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Making a Paradigmatic Convention Normal: Entrenching Means and Variances as Statistics

Published online by Cambridge University Press:  26 September 2008

Martin H. Krieger
Affiliation:
School of Urban Planning and DevelopmentUniversity of Southern California, Los Angeles

Abstract

Most lay users of statistics think in terms of means (averages), variances or the square of the standard deviation, and Gaussians or bell-shaped curves. Such conventions are entrenched by statistical practice, by deep mathematical theorems from probability, and by theorizing in the various natural and social sciences. I am not claiming that the particular conventions (here, the statistics) we adopt are arbitrary. Entrenchment can be rational without its being as well categorical (excluding all other alternatives), even if that entrenchment claims also to provide for categoricity. 1 provide a detailed description of how a science is “normal” and conventionalized. A characteristic feature of this entrenchment of conventions by practice, theorems, and theorizing, is its highly technical form, the canonizing work enabled by apparently formal and esoteric mathematical means.

Type
Article
Copyright
Copyright © Cambridge University Press 1996

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References

Baclawski, K., Rota, G.-C., and Billey, S.. 1989. An Introduction to the Theory of Probability. Cambridge, Mass.: MIT, Department of Mathematics.Google Scholar
Black, F. 1987. “Noise.” In his Business Cycles and Equilibrium, 152–72. New York: Blackwells.Google Scholar
Box, J. F. 1978. R. A. Fisher: The Life of a Scientist. New York: Wiley.Google Scholar
Chandler, D. 1987. Introduction to Modern Statistical Mechanics. New York: Oxford University Press.Google Scholar
Chvatal, V. 1983. Linear Programming. New York: Freeman.Google Scholar
Efron, B., and Tibshirani, R. 1991. “Statistical Data Analysis in the Computer Age.” Science 253:390–95.CrossRefGoogle ScholarPubMed
Eisenhart, C. 1947. “The Assumptions Underlying the Analysis of Variance.” Biometrics 3:121.CrossRefGoogle ScholarPubMed
Feller, W. 1968. An Introduction to Probability Theory and Its Applications. Vol. 1. New York: Wiley.Google Scholar
Feller, W. 1971. An Introduction to Probability Theory and Its Applications. Vol. 2. New York: Wiley.Google Scholar
Feynman, R. P., and Hibbs, A. R. 1965. Quantum Mechanics and Path Integrals. New York: McGraw Hill.Google Scholar
Feynman, R. P., Leighton, R. B., and Sands, M. 1963. The Feynman Lectures on Physics. Vol. 1. Reading, Mass.: Addison-Wesley.Google Scholar
Fisher, R. A. 1971–74. Collected Papers of R. A. Fisher. 5 vols. Edited by Bennett, J. H.. Adelaide: University of Adelaide.Google Scholar
Fisher, R. A. 1915. “Frequency Distribution of the Values of the Correlation Coefficient in Samples from an Indefinitely Large Population.” Biometrika 10:507–21.Google Scholar
Fisher, R. A. 1922a. “On the Interpretation of Chi-Square from Contingency Tables, and the Calculation of p.” Journal of the Royal Statistical Society 85:8794.CrossRefGoogle Scholar
Fisher, R. A. 1922b. “On the Mathematical Foundations of Theoretical Statistics.” Philosophical Transactions A 222:309–68.Google Scholar
Fisher, R. A. 1925. “Theory of Statistical Estimation.” Proceedings of the Cambridge Philosophical Society 22:700–25.CrossRefGoogle Scholar
Fisher, R. A. [1925] 1973. Statistical Methods for Research Workers. Reprinted in R. A. Fisher, Statistical Methods, Experimental Design, and Scientific Inference, A Re-issue of Statistical Methods for Research Workers [1925] (1973), The Design of Experiments [1935] (1971), and Statistical Methods and Scientific Inference [1956](1973). Edited by Bennett, J. H.. Oxford: Oxford University Press.Google Scholar
