SOCIAL AND ECONOMIC THEORY 
17 
to account for the changes, which hypotheses may rest on 
physical facts, i. e. sunspots and harvests ; or economic 
theories, i. e. credit control; or a combination of physical 
fact and economic theory, i. e. aggregate gold production 
and credit based thereon. 
In the second aspect, a theory exists, and a statistical 
inquiry is undertaken ad hoc to test it : 
(1) A new set of aggregated statistics is collected by 
public or private authorities to solve a problem, 
or (2) Samples are made on scientific lines for different 
places or for different times, 
or (8) Existing lines of statistics are put into juxtaposi- 
tion for the first time and correlation tested, 
or the ratio of variation ascertained. In other 
words, it may be ascertained that two series move 
sympathetically, and we wish to know the regu- 
larity and constancy of that sympathy. It is, for 
example, one thing to say that when set A of 
facts varies in one direction set B will vary 
in a specified direction in 95 per cent. of the cases ; 
it is another to determine that when one varies by 
10 per cent. from its own average, the other will 
vary 20 per cent. from its own average. 
In 1918 I made the first use in this country of the linear 
trend, fitted by the method of least squares, to eliminate 
the common time-growth element from various series of 
statistics which had different rates of growth, in order 
that the concomitant variations, free from such constant 
growth, could be correlated. In the Effect of Trade 
Fluctuations upon Profits ’,* I remarked 
‘ In our pre-war experience when monthly statistics 
of foreign trade were quoted or the bankers’ clearing 
house figures were referred to, all kinds of inferences 
were drawn for and against the political features of 
the day. If the “returns” were up by 10 per cent. 
on the previous year, it was held to be something 
for jubilation, if they were down, perhaps the tariff 
1 Journal of the Royal Statistical Society, 1918. 
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