Page:Biometrika - Volume 6, Issue 1.djvu/24

“and the quality of the resulting barley is inferior though the yield may be greater.”

lbs. head corn per acre ​
Price of head corn in
shillings per quarter
​ cwts. straw per acre Value of crop per acre
in shillings^[*] ​
N. K. D.
​ K. D. Diff. N. K. D. K. D. Diff. N. K. D. K. D. Diff. N. K. D. K. D. Diff. ​ 1899 1903 2009 +106 261/2 261/2 0 191/4 25 +53/4 1401/2 152 +111/2 1935 1915 −020 280 261/2 −11/2 223/4 240 +11/4 1521/2 1450 −71/2 1910 2011 +101 291/2 281/2 −10 230 240 +10 1581/2 1610 +21/2 2496 2463 −033 300 290 −10 230 280 +5 2041/2 1991/2 −5 2108 2180 +072 271/2 270 −1/20 221/2 221/2 0 1620 1640 +2 1961 1925 −036 260 260 0 193/4 191/2 −1/40 1420 1391/2 −21/2 2060 2122 +062 290 260 −3 241/2 221/4 −21/4 1680 1550 −13 1900 1444 1482 +038 291/2 281/2 −10 151/2 160 +1/20 1180 1171/2 −1/2 1612 1542 −070 281/2 280 −1/2 180 171/4 −3/4 1281/2 1210 −71/2 1316 1443 +127 300 290 −10 141/4 153/4 +11/2 1091/2 1161/2 +7 1511 1535 +024 281/2 280 −1/20 170 171/4 +1/40 1200 1201/2 +1/2 ​ ​
Average
​ 1841.5 1875.2 +33.7 28.45 27.55 −.91 19.95 21.05 +1.10 145.82 144.68 +1.14 Standard
Deviation — — 63.1 — — .79 — — 2.25 — — 6.67 Standard
Deviation
÷√8 — — 22.3 — — .28 — — 0.80 — — 2.40

↑ * Straw being valued at 15s. per ton.

In this case I propose to use the approximation given by the normal curve with standard deviation ${\frac {s}{\sqrt {(n-3)}}}$ and therefore use Sheppard’s tables, looking up the difference divided by ${\frac {s}{\sqrt {8}}}$. The probability in the case of yield of corn per acre is given by looking up ${\frac {33.7}{22.3}}=1.51$ in Sheppard’s tables. This gives $p=.934$, or the odds are about 14:1 that kiln-dried corn gives the higher yield.

Similarly ${\frac {.91}{.28}}=3.25$, corresponding to $p=.9994$,^[1] so that the odds are very great that kiln-dried seed gives barley of a worse quality than seed which has not been kiln-dried.

Similarly it is about 11 to 1 that kiln-dried seed gives more straw and about 2:1 that the total value of the crop is less with kiln-dried seed.

1. As pointed out in Section V. the normal curve gives too large a value for $p$ when the probability is large. I find the true value in this case to be $p=.9976$. It matters little however to a conclusion of this kind whether the odds in its favour are 1,660:1 or merely 416:1.