About This Item

Share This Item

The AAPG/Datapages Combined Publications Database

AAPG Bulletin


Volume: 47 (1963)

Issue: 2. (February)

First Page: 355

Last Page: 355

Title: Bias Factors in Loose-Grain Data: ABSTRACT

Author(s): Mark A. Dixon

Article Type: Meeting abstract


In loose-grain studies, sampling of grains by point-count or other conventional methods is never equivalent to sampling of the sediment by volume. This causes severe difficulties in comparison of Recent sediments, in which loose-grain data are frequently used, with older sediments, in which thin-section or chemical data are used. Even sieve data are not directly comparable. Correction of loose-grain data to a "volumetric" basis is surprisingly complex and uncertain.

Where a sediment must be described in terms of its volume, all loose-grain point-count data are systematically biased in favor of the finest grains present on any area. Given equal volumes, the frequency of encounter of any grain-size category is cut in half every time the grain diameter is doubled. This can be demonstrated with assorted spheres, by chopping a potato into successively smaller cubes, or by simple algebraic derivations. Shape factors may contribute an additional bias which is not considered here.

After transformation of the raw data to "volumetric" ratios by multiplication, a certain amount of bias is still present, or "uncorrectible," unless every grain in a sediment is counted. In statistical terms.


(where ยต is the un-biased,"parent," "volumetric" model mean)

The "uncorrectible" portion of the original bias is a function of: (1) sorting or "Variance"; (2) the number of points counted, or "sample size"; and (3) Gaussian normality of the un-biased natural property with respect to volume. Bias (1) increases dramatically as the sorting gets poorer, (2) decreases asymptotically toward zero as the number of points is increased, and (3) becomes highly erratic for properties which are not "normal." The effect of this bias on polymodal properties is catastrophic.

Estimation of the "uncorrectible" portion of the bias, from the behavior of mathematical models, is a haphazard procedure at best. Only a few models have been worked out, due to the number of calculations which become necessary. In the model shown here, the "uncorrectible" bias is more than half of the total bias.

Until good methods of bias-correction can be developed, statistical comparisons of loose-grain properties must be considered either: (1) unrelated to sediment volumes, or (2) confounded with sorting and (or) normality. Hence, comparisons of size, and any property dependent upon ("interacting with" or "correlated with") size, must be accompanied by tests demonstrating complete uniformity of sorting ("Homogeneity of Variance", at the "point" or "error" level). Where this is impossible, interpretation of the test results becomes frustrating and virtually futile.

End_of_Article - Last_Page 355------------

Copyright 1997 American Association of Petroleum Geologists