Firms in the Food, Drink and Tobacco Trades, distribution of, (Table 1.17) 23
First hands at whist, distribution of, (Example 12.1) 299—300
First hands at whist, distribution of, (Table 5.4) 128
First Limit Theorem 100—101
First Limit Theorem, converse of 101-103
Fisher, Arne, modified form of Gram — Charlier series 153
Fisher, Arne, modified form of Gram — Charlier series, fitting of Type B to data (Example 6.4) 156
Fisher, Arne, modified form of Gram — Charlier series, refs., Frequency Curves 160
Fisher, R.A., Sheppard's corrections 75—77
Fisher, R.A., Sheppard's corrections, applications of Student's distribution 250
Fisher, R.A., Sheppard's corrections, distribution of  305
Fisher, R.A., Sheppard's corrections, distribution of when parameter estimated from data 301
Fisher, R.A., Sheppard's corrections, distribution of correlation coefficient 250 363
Fisher, R.A., Sheppard's corrections, distribution of extreme 220
Fisher, R.A., Sheppard's corrections, distribution of extreme values 228
Fisher, R.A., Sheppard's corrections, distribution of mean deviation 215 228
Fisher, R.A., Sheppard's corrections, distribution of multiple correlation 386
Fisher, R.A., Sheppard's corrections, distribution of multiple correlation coefficient (Exercises 15.6 and 15.7) 387
Fisher, R.A., Sheppard's corrections, distribution of partial coefficients 386
Fisher, R.A., Sheppard's corrections, distribution of variances and covariance in normal samples 340
Fisher, R.A., Sheppard's corrections, distribution of well-known statistics 250
Fisher, R.A., Sheppard's corrections, introduction of word "cumulant" 85
Fisher, R.A., Sheppard's corrections, inverse probability 184
Fisher, R.A., Sheppard's corrections, k-statistics 256 268 285
Fisher, R.A., Sheppard's corrections, mathematics of statistics 184
Fisher, R.A., Sheppard's corrections, measures of departure from normality, (Exercise 11.16) 289
Fisher, R.A., Sheppard's corrections, normal approximation to 294—295
Fisher, R.A., Sheppard's corrections, random sampling numbers 194 197
Fisher, R.A., Sheppard's corrections, refs., moments and cumulants in specification of distributions 160
Fisher, R.A., Sheppard's corrections, tables of 293
Fisher, R.A., Sheppard's corrections, transformation of correlation coefficient 345
Fisher, R.A., Sheppard's corrections, z-distribution see "z—distribution"
Food, Drink and Tobacco Trades, distribution of firms, (Table 1.17) 23
Footrule, Spearman's 436
Franel, J., theorem on distribution of digits in mathematical tables, footnote 193
Frechet, M., proof of Second Limit Theorem 112 113
Frechet, M., proof of Second Limit Theorem, refs. 114
Frequency (class-frequency), definition of 2
Frequency-distributions, generally 1—28
Frequency-distributions, generally, genesis of 18
Frequency-functions 12—15
Frequency-functions, determined by characteristic function 91—94
Frequency-functions, discontinuous 12
Frequency-functions, normalisation of 156—159
Frequency-polygons 4
Frequency-polygons, bivariate form 20
Friedman, M., tests of significance in m rankings 420
Friedman, M., tests of significance in m rankings, refs. 436
Frisch, R., moments of binomial 58
Frisch, R., moments of binomial and (Exercise 5.3) 135
Frisch, R., moments of binomial, correlation analysis 386
Frisch, R., moments of binomial, refs., moments and cumulants 85 134
Galbrun, H., convergence of Gram — Charlier series 152
Galton's ogive see "Distribution curve"
Galvani, L., refs. (under Gini), median for qualitative characteristics 47
Garwood, F., data from, (Table 12.1) 297—298
Garwood, F., data from, refs., fiducial limits for Poisson distribution 305
Geary, R.C., distribution of measures of departure from normality, (Exercise 11.16) 289
Geary, R.C., distribution of measures of departure from normality, (Exercise 11.16) and refs. 250
Geary, R.C., distribution of measures of departure from normality, (Exercise 11.16), distribution of a ratio, (Exercise 10.9) 253
Geiger, H. see "Rutherford"
Generating functions, for moments and cumulants 90 see
German women, distribution of suicides, (Table 1.6) 7
Gilby, W.H., data from, on intelligence and clothing in schoolchildren, (Table 13.1) 320
Gini, C., coefficient of concentration 43
Gini, C., coefficient of concentration, coefficient of mean difference 42
