6 
BULLETIN 1468, U. S. DEPARTMENT OP AGRICULTURE 
where d= difference, E d = probable error of the difference. N= num- 
ber of ears, and ^ d =weighted mean difference= ^d-£r~ 2 2-g- 2 - 
In all populations of 20 or less, the standard deviation and prob- 
able errors of the mean have been increased by using the correction 
of Pearson (15) for the standard deviation of small numbers. 
In applying this correction in the calculation of probable errors 
Table 1 was found a convenience._ This table was prepared by 
dividing the values of xi = 0.67449/ -yjn of Pearson's tables by the con- 
stants given for the correction of small samples. In use, the ob- 
served standard deviation is multiplied by ^y-> the value opposite 
the number of individuals in the population. 
Table 1 - 
-Factors for converting standard deviations (o-) of small populations 
into prooaole errors 
Number 
Number 
XI 
2/<r 
Number 
XI 
4 
0. 42266 
.35880 
. 31702 
. 28702 
.26417 
. 24601 
10 
0. 23116 
. 21868 
.20805 
.19880 
.19069 
. 18351 
16 
0. 17707 
5 
11 
17 
. 17128 
6 
12 
18 
. 16602 
7 
13 
19 
. 16120 
8 
14. 
20 
. 15679 
9 
15.. 
In comparing the variability of two or more populations it is 
customary to make use of the coefficient of variability. The coef- 
ficient of variability is the standard deviation expressed as a per- 
centage of the mean. When direct physical measurements are 
involved the use of this constant is desirable, since it corrects for 
the change in standard deviation that follows a change in absolute 
magnitude of the measurements. The coefficient of variability is 
of doubtful value, however, when applied to ratios such as rate of 
crossing over or Mendelian percentages. In series of ratios there 
usually is a high negative correlation between the mean and the 
coefficient of variability which can mean only that the coefficient 
of variability is influenced unduly by the magnitude of the mean. 5 
Examples of this relationship may be seen in Tables 3 and 5. On 
the other hand, it is in the nature of ratios to show a decreasing 
variability as the mean ratio departs from 0.5, or 50 per cent. This 
follows, of course, from the fact that the range of ratios is limited 
between and 1. 
The standard deviation of a ratio is Vpq, where p=zthe number 
in one class divided by the total number and q=l—p. The standard 
deviati on of a series of ratios each based on the same number, n, is 
Vpq/n. 
B Gowen (7) has calculated the coefficient of variability of the observed percentages of 
double crossing over in the third chromosome of Drosopliila and concludes that the varia- 
bility in double crossing over is markedly higher than in single crossing over. It would 
appear that the large coefficients in the double-crossover ratio are a direct consequence of 
the very low mean percentages. The observed standard deviations are actually smaller 
than in the single crossing over, but corrected to 50 per cent, the variability ih the two 
groups is of the same order, as would be expected from the close relation existing between 
the two processes. 
