¹ For example see Johnston, J., Econometric Methods (New York: McGraw-Hill, 1963), Chap. 6Google Scholar; Gordon, Robert, “Issues in Multiple Regression,” American Journal of Sociology, 73 (03 1968), 592–616 CrossRefGoogle Scholar; and Blalock, H. M., “Some Implications of Random Measurement Error for Causal Inferences,” American Journal of Sociology, 71 (07 1965), 37–47 CrossRefGoogle Scholar.

² See Duncan, O. Dudley, “Contingencies in Constructing Causal Models,” in Borgatta, Edgar (ed.), Sociological Methodology 1969 (San Francisco: Jossey-Bass, 1969), Chap. 3Google Scholar.

³ See especially Costner, Herbert L., “Theory, Deduction and Rules of Correspondence,” American Journal of Sociology, 75 (09 1969), 245–263 CrossRefGoogle Scholar; and Heise, David R., “Separating Reliability and Stability in Test-Retest Correlation,” American Sociological Review, 34 (02 1969), 93–101 CrossRefGoogle Scholar. See also George W. Bohrnstedt, “Observations on the Measurement of Change,” in Sociological Methodology 1969, op. cit., Chap. 4: Wiley, David E. and Wiley, James A., “The Estimation of Measurement Error in Panel Data,” American Sociological Review, 35 (02 1970), 112–117 CrossRefGoogle Scholar; and Blalock, H. M., “Multiple Indicators and the Causal Approach to Measurement Error,” American Journal of Sociology, 75 (09 1969), 264–272 CrossRefGoogle Scholar.

⁴ See Duncan, op. cit., and Siegel, Paul M. and Hodge, Robert W., “A Causal Approach to the Study of Measurement Error,” in Blalock, H. M. and Blalock, Ann B. (eds.) Methodology in Social Research (New York: McGraw-Hill, 1968), Chap. 2Google Scholar.

⁵ Johnston, op. cit., 149–150.

⁶ See Blalock, “Some Implications of Random Measurement Error,” op. cit.

⁷ See Wald, Abraham, “The Fitting of Straight Lines if Both Variables are Subject to Error,” Annals of Mathematical Statistics, 2 (1940), 284–300 CrossRefGoogle Scholar; and Bartlett, M. S., “Fitting a Straight Line when Both Variables are Subject to Error,” Biometrics, 5 (06 1949), 207–212 CrossRefGoogle Scholar. For an excellent discussion of these and related approaches, as well as an extensive bibliography, see Madansky, Albert, “The Fitting of Straight Lines when Both Variables are Subject to Error,” Journal of the American Statistical Association, 54 (03 1959), 173–205 CrossRefGoogle Scholar.

⁸ Carter, L. F. and Blalock, H. M., “Underestimation of Error Variance when Employing Wald-Bartlett Slope Estimation Techniques: A Monte Carlo Simulation,” Journal of the Royal Statistical Society (in press)Google Scholar.

⁹ For discussions of instrumental variables see Johnston, op. cit., 165–166; Christ, Carl, Econometric Models and Methods (New York: John Wiley, 1966), 404–410 Google Scholar; and Carter and Blalock, op. cit.

¹⁰ Ibid.

¹¹ See Costner, op. cit. and Heise, op. cit.

¹² See Blalock, H. M., “Estimating Measurement Error using Multiple Indicators and Several Points in Time,” American Sociological Review, 35 (02 1970), 101–111 CrossRefGoogle Scholar.

¹³ For discussions of path analysis in the social science literature see Raymond Boudon, “A New Look at Correlation Analysis” in Blalock and Blalock, op. cit., Chap. 6; Duncan, O. Dudley, “Path Analysis: Sociological Examples,” American Journal of Sociology, 72 (07 1966), 1–16 CrossRefGoogle Scholar; and Kenneth C. Land, “Principles of Path Analysis,” in Sociological Methodology 1969, op. cit., Chap. 1.

¹⁴ See especially Tukey, John W., “Causation, Regression and Path Analysis” in Kempthorne, Oscar et. al. (eds.), Statistics and Mathematics in Biology (Ames, Iowa: Iowa State College Press, 1954), 35–66 Google Scholar; and Blalock, H. M., “Causal Inferences, Closed Populations, and Measures of Association,” American Political Science Review, 61 (03 1967), 130–136 CrossRefGoogle Scholar.

¹⁵ See Wright, Sewall, “Path Coefficients and Path Regressions: Alternative or Complementary Concepts?” Biometrics, 16 (06 1960), 189–202 CrossRefGoogle Scholar.

¹⁶ For further discussions of this point see Bohrnstedt, op. cit.; Heise, op. cit.; and Siegel and Hodge, op. cit.

¹⁷ See Blalock, “Estimating Measurement Error,” op. cit.

¹⁸ There is another possibility that we shall not discuss further, namely that the error variance σ_e ² is a function of X. Sometimes it is reasonable to take σ_e ² = a + bX, where b>0, in which case it may be advisable to transform X to log X. However, this may produce nonlinear relationships with other variables in the causal system.

¹⁹ An empirical example where this occurs in connection with floor and ceiling effects has been discussed by Siegel and Hodge, op. cit.

²⁰ For further discussion of regression effects see Campbell, Donald T. and Stanley, Julian C., Experimental and Quasi-Experimental Designs for Research (Chicago: Rand McNally, 1966)Google Scholar.

²¹ It might seem absurd for an analyst to treat this kind of data as an interval scale, but we must remember that ordinal data also involve equally difficult problems of interpretation. Notice that in this particular illustration we are assuming no additional distortions in the intermediate values produced by the numerical values assigned to the categories. That is, the true distance between category limits is always ten. If the analyst used unequal intervals that were scored 1-6, there would be the added complication of nonlinearity in this intermediate range. Obviously, methodological studies of the practical effects of these kinds of distortions are very much needed. For an example of one such study see Labovitz, Sanford, “Some Observations on Measurement and Statistics,” Social Forces, 46 (12 1967), 151–160 CrossRefGoogle Scholar. See also, Thomas P. Wilson, “Critique of Ordinal Variables,” Social Forces (forthcoming).