Gini, C., coefficient of concentration, median for qualitative characteristics 47
Gini, C., coefficient of concentration, refs., mean difference 47
Gini, C., coefficient of concentration, standard error 216 225
Glossina, morsitans (tsetse fly), distribution of trypanosomes in, (Table 1.13) 12
Goring, C., data on alcoholism and crime, (Table 14.6) 356
Gosset, W.S. see "Student"
Grades 408
Grades, relation with ranks 408—410
Graduation curve see "Distribution curve"
Grain, distribution of plots according to yield of, (Table 1.18) 23
Gram — Charlier series, Type A 147—154
Gram — Charlier series, Type A, distribution of means from, (Exercise 10.7) 252
Gram — Charlier series, Type A, Edge-worth's form 148—150
Gram — Charlier series, Type A, fitting to bean data, (Example 6.2) 151
Gram — Charlier series, Type A, Type B 154—156
Gram — Charlier series, Type A, Type C 160
Greenwood, M., data on industrial accidents on inoculation against cholera, (Example 13.1) 309
Greenwood, M., data on industrial accidents, (Table 5.3) 124
Grouping of frequency-distributions, corrections for see "Sheppard's corrections"
Gumbel, E.J., distribution of mth values 220—222
Gumbel, E.J., distribution of mth values and refs. 228
Haines, J., refs. (under Pearson), use of range 228
Hair-colour, relation with eye-colour, (Example 12.3) 299—300
Haldane, J.B.S., refs., cumulants and moments of binomial 134
Haldane, J.B.S., refs., cumulants and moments of binomial and (Exercise 12.1) 306
Haldane, J.B.S., refs., cumulants and moments of binomial and (Exercise 5.1) 135
Haldane, J.B.S., refs., cumulants and moments of binomial, with small expectations 305
Haldane, J.B.S., refs., cumulants and moments of binomial, normalisation of frequency functions 305
Half-invariants (seminvariants) see "Cumulants"
Hall, P., refs., distribution of mean from rectangular population 250
Hall, P., refs., distribution of mean from rectangular population, multiple correlation 386
Hamburger, H., problem of moments 107
Hamburger, H., problem of moments and refs. 114
Hartley, H.O., distribution of range 224
Hartley, H.O., distribution of range and refs. 228
Health of son and alcoholism of parent, (Exercise 14.12) 366
Height in fathers and sons, (Table 14.3) 327
Height in fathers and sons, correlation, (Example 14.5) 337
Height, distribution of men according to, (Table 1.7) 8
Height, distribution of men according to, distribution curve, (Figure 2.2) 37
Height, distribution of men according to, factorial and ordinary moments (Example 3.7) 59—60
Height, distribution of men according to, fitted to normal curve, (Table 5.5) 132
Height, distribution of men according to, frequency-polygon of, (Figure 1.3) 8
Height, distribution of men according to, mean deviation and standard deviation, (Example 2.6) 39—40
Height, distribution of men according to, mean difference, (Example 2.8) 45—46
Height, distribution of men according to, mean, (Example 2.1) 30—31
Height, distribution of men according to, median, (Example 2.4) 35
Height, distribution of men according to, quartiles, (Example 2.5) 36
Height, distribution of men according to, standard error of mean, (Example 9.1) 207
Height, distribution of plants according to, (Table 8.1) 187
Hellman, M., data on teeth and feeding in infants, (Example 12.5) 304
Helly, W., theorems on convergent sequences of functions 100 112
Helmert, W., distribution of mean deviation 215
Helmert, W., distribution of mean deviation, distribution of sums of squares 250 305
Henderson, J., refs., expansion in tetrachoric functions 160
Hermite, C., polynomials 145 160 see
Heron, D., refs., (under Pearson), coefficients of association 322
Heterotypic frequency-distributions 145
Highest audible pitch and age, bivariate distribution according to, (Table 14.1) 325
Highest audible pitch and age, bivariate distribution according to, correlation ratios (Example 14.11) 351—352
Highest audible pitch and age, bivariate distribution according to, correlations and regressions, (Example 14.1) 331
Hilferty, M.M., limiting distribution of 294—296
Hilferty, M.M., limiting distribution of and refs., (under Wilson) 305
Hilton, J., refs., inquiry by sample 202
histogram 4
Histogram, bivariate 20
Hojo, T., refs., distribution of median, quartiles and semi-interquartile range 228
Homoscedastic distributions 335
Hooker, R.H., data on weather and crops and refs. 386
