Page:Biometrika - Volume 6, Issue 1.djvu/23

The average gain by the use of sulphate of potash was 15.25 cwt. and the S.D. 9 cwt., whence, if we want the odds that the conclusion given below is right, $z=1.7$ corresponding, when $n=4$, to $p=.9698$ or odds of 32:1; this is midway between the odds in the former example. Dr Voelcker says ‘It may now fairly be concluded that for the potato crop on light land 1 cwt. per acre of sulphate of potash is a better dressing than kainit.’

As an example of how the tables should be used with caution, I take the following pot culture experiments to test whether it made any difference whether large or small seeds were sown.

Illustration III. In 1899 and in 1903 “head corn” and “tail corn” were taken from the same bulks of barley and sown in pots. The yields in grammes were as follows:

	1899		1903
Large seed	13.9		7.3
Small seed	14.4		8.7
	+.5		+.6

The average gain is thus .55 and the S.D. .05, giving $z=11$. Now the table for $n=2$ is not given, but if we look up the angle whose tangent is 11 in Chambers’ tables,

$p={\frac {{\textrm {tan}}^{-1}11}{180^{\circ }}}+.5={\frac {84^{\circ }47'}{180^{\circ }}}+.5=.971$,

so that the odds are about 33:1 that small corn gives a better yield than large. These odds are those which would be laid, and laid rightly, by a man whose only knowledge of the matter was contained in the two experiments. Anyone conversant with pot culture would however know that the difference between the two results would generally be greater and would correspondingly moderate the certainty of his conclusion. In point of fact a large scale experiment confirmed the result, the small corn yielding about 15 per cent. more than the large.

I will conclude with an example which comes beyond the range of the tables, there being eleven experiments.

To test whether it is of advantage to kiln-dry barley seed before sowing, seven varieties of barley were sown (both kiln-dried and not kiln-dried) in 1899 and four in 1900; the results are given in the table.

It will be noticed that the kiln-dried seed gave on an average the larger yield of corn and straw, but that the quality was almost always inferior. At first sight this might be supposed to be due to superior germinating power in the kiln-dried seed, but my farming friends tell me that the effect of this would be that the kiln-dried seed would produce the better quality barley. Dr Voelcker draws the conclusion “In such seasons as 1899 and 1900 there is no particular advantage in kiln-drying before sowing.” Our examination completely justifies this and adds