Skip to main content

Randomized Experiments

  • Chapter
Observational Studies

Part of the book series: Springer Series in Statistics ((SSS))

  • 3776 Accesses

Abstract

Observational studies and controlled experiments have the same goal, inference about treatment effects, but random assignment of treatments is present only in experiments. This chapter reviews the role of randomization in experiments, and so prepares for discussion of observational studies in later chapters. A theory of observational studies must have a clear view of the role of randomization, so it can have an equally clear view of the consequences of its absence. Sections 2.1 and 2.2 give two examples: a large controlled clinical trial, and then a small but famous example due to Sir Ronald Fisher, who is usually credited with the invention of randomization, which he called the “reasoned basis for inference” in experiments. Later sections discuss the meaning of this phrase, that is, the link between randomization and statistical methods. Most of the material in this chapter is quite old.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Ahlswede, R. and Daykin, D. (1978) An inequality for the weights of two families of sets, their unions, and intersections. Z. Wahrsch. Verus Gebiete, 43, 183–185.

    Article  MathSciNet  MATH  Google Scholar 

  • Anderson, I. (1987) Combinatorics of Finite Sets. New York: Oxford University Press.

    MATH  Google Scholar 

  • Birch, M. W. (1964) The detection of partial association, I: The 2 × 2 case. Journal of the Royal Statistical Society, Series B,26, 313–324.

    MathSciNet  MATH  Google Scholar 

  • Birch, M. W. (1965) The detection of partial association, II: The general case. Journal of the Royal Statistical Society, Series B,27, 111–124.

    MathSciNet  MATH  Google Scholar 

  • Bollobas, B. (1986) Combinatorics. New York: Cambridge University Press.

    MATH  Google Scholar 

  • Campbell, D. and Stanley, J. (1963) Experimental and Quasi-Experimental Designs for Research. Chicago: Rand McNally.

    Google Scholar 

  • Cochran, W. G. (1963) Sampling Techniques. New York: Wiley.

    Google Scholar 

  • Cox, D. R. (1958a) Planning of Experiments. New York: Wiley.

    MATH  Google Scholar 

  • Cox, D. R. (1958b) The interpretation of the effects of non-additivity in the Latin square. Biometrika, 45, 69–73.

    MATH  Google Scholar 

  • Cox, D. R. (1966) A simple example of a comparison involving quantal data. Biometrika, 53, 215–220.

    Article  MathSciNet  Google Scholar 

  • Cox, D. R. (1970) The Analysis of Binary Data. London: Methuen.

    MATH  Google Scholar 

  • Cox, D. R. and Hinkley, D.V. (1974) Theoretical Statistics. London: Chapman & Hall.

    MATH  Google Scholar 

  • Cox, D. R. and Reid, N. (2000) The Theory of the Design of Experiments. New York: CRC Press.

    MATH  Google Scholar 

  • Eaton, M. (1967) Some optimum properties of ranking procedures. Annals of Mathematical Statistics, 38, 124–137.

    Article  MathSciNet  MATH  Google Scholar 

  • Eaton, M. (1982) A review of selected topics in probability inequalities. Annals of Statistics, 10, 11–43.

    Article  MathSciNet  MATH  Google Scholar 

  • Eaton, M. (1987) Lectures on Topics in Probability Inequalities. Amsterdam: Centrum. voor Wiskunde en Informatica.

    MATH  Google Scholar 

  • Efron, B. (1971) Forcing a sequential experiment to be balanced. Biometrika, 58, 403–417.

    Article  MathSciNet  MATH  Google Scholar 

  • Fisher, R. A. (1935, 1949) The Design of Experiments. Edinburgh: Oliver & Boyd.

    Google Scholar 

  • Fortuin, C., Kasteleyn, P., and Ginibre, J. (1971) Correlation inequalities on some partially ordered sets. Communications in Mathematical Physics, 22, 89–103.

    Article  MathSciNet  MATH  Google Scholar 

  • Freidlin, B. and Gastwirth, J. L. (2000) Should the median test be retired from general use? American Statistician, 54, 161–164.

    Google Scholar 

  • Friedman, L. M., DeMets, D. L., and Furberg, C. D. (1998) Fundamentals of Clinical Trials. New York: Springer-Verlag.

    Google Scholar 

  • Gastwirth, J. L. (1966) On robust procedures. Journal of the American Statistical Association, 61, 929–948.

    Article  MathSciNet  MATH  Google Scholar 

  • Gehan, E. (1965) A generalized Wilcoxon test for comparing arbitrarily singly censored samples. Biometrika, 52, 203–223.

