### Abstract:

This study was initiated to determine the relative efficiency
of systematic, stratified and simple random sampling for crown area
and tree frequency estimation of five of the major forest types found
in the Pacific Northwest. Several of the more common methods of
estimating spatial distribution coefficients were evaluated. Finally
the effect of spatial distribution of trees in these forest types on the
relative efficiency of two-dimensional systematic sampling was
analyzed.
Crown maps of five 48-acre tracts of the following types were
made from large scale (1:2500) aerial photographs and photographically
enlarged to the scale of 1:624:
1.Typical ponderosa-pine of Eastern Oregon
2.Mixed species of Oregon’s Coastal type
3.Mixed pine stands of Northeastern Oregon
4.Even aged Douglas-fir stands common to the Pacific Northwest
5.Typical old growth Douglas-fir of the Pacific Northwest.
The basic data consisted of the location (by grid coordinates)
and size of each tree crown as obtained from crown maps. These
data were committed to the memory of the CDC 3300 computer and
the entire analyses executed through computer simulation techniques
as follows:
Exhaustive two-dimensional systematic sampling was taken
using one quarter acre sampling units, Sample mean variances
were computed for the three sampling schemes using analysis of
variance principles. Relative efficiency of systematic and stratified
sampling was also computed. The same parameters were also
estimated by variable plot sampling based on 24 points systematically
located at the middle 24 acre of each type. The same principles
were used to compute variances as close approximations.
Eight of the more common non-randomness measures were
compared. To evaluate these methods and obtain the required data
for examining the effect of spatial variation on relative efficiency of
systematic sampling, four new populations were generated from
each forest type. These newly computer generated populations were
sampled in the same way as for the original forest types. Spatial
distribution coefficients of these populations were also computed.
Multiple regression analysis was employed using stepwise
computer program to establish relationships between the relative
efficiency of systematic sampling and the coefficients of randomization.
Logarithmic transformation was used to satisfy equality of
variances in establishing regression equations.
The results of this study indicated that the relative efficiency
of two-dimensional systematic sampling may vary greatly depending
on the parameter being estimated. For tree frequency estimation
(a discrete variable) of the original forest types the gain in precision
of systematic sampling varied from 20 to 167 percent. In estimating
crown area (a continuous variable) systematic sampling was less
precise than simple random sampling on one forest type, while
yielding gains in precision ranging from 10 to 179 percent for the
other original forest types.
There were no significant differences in precision obtained by
the three sampling schemes for estimating both parameters when
applied to completely randomly dispersed populations. Systematic
sampling was less precise than both stratified and random sampling
when applied to uniformly spaced populations. The loss in precision
in this case ranged from 15 to about 79 percent.
Of the eight non-randomness measures (measures of spatial
distribution) the point method proved to be best. Grosenbaugh' s
Q-factor which is considered to be the most practical method was
rejected as being invalid. All original forest types were found to
be clustered.
Regression equations of relative efficiency on the coefficient
of randomization for crown area estimation of the five forest types
were mostly non-linear. Since these predicting models produced
low correlations and were obviously different from each other, no
attempt was made to establish a generalized model. Relative efficiency
of systematic sampling for tree frequency estimation was
highly correlated with the coefficient of randomization. Of the five
equations established, four were not significantly different from
each other, thus they were pooled and a generalized model developed
which turned out to be y = 1.402x with simple correlation coefficient
of r=0.81
where:
y = common log of relative efficiency of systematic sampling
x = common log of spatial distribution coefficient measured
by the point method.
Therefore, when an estimate of spatial distribution of trees
in a forest is known, the relative efficiency of systematic plot sampling can be predicted with a high degree of accuracy. Such
relationships could also be applied as adjustment factors to systematic
sampling variance when being treated as simple random
samples.