 Power of a test, 219, 235 Precision of a distribution, 377 Predictive intervals, 388 Predictive point estimate, 388 Prior and posterior distributions, 372, 388 when sampling from a binomial population, 375, 390 when sampling from a Poisson population, 376, 391 when sampling from a normal population, 377, 391
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