THEORY OF STATISTICS.
199, fluctuation method, 199-201. Earnings of agricultural labourrefs.,
 208-209, 391-392, 360, 397 ; ers, pauperism and out-relief, 177—
elementary methods for cases of 181 ; constants, (qu. 2) 189, 239 ;
non-linear regression, 201-202; correlation-ratios, 207 ; treatment
rough methods for estimating co- by partial correlation, 239-241 ;
efficient, 202-204 ; correlation- geometrical representation, 245-ratio,
 204-207, 252; effect of 247.
errors of observation on the co- Old-age pauperism and outefficient,
 213-214; correlation relief, 182-185.
between indices, 215-216; co- Changes in pauperism, outefficient
 for a fourfold table, relief, proportion of old and popudirect,
 216-217, on assumption of lation, 192-195; partial correlanormal
 correlation (Pearson’s co- tion, 241-245.
efficient) ( refs.), 40, 333, 390 ; for Lengths of mother- and
all possible pairs of NV values, 217 daughter-frond in Lemna minor,
218; correlation due to hetero- 185-187.
geneity of material, 218-219; Weather and crops, 196-197.
effect of adding uncorrelated pairs Movements of infantile and
to a given table, 219-220 ; appli- general mortality, 197-199.
cation to theory of weighted mean, Movements of marriage-rate and
221-223 ; correlation in theory of foreign trade, 199-201.
sampling, 271, 286-289, 342, 349—' Correlation, normal, 317-334; de-350
 ; standard error of coefficient, duction of expression for two
352. Refs., 188, 208-209, 225-226, variables, 318-319 ; constancy of
390, 391, 392. For Illustrations, standard-deviation of arrays and
Normal, Partial, Ratio, see below. linearity of regression, 319-320 ;
Correlation, Illustrations and Ex- contour lines, 320-321 ; normality
amples, correlation between :— of linear functions of two nor-Two
 diameters of a shell mally distributed variables, 321 ;
(Pecten), 158 ; constants (qu. 3), principal axes, 321-322; testing
189. for normality of correlation table
Ages of husband and wife, 159 ; for stature, 312-328 ; isotropy of
diagram, 173 ; constants (qu. 3), normal correlation table, 328-331 ;
189. outline of theory for any number
Statures of father and son, 160 ; of variables, 331-332 ; coefficient
diagrams, facing 166, 174 ; con- for a normal distribution grouped
stants (qu. 3), 189; correlation- to fourfold form round medians
ratios, 206-207 ; testing normality (Sheppard’s theorem), (qu. 4) 334 ;
of table, 322-328 ; diagram of dia- applications to theory of qualigonal
 distribution, 325; of con- tative observations (refs.), 333.
tour-lines fitted with ellipses of Refs., 332-333, 390, 391.
normal surface, 327. — partial, 229-253; the problem,
Fertility of mother and daugh- partial regressions and correlater,
 161, 195-196 ; diagram, 175 ; tions, 229-231 ; direct deduction,
constants (qu. 3), 189. 365-366 ; notation and defini-Discount
 rates and percentage tions, 233-234; normal equaof
 reserves on deposits, 162; tions, fundamental theorems on
diagram, facing 166. product-sums, 234-235; signi-Sex-ratio
 and numbers of births ficance of generalised regressions
in different districts, 163, 175; and correlations, 236 ; reduction
diagram, 176 ; constants (qu. 3), of standard-deviation, 236-237 ; of
189; correlation - ratios, 207 ; regression, 237-238; of correlastandard-deviations
 of arrays and tion, 238 ; arithmetical treatment,
comparison with theory of sam- 238-245; representation by a
pling (qu. 7) 275 and (qu. 1) 289. model, 245-247 ; coefficient of

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