April, ’24] hartzell: interpretation of codling moth data 189 
mean. Two formulae commonly used are Bessel’s and Peter’s Approx- 
HI > 
a 
imation Formula. Bessie’s Formula is E m = ± .6745 —-and Peter’s 
Vn-1 
2(d) 
Approximation Formula is E .8543 —7= in which the deviations of the 
nvn-l 
observations from the mean (d) are added, paying no regard to the signs- 
In Table 3 is set forth the means of the several plats together with the 
probable errors of the means calculated by the several formulae. It 
will be noted that the probable errors computed by the Gaussian for¬ 
mula are generally the lowest, the Bessel formula giving higher values, 
Table 3. Means and Probable Errors Calculated by Different Methods, 
Codling Moth Data 
Probable Errors of Mean 
Plat 
Mean 
Gaussian Bessel 
Total Infested Apples 
Peters 
Check 
993.00 
±77.74 
±109.94 
±137.79 
1 
503.75 
±.54.01 
± 62.37 
± 65.77 
2 
763.00 
±67.62 
± 72.29 
± 62.25 
3 
381.29 
±25.56 
Worthless Apples 
± 27.62 
± 26.23 
Check 
489.00 
±51.51 
± 72.84 
± 91.30 
1 
199.00 
±15.76 
± 18.20 
± 19.40 
2 
158.00 
±15.89 
± 16.99 
± 15.58 
3 
102.86 
± 9.04 
= 9.76 
± 9.92 
'able 4. Comparisons of Plats Using Gausian 
Errors 
, Bessel and Peters Probable 
Plats 
Differ¬ 
Probable Errors of Difference Difference divided by 
compared 
ences 
Gaussian Bessel Peters 
Total Infested Apples 
Gaus¬ 
sian 
Bessel Peters 
Check & 1 
489.25 
±994,41 ±126.40 
±152.68 
5.18 
3.87 3.20 
Check & 2 
230.00 
±102.81 ±131.58 
±154.21 
2.24 
1.75 1.49 
Check & 3 
611.71 
± 81.55 ±113.36 
±140.26 
7.50 
5.40 4.36 
1 and 2 
259.25 
± 86.54 ± 95.48 
± 95.51 
3.00 
3.09 3.09 
1 and 3 
122.46 
± 59.75 ± 68.21 
± 70.81 
2.05 
1.79 1.73 
2 and 3 
381.71 
± 72.29 ± 77.39 
Worthless Apples 
± 74.05 
5.24 
4.93 5.15 
Check & 1 
290.00 
± 53.87 ± 75.08 
± 93.34 
5.38 
3.86 3.11 
Check & 2 
331.00 
± 53.91 ± 74.80 
± 92.62 
6.14 
4.43 3.57 
Check & 3 
386.14 
± 52.30 ± 73.50 
± 91.84 
7.38 
5.25 4.20 
1 and 2 
41.00 
± 22.38 ± 23.68 
±24.88 
1.83 
1.73 1.65 
1 and 3 
96.14 
± 18.17 ± 20.65 
± 21.79 
5.29 
4.66 4.41 
2 and 3 
55.14 
± 18.28 ± 19.59 
± 18.47 
3.02 
2.81 2.99 
