GRASSHOPPER EGG-POD DISTRIBUTION 
11 
It will be recalled that 70 fields per county were sampled and the fields 
sampled were prorated among the different habitats according to their 
acreages Five pairs of K-square-foot samples were taken in each field 
and 10 1^-square-foot samples along each margin. The survey data 
were treated by using variance between fields within each county. The 
results are shown in table 8. 
Where the mean egg populations for the county ranged from 0.5 to 
0.8 pod per square foot, from 15 to 35 field stops were required in order 
to obtain county means within the prescribed standard error in a survey 
by counties. The average number of fields needed was 20. For county 
means of about 0.4 egg pod per square foot, from 9 to 27 fields, or an 
average of 15, were needed. In South Dakota, where the mean population 
was about 0.2 egg pod per square foot, 10 fields were adequate. For 
Judith Basin County, Mont., with a mean population of 0.1, only 3 
fields would have been necessary. Thus, it can be seen that the number 
of field stops needed per county for a survey on a county basis is largely 
affected by the population level. In low populations more than the cal¬ 
culated minimum just mentioned will be required for a representative 
survey. 
Variation between county populations was not marked, but with the 
large number of fields used (70 per county) it appeared as highly signifi¬ 
cant. Analyzing with field means as units, the variance between counties 
was 2.14 and between fields within counties 0.29. It was found, however, 
that the number of fields necessary to represent the district with the re¬ 
quired degree of precision was but a little greater than the number needed 
for a county having the same population level. 
Moderate numbers of fields per county tended to give an unsatisfactory 
standard error- for the county, and a standard error lower than needed 
for the mean of a group of similar counties. Less than 30 fields would 
have been required to give a standard error of 0.125 in the 10-county 
district considered (table 8); whereas for county units they total 182, and 
more would be required for representativeness in one or two of the 
counties. It is thus indicated that considerable economy might be effected 
by surveys of homogeneous groups of counties, rather than of individual 
counties as units. 
Since the number of stops required for a given standard error increases 
with the density of population, a procedure with some elasticity in number 
of fields would seem desirable. A given minimum (say 8 or 10) sufficient to 
provide representativeness might be surveyed. If the standard deviation 
were calculated among the first 10, the number required for the desired 
standard error (s x ) of the mean could be tentatively determined by solving 
the well-known equation s x = s V n in which s equals standard deviation 
among field means and n equals the number of fields. 
Distribution of Stops Within a County or District 
The field stops are the real sample units and their distribution is of 
considerable importance. To obtain complete randomness of distribution 
is not practical. In a statistical sense randomness is used in order to give 
every unit in a population a chance to be represented in the sample. 
Applications of error formulas in a strict sense are based on this concept. 