Hooker, R.H., data on weather and crops, (Example 15.1) 373
Hotelling, H., distribution of Spearman's p 401
Hotelling, H., distribution of Spearman's p and refs. 436
Hsu, C.T., sampling cumulants of normal distribution 275
Hsu, C.T., sampling cumulants of normal distribution and refs. 286
Hypergeometric distribution, generally 126—128
Hypergeometric distribution, generally, example of, (Table 5.4) 128
Hypergeometric distribution, generally, factorial moments of, (Exercise 5.4) 135
Hypergeometric distribution, generally, limiting forms of 132—133
Hypergeometric distribution, generally, moments of 127
Hypergeometric, function 127
Hypothetical population 187
Illusory association 317
Income, distribution curve of, (Figure 2.1) 37
Income, distribution of persons by, (Table 1.2) 3
| Income, histogram of, (Figure 1.2) 4
Incomplete moments 43
Incomplete moments and (Exercises 5.2, 5.3) 135
Incomplete moments of binomial, refs. 134
Independence, definition 21
Independence, definition in association tables 309
Independence, definition in bivariate frequency tables 326
Index, distribution of see "Ratio"
Induction, in finding sampling distributions 246—248
Inequalities for moments 56
Inequalities for moments and (Exercise 3.14) 88
Inequalities for moments, Liapounoff's 56
Inequalities for moments, refs. (Shohat) 86
Inoculation against cholera see "Cholera"
Inoculation, against tuberculosis in cattle, (Exercise 12.7) 307
Intelligence, distribution of schoolchildren according to, (Example 13.6) 320
Interdecile range 38
Interquartile range 38
Interquartile range, standard error of semi-interquartile range, (Example 9.8) 214
Interval (class-interval) see "Class"
Intra-class correlation 358—362
Inverse probability 176 see
Inversion theorem 91—98
Inversion theorem, examples of use of 94—98
Irregular Kollektiv of von Mises 171—172
Irwin, J.O., distribution of means, (Exercises 10.3 and 10.4) 251
Irwin, J.O., distribution of means, (Exercises 10.3 and 10.4) and refs. 251
J-shaped distribution 10
Jackson, Dunham, on indeterminacy of median 46
Jackson, Dunham, on indeterminacy of median and refs. 47
Jeffreys, H., logic of probability 166
Jeffreys, H., logic of probability, refs., Theory of Probability 184
Jensen, A., refs., representative method in statistics 202
Johannsen, W., bean data cited by Pretorius, (Table 1.15) 20
Johnson, W.E., logic of probability 166
Johnson, W.E., logic of probability, refs., Logic 184
Jordan, C., refs., Statistique mathematique 160
Jordan, C., refs., Statistique mathematique, Type B series (Exercises 6.4 and 6.6) 161—162
Jorgensen, N.R., tables of Tchebycheff — Hermite polynomials 147 151
Jorgensen, N.R., tables of Tchebycheff — Hermite polynomials, refs., Undersegelser over Frequensflader og Korrelation 160
k-statistics, definition 256
k-statistics, definition in multivariate case 281—283
k-statistics, definition, general properties 256—260
k-statistics, definition, sampling cumulants of 260—289
Kelley, T.L., tables of 293
Kelley, T.L., tables of and refs. 386
Kelley, T.L., tables of , refs., Kelley Statistical Tables 386
Kelley, T.L., tables of , tables of correlation coefficient 376
Kendall, M.G., data from, (Table 1.4) 6
Kendall, M.G., data from, data from, (Table 8.3) 189
Kendall, M.G., data from, k-statistics 285
Kendall, M.G., data from, maximum likelihood 179 184
Kendall, M.G., data from, multivariate cumulants 80
Kendall, M.G., data from, multivariate sampling formulae 85
Kendall, M.G., data from, Random Sampling Numbers 193 197
Kendall, M.G., data from, randomness 172 184
Kendall, M.G., data from, randomness and random sampling numbers 202
Kendall, M.G., data from, rank correlation and paired comparisons 436
Kendall, M.G., data from, refs., Sheppard corrections 85
Kendall, M.G., data from, Sheppard corrections 76
Kendall, S.F.H., refs., distribution of Spearman's  436
Keynes, J.M., (now Lord Keynes), on probability 165
Keynes, J.M., (now Lord Keynes), on probability, refs., Treatise on Probability 184
Kiser, C.V., refs., pitfalls in sampling 202
Koga, Y., data from, (Table 14.1) 326
Kollektiv of von Mises 171—172
Kolmogoroff, A., probability as abstract ensembles 165
Kolmogoroff, A., probability as abstract ensembles, refs., Grundbegriffe der Wahrscheinlichkeitstheorie 184
Kondo, T., refs., standard error of mean square contingency 321 322
