JOURNAL OF ECONOMIC ENTOMOLOGY 
190 
[Vol. 17 
while Peters formula gives results sometimes lower than the Gaussian 
but generally higher than those of the Bessel formula. 
Table 4 shows the difference of the means of the several plats to¬ 
gether with the probable errors of the differences, using the Gaussian, 
Bessel and Peters probable errors. It should be noted that a number of 
plat differences show significance when judged by the Gaussian and 
Bessel errors, altho five differences in each series lack odds of 30 to 1. 
When compared by means of Peter’s probable errors, seven differences 
are not significant. Of the Bessel and Peters formulae, the writer 
prefers the former (i. e., when the number of observations is less than 
16) because it shows greater consistancy. However, the data should be 
tested by both formulae and, if a difference tested by either formula shows 
odds of less than 30 to 1, the results should be accepted with caution. 
The results shown in Table 4 point to the conclusion that, while the 
experiment is indicative that increased amounts of arsenate of lead give 
better control of the codling moth, it lacks much of proving the point. 
The Probable Error of a Standard Deviation of a Small Number 
of Observations 
Since the probable error of a standard deviation may be calculated 
from the probable error of the mean of the same observations by dividing 
the latter by \/2, it follows that a simple method of computing the 
probable error of the standard deviation, when the number of observa¬ 
tions is 15 or less, is to calculate the probable error of the mean by either 
Bessel or Peter’s formula and divide this number by y/2. The values of 
the probable errors of the standard deviations given in Table 2 were 
secured in this manner, using the formula of Bessel. 
The Influence of Numbers on the Confidence That Can be 
Placed in the Data of an Experiment 
To give an idea of the number of trees per plat required to secure 
chances of 30 to 1 in this experiment, a few additional calculations have 
been added. Assuming that the means and standard deviations of all 
the plats remained the same but that 16 trees were used in each plat, 
would the results have been significant? With 16 trees per plat the 
Gaussian formula would be reasonably safe. The results are set forth 
in Table 5. It will be noted that, with one exception, the twelve com¬ 
parisons show significant differences. These figures strongly indicate 
that, in the writers experiments, at least 16 trees should have been used 
