Advertisement

Effect of a Single Nonzero Open Covariance on the Simple Closure Test

  • Felix Chayes
Chapter
Part of the Computer Applications in the Earth Sciences book series

Abstract

In small samples the simple closure test is markedly, and rather disappointingly, insensitive to a nonzero open covariance if the number of variables, m, is small. Only trivial results will be obtained if m < 4. If m = 4 but one of the open variances is small relative to the others, the situation is little changed. Even if open variances do not differ greatly in size, or are homogeneous, there will be a complementary relationship between sij and skℓ if m = 4, so that if rij is incompatible with ρij, rkℓ may be incompatible with ρkℓ. Interactions weaken rapidly with increase in m. Experimental evidence reviewed suggests that if m ≥ 8 the test detects a single fairly strong nonzero open covariance with remarkable reliability, provided rather large samples (N > 30) are used. The probability that the null hypothesis will be rejected for the wrong reason, i.e., because the test points to nonrandom association between open variables known to be uncorrelated, is large if m is small but decreases rapidly with increase in m. Except when the open variances are homogeneous, however, it seems to be materially greater than expected even if m = 10, the largest value used in the work reported here.

Keywords

Open Variance Open Parent Variance Partition Sample Correlation Inal Variance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Chayes, F., and Kruskal, W., 1966, An approximate statistical test for correlations between proportions: Jour. Geology, v$174, no. 5, pt. 2, p. 692–702.Google Scholar
  2. Chayes, F., and Kruskal, W., 1970, An approximate statistical test for correlations between proportions: Some corrections: Jour. Geology, v. 78, no. 3, p. 380.CrossRefGoogle Scholar
  3. Miesch, A. T., 1969, The constant sum problem in geochemistry, in Computer applications in the earth sciences: Plenum Press, New York, p. 161–176.Google Scholar

Copyright information

© Plenum Press, New York 1970

Authors and Affiliations

  • Felix Chayes
    • 1
  1. 1.Carnegie Institution of WashingtonUSA

Personalised recommendations