By Student 
21 
table for ten experiment we find by interpolating between '8697 and '91 61 that '44 
corresponds to "8873, or the odds are '887 to "llS that the mean is positive. 
That is about 8 to 1 and would correspond in the normal curve to about 
1"8 times the probable error. It is then very likely that 1 gives an increase of 
sleep, but would occasion no surprise if the results were reversed by further 
experiment.?. 
If now we consider the chance tliat 2 is actually a soporific we have the mean 
2'33 
increase of sleep = j^^^ or 1'23 times the s.D. From the table the probability 
corresponding to this is "9974, i.e. the odds are nearly 400 to 1 that such is the 
case. This corresponds to about 4'15 times the probable error in the normal 
curve. But I take it the real point of the authors was that 2 is better than 1. 
This we must test by making a new series, subtracting 1 from 2. The mean 
value of this series is + 1'58 while the S.D. is 1"17, the mean value being + 1"35 
times the s.D. From the table the probability is ■9985 or the odds are about 66G 
to 1 that 2 is the better soporific. The low value of the S.D. is probably due to 
the different drugs reacting similarly on the same patient, so that there is corre- 
lation between the results. 
Of course odds of this kind make it altnost certain that 2 is the better soporific, 
and in practical life such a high probability is in most matters considered as 
a certainty. 
Illustration II. Cases where the tables will be useful are not uncommon in 
agricultural work, and they would be more numerous if the advantages of being 
able to apply statistical reasoning were borne in mind when planning the experi- 
ments. I take the following instances from the accounts of the Woburn farming 
experiments published yearly by Dr Voelcker in the Journal of the Agricultui'al 
Society. 
A short series of pot culture experiments were conducted in order to deter- 
mine the causes which lead to the production of Hard (glutinous) wheat or Soft 
(starchy) wheat. In three successive years a bulk of seed corn of one variety was 
picked over by hand and two samples were selected, one consisting of " hard " 
grains and the other of " soft." Some of each of these were planted in both heavy 
and light soil and the resulting crops were weighed and examined for hard and 
soft corn. 
The conclusion drawn was that the effect of selecting the seed was negligible 
compared with the influence of the soil. 
This conclusion was thoroughly justified, the heavy soil producing in each case 
nearly 100 per cent, of hard corn, but still the effect of selecting the seed could 
just be ti'aced in each year. 
But a curious point, to which Dr Voelcker draws attention in the 2nd year's 
report, is that the soft seeds produced the higher yield of both corn and straw. In 
