Full text: An Introduction to the theory of statistics

Te THEORY OF STATISTICS. 
effect of the varying age at marriage must be estimated 
afterwards. 
10. But the correlation between (1) number of children of a 
woman and (2) number of children of her daughter will be further 
affected according as we include in the record all her available 
daughters or only one. Suppose, e.g., the number of children in 
the first generation is 5 (say the mother and her brothers and 
sisters), and that she has three daughters with 0, 2, and 4 
children respectively: are we to enter all three pairs (5, 0), 
(5, 2), (5, 4) in the correlation-table, or only one pair? If the 
latter, which pair? For theoretical simplicity the second process 
is distinctly the best (though it still further limits the available 
data). Ifit be adopted, some regular rule will have to be made 
for the selection of the daughter whose fertility shall be entered 
in the table, so as to avoid bias: the first daughter married 
for whom data are given, and who fulfils the conditions as to 
duration of marriage, may, for instance, be taken in every case. 
(For a much more detailed discussion of the problem, and the 
allied problems regarding the inheritance of fertility in the horse, 
the student is referred to the original.) 
11. Illustration iii. —The subject for investigation is the 
relation between the bulk of a crop (wheat and other cereals, 
turnips and other root crops, hay, etc.), and the weather. (Cf. 
Hooker, ref. 7.) 
Produce-statistics for the more important crops of Great 
Britain have been issued by the Board of Agriculture since 
1885: the figures are based on estimates of the yield furnished 
by official local estimators all over the country. Estimates are 
published for separate counties and for groups of counties 
(divisions). But the climatic conditions vary so much over the 
United Kingdom that it is better to deal with a smaller area, 
more homogeneous from the meteorological standpoint. On the 
other hand, the area should not be too small; it should be large 
enough to present a representative variety of soil. The group 
of eastern counties, consisting of Lincoln, Hunts, Cambridge, 
Norfolk, Suffolk, Essex, Bedford, and Hertford, was selected as 
fulfilling these conditions. The group includes the county with 
the largest acreage of each of the ten crops investigated, with 
the single exception of permanent grass. 
12. The produce of a crop is dependent on the weather of 
a long preceding period, and it is naturally desired to find the 
influence of the weather at all successive stages during this 
period, and to determine, for each crop, which period of the 
year is of most critical importance as regards weather. It must 
be remembered, however, that the times of both sowing and 
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