THEORY OF STATISTICS. 
Interpolating in the table of areas of the normal curve on 
p. 310, or taking the required figure directly from Table II. of 
Tables for Statisticians, we have: — 
Greater fraction of area for a deviation of ‘84 in 
the normal curve . . : . 7990 
Area in the tail . : : g 452005 
Area in both tails 401 
That is to say, the probability of getting a difference, of either 
sign, as great as or greater than that actually observed is "401, 
agreeing, within the accuracy of ‘the arithmetic, with the 
probability given by the x* method. 
The same result would again have been obtained had we worked 
from the columns instead of from the rows, and considered the 
difference between the proportions of white flowers for prickly and 
for smooth fruits respectively. 
Example ii.—(Data from ref. 6 of Chapter III, Table XIV.) 
The following table shows the result of inoculation against cholera 
on a certain tea estate :— 
Not-attacked. Attacked. Total. 
Inoculated . Wie Be 2k 
: AL 9 200 
Not-inoculated 2943 Sr 
Total . : 2 ‘ 3 
As in the last example, the independence-frequencies have been 
given below the numbers observed. The value of 8 is 3:3, and 
1 1 1 EB) 
2 =(3" A B — ee —— = i 
X= rr + 53 mars 51) ~ 32 
From the table on p. 386 P is “0706. 
Working from the proportions attacked, we can arrive at the 
same result. 
Proportion attacked amongst inoculated . . 01147 
> ys i not-inoculated . ‘03000 
Difference . 01853 
The standard error of the difference is 
Fos 
98098 x 01902( 1 200) 01025. 
\ = 36 7300 ? 
382 
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1a 
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