Comment on: Despotism and Differential Reproduction by L.L. Betzig

Linda Mealey and Robert K. Young Department of Psychology, University of Texas, Austin, Texas

A recent article is criticized on statistical grounds. These problems are not restricted to the article in point, but are common to studies utilizing preexisting data such as that of the HRAF. Specific suggestions are presented, as well as a comment on the importance of statistical in-

tegrity for sociobiology.

Key Words: Statistics; Demography; Polygamy.

In a recent issue of Ethology and Sociobiology, L.L. Betzig presented an interesting cross-cul- tural analysis of the relationship between several socio-political variables and reproductive suc- cess. As one of us (LM) is presently analyzing the relationship between some of these same variables in a single, well-documented society (early 19th century Mormon Utah), we found the article particularly timely and encouraging. At the same time, we feel that there are some short- comings in the statistical analysis which require serious attention. Comparison of cross-cultural data which have been collected by a variety of researchers for a variety of purposes is difficult, but for the time being, that is all that is available to many of us. This lack of control over meth- odology makes the appropriate use of statistics all the more essential.

There are several problems with the Betzig analysis. First, Betzig computes Pearson Prod- uct Moment correlations on data which clearly do not meet the assumptions of the test. In some cases the ordinal scale data used is not normally distributed while in others only two values are present. This could have a profound impact on the sampling distributions of the correlation

Revised April 17, 1984. Address reprint requests to: Linda Me&y, Department

of Psychology, University of Texas, Austin, TX 78712.

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coefficients and make the use of a standard cor- relation table inappropriate. There are other problems.

It would be impossible, for example, for the leader of a society with a population of 50 or less (a rating of 1 on the population scale) to have more than 100 wives (a rating of 4 on the poly- gyny scale). Consideration of demographic var- iables such as age and sex make several other combinations essentially impossible. The effect of all this is to build a positive correlation into the population size-polygyny relationship and make the p value derived from a null hypothesis of zero invalid. The correlations between group size and complexity of hierarchical organization and degree of polygamy are likewise flawed.

To test the effect of this bias we selected ran- dom pairs (i.e., the correlation in the population is zero) from restricted populations such as de- scribed above. In our case, we required that the 1 to 4 rating of one variable be equal to or less than the 1 to 4 rating on the second variable. Computing 1000 correlations each for sample sizes of 24, 15, and 8, respectively, gives mean correlations of about SO and three distributions of sample correlations from which the 5% points for the sample distributions can be estimated for such a population of correlations. For N = 24, the cutting point was .749 (i.e., correlations above .749 were significant at the .05 level), for N = 15, the .05 point was .793 and for N = 8, the .05 point was .911. These are, of course, con- siderably different from those found in a table of Pearson correlations (.404, .514, and .707 re- spectively), and made use of by Betzig.

Given the constraints of HRAF data, these problems probably cannot be remedied by changing the scaling of variables; they can how- ever, be overcome by choice of 1) an appropriate

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76 Linda Mealey and Robert K. Young

statistic. and 2) an appropriate null model. We suggest that Betzig reassess the reported cor- relations, using these or similarly obtained cutoff values.

There are other problems with the paper such as the use of “Gee whiz graphs” as popularized by Darrell Huff (1954). Betzig uses the diameter of a dot to represent the size of a data set while the eye of the reader uses the area of the dot. Thus, a population represented by a dot with twice the diameter of another dot would be seen as four times larger. In addition, Betzig rates the number of wives of the leader, in eight societies with no hierarchy. But these seem minor in com- parison to the problems raised above. While the arguments Betzig makes may have value, we simply cannot evaluate them from the data pre- sented.

The best argument that human sociobiology does not simply consist of a compilation of “‘just- so” stories, is repeated positive empirical find- ings. And for that argument to be sound, our statistics must be impeccable. We hope that we can find useful ways to manage the valuable but unwieldy data provided by the HRAF and other data compilations. We need to.

References

Betzig, L.L. Despotism and differential reproduction:

A cross-cultural correlation of conflict, asymmetry,

hierarchy, and degree of polygyny. Ethology and

Sociobiology 3: 209-221 (1982).

Huff, D. How to Lie with Statistics. New York: W. W. Norton & Company. 1954.