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Causal Inferences, Closed Populations, and Measures of Association*

Published online by Cambridge University Press:  01 August 2014

Hubert M. Blalock
Hubert M. Blalock*
Affiliation:
University of North Carolina
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Extract

Two of the most important traditions of quantitative research in sociology and social psychology are those of survey research and laboratory or field experiments. In the former, the explicit objective is usually that of generalizing to some specific population, whereas in the latter it is more often that of stating relationships among variables. These two objectives are not thought to be incompatible in any fundamental sense, but nevertheless we lack a clear understanding of their interrelationship.

One of the most frequent objections to laboratory experiments turns on the question of generalizability, or what Campbell and Stanley refer to as “external validity.” In essence, this question seems to reduce to at least two related problems: (1) that of representativeness or typicality, and (2) the possibility of interaction effects that vary with experimental conditions. In the first case, the concern would seem to be with central tendency and dispersion of single variables, that is, whether the means and standard deviations of variables in the experimental situation are sufficiently close to those of some larger population. The second involves the question of possible disturbing influences introduced into the experimental setting that produce non-additive effects when combined with either the experimental variable or the premeasurement. These same variables may of course be operative in larger populations. But presumably they take on different numerical values, with the result that one would infer different relationships between major independent and dependent variables in the two kinds of research settings.

Type
Research Notes
Information
American Political Science Review , Volume 61 , Issue 1 , March 1967 , pp. 130 - 136
Copyright
Copyright © American Political Science Association 1967

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Footnotes

*

I am indebted to the National Science Foundation for support of this research.

References

1 See especially Campbell, Donald T. and Stanley, Julien S., “Experimental and Quasi-experimental Designs for Research on Teaching,” in Gage, N. L. (ed.), Handbook of Research on Teaching (Chicago: Rand McNally & Company, 1963), pp. 171–246.Google Scholar See also Kish, Leslie, “Some Statistical Problems in Research Design,” American Sociological Review, 24 (1959), pp. 328–338.CrossRefGoogle Scholar

2 For a systematic discussion of the handling of various interaction effects in experimental designs see Ross, John A. and Smith, Perry, “Experimental Designs of the Single-Stimulus, All-or-Nothing Type,” American Sociological Review, 30 (1965), pp. 68–80.CrossRefGoogle ScholarPubMed

3 See Wold, Herman and Jureen, Lars, Demand Analysis (New York: John Wiley & Sons, 1953), Ch. 2.Google Scholar

4 There will of course be numerous dynamic models all of which predict the same stability conditions. Ideally, theories should be formulated in dynamic terms in such a way that time enters in in an essential way (as in difference equations). The approach of “comparative statics” can then be used to study equilibrium conditions. For a very readable discussion of this question see Baumol, William J., Economic Dynamics (New York: The Macmillan Company, 1959).Google Scholar See also Samuelson, Paul A., The Foundations of Economic Analysis (Cambridge: Harvard University Press, 1947)Google Scholar; and Simon, Herbert A., Models of Man (New York: John Wiley & Sons, 1957), Chs. 6–8.Google Scholar

5 Of course somewhat less restrictive assumptions concerning the error terms might be used. Whatever set of assumptions are used, however, it would seem necessary to assume that the population is “closed” in the sense of meeting these assumptions.

6 Miller, Warren E. and Stokes, Donald E., “Constituency Influence in Congress,” this Review, 57 (1963), pp. 45–56.Google Scholar

7 Cnudde, Charles F. and McCrone, Donald J., “The Linkage Between Constituency Attitudes and Congressional Voting Behavior: A Causal Model,” this Review, 60 (1966), pp. 66–72.Google Scholar

8 Boudon, Raymond, “A Method of Linear Causal Analysis: Dependence Analysis,” American Sociological Review, 30 (1965), pp. 365–374.CrossRefGoogle Scholar See also Wright, Sewall, “Path Coefficients and Path Regressions: Alternative or Complementary Concepts?,” Biometrics, 16 (1960), pp. 189–202CrossRefGoogle Scholar; and Duncan, Dudley, “Path Analysis: Sociological Examples,” American Journal of Sociology, 72 (1966), pp. 1–16.CrossRefGoogle Scholar

9 This position is basically similar to that taken by Tukey, John W. in “Causation, Regression, and Path Analysis,” in Kempthorne, Oscaret. al. (eds.), Statistics and Mathematics in Biology (Ames, Iowa: Iowa State College Press, 1954), Chap. 3.Google Scholar

10 The numerical value of byx is of course also affected by one's choice of units of measurement. Unlike the expression sx/sy, however, these units of measurement are interrelated by purely a priori or definitional operations (e.g., 100 pennies = one dollar). It is true, as McGinnis notes, that one can transform rxy into byx by multiplying by a simple scalar quantity. It does not follow, however, that correlation and regression coefficients are essentially interchangeable as McGinnis implies. For this scalar quantity sy/sx is a function of standard deviations peculiar to each population. A reader who is given only the correlation coefficient is therefore likely to be misled in interpreting results of comparative studies. For a further discussion of this point see Blalock, H. M., Causal Inferences in Nonexperimental Research (Chapel Hill: University of North Carolina Press, 1964), Ch. 4.Google Scholar See also McGinnis, Robert, “Review of Causal Inferences in Nonexperimental Research,” Social Forces, 44 (1966), pp. 584–586.Google Scholar

11 In particular, one must assume that the error terms in each equation have zero means and are uncorrelated with each other and with any of the independent variables that appear in their respective equations.

12 If interest is in generalizing to a population, it might make more sense to use a measure that, does not involve any hypothetical manipulations. One may of course break down R 24.124 into the components r 214, r 224.1 (1—r 214), and r 234.12(1—R 24.12). Since x 2, x 3, and x 3 are intercorrelated, these components cannot be directly associated with these variables. However, the exogenous causes of the X, are assumed orthogonal in the case of simple least squares, and therefore one may—if he wishes—link the above components of R 24.123 with the respective error terms, given these assumptions about the causal ordering of x 1, x 2, and x 3. This of course raises the question of why one would want to associate components with exogenous variables that have not been included in the theoretical system.

13 Turner, Malcolm E. and Stevens, Charles D., “The Regression Analysis of Causal Paths,” Biometrics, 15 (1959), pp. 236–258.CrossRefGoogle Scholar

14 Tukey, op. cit.

15 Wright, op. cit.