Sampling error as a misleading artifact in “key factor analysis”

Abstract

SummaryThe influences of sampling error in key factor analysis are investigated statistically. The error involved in the data distorts the results in various misleading ways. In the course of detecting key factors by correlation analysis, the distortion arises in the following two ways: (1) the contributions made by the first and the last components of population trend index (log I or K) to the total variation are overrated as compared with the others; and (2) spurious negative correlation arises between successive two components. The risk of misinterpretation due to such disturbance is usually increased further if the error is concentrated on any particular developmental stages. In the tests to detect density‐dependence by using regression analysis, the error consistently acts as if it were a density‐dependent factor: under the effect of sampling error, the slope b for the regression of log Ni+1 on log Ni, for example, is expected to become<1 even where there is no density‐dependent factor at all. A set of formulas are derived which may serve to check and correct these misleading distortions caused by the error. It is also shown that such undesirable influences can be avoided, at least to a considerable extent, if appropriate sampling plans are adopted for the study. The validity of key factor analysis is discussed in reference to this and some related problems.