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 b_yx is of course also affected by one's choice of units of measurement. Unlike the expression s_x/s_y, 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 r_xy into b_yx 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 s_y/s_x 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 ²_4.124 into the components r ²₁₄, r ²_24.1 (1—r ²₁₄), and r ²_34.12(1—R ²_4.12). 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 ²_4.123 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.