8 CIRCULAR 816, U. S. DEPARTMENT OF AGRICULTURE 
the means given in the columns “All fields and margins and Fields 
other than grain and their margins.” It may be seen that the popula¬ 
tions in field margins ran consistently higher than did those in the fields; 
however, the weighted means for both fields and margins were only 
slightly greater than those for the fields. A comparison of the weighted 
means for fields and margins with the means for the grain-stubble fields 
alone shows that the two groups of figures are close together. Possibly 
the most critical comparison is that of the average populations in small- 
grain stubble with those in the fields other than small grain and their 
margins, given in the last two columns. These sets of figures, although 
somewhat farther apart, still are close enough together to allow the grain- 
field figures to serve as a fairly reliable estimate of the general population. 
As a rule, grainfield populations appear the lighter. Standard errors of 
weighted averages are calculated as shown by Snedecor. 5 
Although these data substantiate the theory that the populations in 
grain stubble are a reliable index of the general population, there are 
reasons why it would not be advisable to sample grain stubble only. In 
the first place, small-grain fields, which comprise about 80 percent of the 
farmed acreage in the northern Great Plains, represent a preponderance 
of the agricultural area; therefore a general survey of this region, with 
stops prorated among the different habitats, would automatically be made 
up largely of small-grain fields. In the second place, the inclusion of the 
20 percent of nongrain fields and field margins would provide for explora¬ 
tory sampling to locate concentrations that otherwise might not be 
discovered. 
SAMPLING AND SURVEY METHODS 
In studying survey methods, the general nature of the population 
studied must be considered. If egg-pod distribution were entirely random, 
it would conform to the Poisson series, 6 and samples would reflect this 
distribution. In practice, a departure from the random or Poisson condi¬ 
tion occurs, population being “bunched,” and this departure is greater 
in dense infestations. In many sparse infestations the Poisson is nearly 
realized. In dense infestations variation is absolutely greater and pro¬ 
portionally less than in light ones. 
The nearness to the Poisson, or random, distribution can be judged by 
the variance. In a true Poisson series the variance is equal to the mean. 
In the typical “bunched” condition the variance becomes greater than 
the mean. Under field conditions it is practically never found to be less 
than that of the Poisson. For this reason a greater degree of precision 
than that limited by the total number of sample units and a variance 
equal to the mean cannot be expected. An example may be drawn from 
the analysis of variance of the South Dakota data (table 5). In this 
rather sparse infestation the mean was 0.18, the variance between adja¬ 
cent units was 0.20, and that between units well separated in the field 
was 0.26. 
5 See p. 3, footnote 4, (ch. 17). 
6 The Poisson series is explained by Snedecor’s text (see p. 3, footnote 4). It is 
based on simple probability in population problems such as this, of the numbers of 
units with no egg pods, and with one, two, or more. 