Fisher, R. A. 1990. Statistical Methods, Experimental Design, and Scientific Inference, A Re-issue of Statistical Methods for Research Workers [1925] (1973), The Design of Experiments [1935] (1971), and Statistical Methods and Scientific Inference[1956](1973). Edited by Bennett, J. H.. Oxford: Oxford University Press.Google Scholar
Gillies, D., ed. 1992. Revolutions in Mathematics. Oxford: Clarendon Press.CrossRefGoogle Scholar
Hacking, I. 1990. The Taming of Chance. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Hoyningen-Huene, P. 1995. “Two Letters of Paul Feyerabend to T. S. Kuhn on a Draft of The Structure of Scientific Revolutions.” Studies in the History and Philosophy of Science 26:353387.CrossRefGoogle Scholar
Huber, P. J. 1972. “Robust Statistics: A Review.” Annals of Mathematical Statistics 43:1041–67.CrossRefGoogle Scholar
Iranpour, R., and Chacon, P. 1988. Basic Stochastic Processes: The Mark Kac Lectures. New York: Macmillan.Google Scholar
Kac, M. 1959. Statistical Independence in Probability, Analysis and Number Theory. Providence, R.I.: Mathematical Association of America.CrossRefGoogle Scholar
Kennedy, P. 1985. A Guide to Econometrics. Cambridge, Mass.: MIT Press.Google Scholar
Krieger, M. H. 1989. Marginalism and Discontinuity: Tools for the Crafts of Knowledge and Decision. New York: Russell Sage Foundation.Google Scholar
Krieger, M. H. 1991. “Theorems as Meaningful Cultural Artifacts: Making the World Additive.” Synthese 88:135–54.CrossRefGoogle Scholar
Krieger, M. H. 1992. Doing Physics: How Physicists Take Hold of the World. Bloomington: Indiana University Press.Google Scholar
Krieger, M. H. 1995. “Could the Probability of Doom be Zero or One?” Journal of Philosophy 92:382–87.CrossRefGoogle Scholar
Krieger, M. H. 1996. Constitutions of Matter: Mathematically Modeling the Most Everyday of Phenomena. Chicago: University of Chicago Press.Google Scholar
Kuhn, T. S. 1970. The Structure of Scientific Revolutions. Chicago: University of Chicago Press.Google Scholar
Kuhn, T. S. 1984. “Revisiting Planck.” Historical Studies in the Physical Sciences 14:231–52.CrossRefGoogle Scholar
Levins, R., and Lewontin, R. 1985. The Dialectical Biologist. Cambridge, Mass.: Harvard University Press.Google Scholar
Loève, M. 1960. Probability Theory. Princeton, N.J.: Van Nostrand.Google Scholar
Mandelbrot, B. 1982. The Fractal Geometry of Nature. San Francisco: Freeman.Google Scholar
Merton, R. C. 1990. Continuous-Time Finance. Cambridge, Mass.: Blackwells.Google Scholar
Mosteller, F., and Tukey, J. W. 1977. Data Analysis and Regression: A Second Course in Statistics. Reading, Mass.: Addison-Wesley.Google Scholar
Particle Data Group. 1996. “Review of Particle Properties.” Physical Review D 54, part 1:1720.CrossRefGoogle Scholar
Porter, T. 1986. The Rise of Statistical Thinking. Princeton, N.J.: Princeton University Press.Google Scholar
Roth, A. E., and Sotomayor, M. 1990. Two-Sided Matching. New York: Cambridge University Press.CrossRefGoogle Scholar
Samuelson, P. 1970. “The Fundamental Approximation Theorem of Portfolio Analysis in Terms of Means, Variances and Higher Moments.” Review of Economic Studies 37:537–42.CrossRefGoogle Scholar
Scheffè, H. 1956. “Alternative Models for the Analysis of Variance,Annals of Mathematical Statistics 27:251–71.CrossRefGoogle Scholar
Stigler, S. 1986. The History of Statistics before 1900. Cambridge, Mass.: Harvard University Press.Google Scholar
Wheeler, J. A., and Feynman, R. P. 1945. “Interaction with the Absorber as the Mechanism of Radiation.” Reviews of Modern Physics 17:157–81.CrossRefGoogle Scholar
Wonnacott, R. J., and Wonnacott, T. H. 1979. Econometrics. New York: Wiley.Google Scholar