Kullback, S., refs., distributions and characteristic functions 251 363
Kullback, S., refs., distributions and characteristic functions and (Exercises 10.2 and 10.5) 251 252
Kullback, S., refs., distributions and characteristic functions, (Exercise 14.7) 364—365
kurtosis 82
Lagrange, J.L., distribution of mean from rectangular population 250
Laplace, P.S. (Marquis de), characteristic functions 113
Laplace, P.S. (Marquis de), characteristic functions, continued fraction for the normal distribution 129—130
Laplace, P.S. (Marquis de), characteristic functions, early work on Central Limit Theorem 180
Laplace, P.S. (Marquis de), characteristic functions, succession rule, (Example 7.7) 177
Large samples, approximations in theory of 201—202 see
Laterality of hand and eye, (Exercise 13.5) 323
Latter, O.H., data on length of cuckoo's eggs, (Exercise 14.13) 366
Lawley, D.N., sampling cumulants of k-statistics 275
Lawley, D.N., sampling cumulants of k-statistics and refs., (under Hsu) 285
Least squares, in determination of regression lines 328—329 368
Lee, A., data from, on fecundity of mares on stature of fathers and sons, (Table 14.3) 327
Lee, A., data from, on fecundity of mares, (Table 1.20) 24
Lee, A., data from, on fecundity of mares, refs., sampling of correlation coefficient, (under Co-operative Study) 363
Leibniz, G.W., logic of probabilities 165
Leptokurtosis 82
Levy, P., refs., Calcul des Probabilites 22 184
Levy, P., refs., Calcul des Probabilites, characteristic functions 113 114
Liapounoff, A., inequality for moments 66
Liapounoff, A., inequality for moments and (Exercise 3.14) 88
Liapounoff, A., inequality for moments, proof of Central Limit Theorem 180 183
Liapounoff, A., inequality for moments, refs., limit theorems in probability 184
Likelihood 176
Likelihood in estimating proportion of attributes 199—200
Likelihood, principle of maximum likelihood 178—180
Likelihood, relation with Bayes' theorem 178—180
Likelihood, relation with Bayes' theorem and (Exercise 8.6) 203
Limit theorems for distributions see "First Limit Theorem" "Second
Lindeberg, J.W., condition for validity of Central Limit Theorem 181
Linear regression 327—329 368—376
Location, measures of 29—38 see
Lottery sampling 192
m rankings 410—421
Macaulay's essays, distribution of sentence length in, (Table 1.21) 25
Male births, distribution of registration districts according to, (Table 14.2) 326
Male births, distribution of registration districts according to, constants of, (Example 14.2) 364
Malocclusion of teeth in infants, (Example 12.6) 304
Markoff, A., refs., Second Limit Theorem 113
Marriages, distribution of Australian see "Australian"
Marriages, distribution of Australian of deaf in America, (Table 1.19) 24
Martin, E.S., refs., corrections to moments 85
Maximum likelihood 178 see
Mean difference 42
Mean difference and (Exercise 2.10) 48
Mean difference, calculation of 45
Mean difference, standard error 216—217 225
Mean, arithmetic, definition of 29
Mean, as first moment 39
Mean, deviation, about mean 38
Mean, deviation, about median 38
Mean, deviation, standard error of 216
Mean, distribution of, in normal samples, (Example 10.5) 238—239
Mean, geometric 32
Mean, geometric from rectangular population, (Example 10.13) 245
Mean, geometric from Type III distribution (Exercise 10.2) 251
Mean, geometric, distribution of 246—246
Mean, geometric, less than arithmetic mean 33—34
Mean, harmonic 32
Mean, harmonic, less than arithmetic and geometric means 33—34
Mean, in binomial, (Example 10.8) 243
Mean, in Poisson distribution, (Example 10.9) 243
Mean, in rectangular samples (Examples 10.7 and 10.12) 240—242 244
Mean, in Type III distribution (Example 10.11) 244
Mean, properties of 32
Mean, relation with median and mode 35 46
Mean, square contingency 319
Mean, standard error of 224
Mean, values 84
Mean, values in sampling problems 254—256
Measures of location, dispersion and, skewness 29—48 81—82
Median 34
Median, relation with mean and mode 35 46
Median, standard error of (Example 9.7) 213 225
Mehler, G., refs., expansion in tetrachoric series 363
Mendelian law, test of, as sampling of attributes 197—198
Mendelian law, test of, as sampling of attributes in pea breeding, (Example 12.2) 299
Mercer, W., data from, (Table 1.18) 23
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