VARIABILITY IN LINKAGE OF CHARACTERS OF MAIZE 5 
(observed measures) depends upon the choice of a method for calcu- 
lating the probable errors. Throughout the present bulletin the 
attempt is made to apply to the observed means and differences the 
method that would be most critical. 
In general, three formulae have been used in dealing with the prob- 
able errors of ratios. 
For the probable error of percentages on individual ears use is 
made of the familiar formula 
0.67449 
where w=the number of seeds, /?=the percentage, and #=100 minus 
the percentage of the character concerned. 
In this operation the calculations are greatly facilitated by the use 
of the tables of Miner (12) for the value of pq and of Pearson (14) 
for the values of 0. 67449/ -yfn. 
For the probable error of the mean percentage or rate of crossing 
over in a progeny or group of individuals this formula gives too 
small a value except in those cases where there is no individual 
diversity. If the crossover values of the individual ears are not 
chance departures from a common mean, the reliability of the general 
mean is influenced by the number of ears involved. 
For these cases the observed percentages of the individual ears 
have been treated as an array for which the standard deviation was 
calculated. Since the ears vary in size, the squared departures from 
the mean were weighted by the number of seeds on the ear. 
For the probable error of the mean percentage, use is made of 
the formula 
0.67449 0.67449 /^ ~ 
where £>=the percentage, w— the number of seeds, J/ P =mean per- 
centage, and N=the number of ears. 
Where the problem involved differences between pairs of ears, 
still a third method was used. For these cases the differences be- 
tween the paired ears were taken as an array for which the stand- 
ard deviation was caiuculated. 
Since the differences were between ears of various sizes, it was 
essential to employ a weighting factor, but the differences may not 
be weighted by the number of seeds, because the ears of a pair vary in 
size. Thus a given difference based on two ears, one of 100 seeds 
and the other of 800, calculated by the mean number of seeds, would 
have the same weight as a difference between two ears each of 450 
seeds, whereas the significance of the latter difference would be very 
much greater. 
Accordingly, recourse is had to weighting the differences by the 
reciprocal of the square of the probable error of the difference where 
the errors of each ear were calculated by formula 1. 
The formula for the probable error of a mean difference is 
D77 0.67449 0.67449 / . 1 / I 771 
