INDEPENDENT MENDELIAN INHERITANCE 101 
sents the sum of all the terms of such aratio. This gives for the probable 
error H, of a given term N of a Mendelian ratio the value 
E, = £ 0.6745 ee stk 
nr 
In this formula n = the total number of individuals classified. 
The actual application of this formula may be illustrated by the use 
of data from East and Hayes givenin Table XI. The totals in this table 
give observed frequencies as shown in Table XVII. 
Taste XVII.—Goopness or Fir in a Menpetan ExperiIMENT 
Phenotypes | Observed 
| beet yes | Tacos! | E | Probability 
. zl tele 
Purple starchy.... 1,861 | 9.190 | 9 | +0.094 1:4.64 
Purple sweet...... 614 3.032 | 3 +0.074 1:1 
White starchy..... 548 | 2.706 3 +0.074 1:142.26 
White sweet....... 217) | tore 1 +0.046 | 1:2.57 
Totals.......... | 3,240 | 16.000 | | 
The results are expected to be in agreement with a 9:3:3:1 ratio; 
therefore these observed results are first reduced to the form of a ratio 
per 16 by dividing each term by 14 of the total number of individuals, 
or by —~ = 202.5. By this method the observed ratio in ‘Table 
XVII was calculated. 
To obtain the probable error for the purple starchy abe values are 
substituted in the above formula as follows: 
9(16 — 9) 
E, = + 0.6745 eee 
ee 3240 
+ 0.094 
The observed deviation 0.19 is approximately twice the value of the 
probable error. For practical purposes a deviation less than three or four 
times the probable error is not considered significant. A deviation of the 
above magnitude in comparison to the probable error occurs about once 
in four times. In Table XVII the values of the probable error have been 
calculated for all four of the terms of this ratio. One term lies considerably 
within the probable error and its probability has been put down as 1:1. 
This is not strictly correct but serves the purposes of these calculations. 
It will be noted that there is one serious deviation, that of the white 
starchy class which could occur only once in 142 times. This deviation 
is not serious enough, however, to lead us to reject the hypothesis of 
two factor differences for this case, but it may indicate that other dis- 
turbing forces are in operation in this experiment. 
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