14 
CIRCULAR 816, U. S. DEPARTMENT OF AGRICULTURE 
instead of 12, have been tested. Approximate best combinations for these 
conditions and estimated standard errors have been worked out and are 
presented in table 9. 
Table 9. —Estimated best combinations for field sampling to determine 
grasshopper egg-pod distribution, with limited total cost, in north-central 
M ontana 
County 
Variance 
Best combinations and resulting standard 
error per square foot 
Be¬ 
tween 
fields 
C v f ) 
Within 
helds 
(V w ) 
12-Hour total 
16-hour total, 
(3 minutes 
per unit) 
4 minutes 
per unit 
3 minutes 
per unit 
Blaine. 
0.06 
0.38 
17 X10 
2 0.24 
18 Xll 
2 0.22 
HO Xll 
2 0.20 
Cascade. 
.05 
.42 
7 Xll 
.23 
7 X 13 
.21 
10 X 13 
.18 
Chouteau. 
.05 
.34 
7 X 10 
.22 
8 X 12 
.20 
10 X 12 
.18 
Fergus. 
.02 
.31 
6X15 
.17 
6X18 
.16 
8X18 
.14 
Hill. 
.06 
.44 
7 X 10 
.24 
8 X 12 
22 
10 X 12 
.20 
Judith Basin.... 
.00 + 
.06 
5X17 
.07 
6 X 20 
!06 
8 X 20 
.05 
Liberty. 
.02 
.20 
7X12 
.15 
7X14 
.14 
9X14 
.12 
Pondera. 
.02 
.40 
5 X 17 
.19 
6 X 20 
.16 
8 X 20 
.14 
Teton. 
.08 
.62 
7 Xll 
.28 
8 X 12 
.26 
10 X 12 
.23 
Toole. 
.05 
.21 
8X8 
.20 
8X9 
.19 
11X9 
.16 
l n (number of fields) X k (number of J+square-foot units per field), 
standard error per square foot for the combinations. 
In the general survey in north-central Montana a frequent combination 
is 7 or 8 fields per county and 10 units (5 square feet) per field. This is 
seen (table 9) to be a fairly efficient combination when cost is considered. 
With low population and small differences among fields, as in Fergus 
and Judith Basin Counties, Mont., the taking of more unit samples per 
field from fewer fields would seem to be practicable and economical. With 
higher populations and great between-held variation, the sampling of a 
larger number of fields with fewer within-held units would be better. In 
any event, it is necessary to sample a fairly large number of helds to avoid 
risk of missing altogether some important local infestation. 
DISCUSSION 
The hndings from these studies of egg-pod populations may be briefly 
summarized as follows: Variation between helds is dehnitely higher than 
that within helds. Variation between units within helds does not follow 
a dehnite location pattern. Although this variation is such as to make 
advisable the taking of unit samples from several well-separated locations 
in a held, little is gained by taking more than hve samples. Randomness 
is not needed within helds, but there should be freedom from personal 
choice. The reduction of area per unit from 1 square foot to square 
foot causes marked loss in precision unless the number is nearly doubled. 
Margins are higher and more variable in population than helds, but need 
not receive much consideration because of their comparatively small area. 
