
The same data provided the information for Table 3, which gives 
figures by flyways instead of by regions. The latter grouping per- 
riits more accurate statistical analysis. Figures for all four fly- 
ways were subjected to the null hypothesis and it was found that no 
significant change in population from 1955 to 1956 was indicated in 
any flyway or for the country as a whole. 
Appraisal of Sample Size. 
In order to anvraise the accuracy of the present methods and 
to plan intelligently for the type and amount of coverage that is 
required to give the information we need in the future, several 
statistical tests have been applied to the data obtained through 
mid-winter counts and Christmas season counts. 
Since the data are not normally distributed, but highly skewed, 
a logarithmic transformation was determined to be proper. Since the 
logarithm of zero does not exist, it was necessary to add a constant 
fivure to each observation papore making the transformation. The 
nunber 1 was selected arbitrarily, as this also eliminated the neces- 
sity of using any negative logarithms. The coefficient of variation 
"gt" was conmuted by analysis of variance for each flyway and for the 
country as a whole, for both sets of data: the Mid-winter Count and 
the Christmas Season Count. Then the sample size needed to detect 
chanzes in pooulation of snecified amounts was obtained by the formula 
peer 
C | 
n= p@ , where t is the number of standard errors for a 95 percent 
orobability of occurrence (roughly 2, but varying according to the 
size of each samole), and p is the percent of sampling error allowed 
(or the amount of change that the population must exceed in order 
that the change can be detected). 
Table shows the number of trips (computed on the basis. of 1955 
and 1956 fisures ) necessary in each flyway and for the entire country 
in order to detect population changes exceeding certain percentages. 
The underscored numbers show the category into which the 1955-56 ob- 
servations fall, giving an approximation of amount of population 
change that could be detected in each flyway by each set of data. 
Tt is acknowledged that neither set of data has been set up on 
a random basis, thus violating a cardinal assumption on which statis- 
tical treatment is based. Yurthermore, the only uniformity in cover- 
aze is through the nresentation of all data in terms if birds ner 
unit time of coverage and the insistance that each area be covered 
as uniformly as nossible from year to year. It is believed that with- 
in areas of low snipe density (which would include nearly all parts 
of the country except California and the Gulf Coast area) the errors 
resulting from lack of random distribution and identical coverage are 
60 