    MathSciNet  MATH  Google Scholar 

  • Gibbons, J. D. (1982) Brown-Mood median test. In: Encyclopedia of Statistical Sciences, Volume 1, S. Kotz and N. Johnson, eds., New York: Wiley, pp. 322–324.

    Google Scholar 

  • Hamilton, M. (1979) Choosing a parameter for 2 × 2 table or 2 × 2 × 2 table analysis. American Journal of Epidemiology, 109, 362–375.

    Google Scholar 

  • Hettmansperger, T. (1984) Statistical Inference Based on Ranks. New York: Wiley.

    MATH  Google Scholar 

  • Hodges, J. and Lehmann, E. (1962) Rank methods for combination of independent experiments in the analysis of variance. Annals of Mathematical Statistics, 33, 482–497.

    Article  MathSciNet  MATH  Google Scholar 

  • Hodges, J. and Lehmann, E. (1963) Estimates of location based on rank tests. Annals of Mathematical Statistics, 34, 598–611.

    Article  MathSciNet  MATH  Google Scholar 

  • Holland, P. (1986) Statistics and causal inference (with discussion) . Journal of the American Statistical Association, 81, 945–970.

    Article  MathSciNet  MATH  Google Scholar 

  • Hollander, M., Proschan, F., and Sethuraman, J. (1977) Functions decreasing in transposition and their applications in ranking problems. Annals of Statistics, 5, 722–733.

    Article  MathSciNet  MATH  Google Scholar 

  • Hollander, M. and Wolfe, D. (1973) Nonparametric Statistical Methods. New York: Wiley.

    MATH  Google Scholar 

  • Holley, R. (1974) Remarks on the FKG inequalities. Communications in Mathematical Physics, 36, 227–231.

    Article  MathSciNet  Google Scholar 

  • Jureckova, J. (1984) M-, L- and R-estimators. In: Handbook of Statistics, Volume IV, P. R. Krishnaiah and P. K. Sen, eds., New York: Elsevier, pp. 463–485.

    Google Scholar 

  • Kempthorne, O. (1952) The Design and Analysis of Experiments. New York: Wiley.

    MATH  Google Scholar 

  • Krieger, A. M. and Rosenbaum, P. R. (1994) A stochastic comparison for arangement increasing functions. Combinatorics, Probability and Computing, 3, 345–348.

    Article  MathSciNet  MATH  Google Scholar 

  • Lehmann, E. L. (1959) Testing Statistical Hypotheses. New York: Wiley.

    MATH  Google Scholar 

  • Lehmann, E. L. (1975) Nonparametrics: Statistical Methods Based on Ranks. San Francisco: Holden-Day.

    MATH  Google Scholar 

  • MacLane, S. and Birkoff, G. (1988) Algebra. New York: Chelsea.

    MATH  Google Scholar 

  • Mann, H. and Whitney, D. (1947) On a test of whether one of two random variables is stochastically larger than the other. Annals of Mathematical Statistics, 18, 50–60.

    Article  MathSciNet  MATH  Google Scholar 

  • Mantel, N. (1963) Chi-square tests with one degree of freedom: Extensions of the Mantel-Haenszel procedure. Journal of the American Statistical Association, 58, 690–700.

    MathSciNet  MATH  Google Scholar 

  • Mantel, N. (1967) Ranking procedures for arbitrarily restricted observations. Biometrics, 23, 65–78.

    Article  Google Scholar 

  • Mantel, N. and Haenszel, W. (1959) Statistical aspects of retrospective studies of disease. Journal of the National Cancer Institute, 22, 719–748.

    Google Scholar 

  • Maritz, J. (1981) Distribution-Free Statistical Methods. London: Chapman & Hall.

    MATH  Google Scholar 

  • Marshall, A. and Olkin, I. (1979) Inequalities: Theory of Majorization and Its Applications. New York: Academic.

    MATH  Google Scholar 

  • McNemar, Q. (1947) Note on the sampling error of the differences between correlated proportions or percentage. Psychometrika, 12, 153–157.

    Article  Google Scholar 

  • Murphy, M., Hultgren, H., Detre, K., Thomsen, J., and Takaro, T. (1977) Treatment of chronic stable angina: A preliminary report of survival data of the randomized Veterans Administration Cooperative study. New England Journal of Medicine, 297, 621–627.

    Article  Google Scholar 

  • Neyman, J. (1923) On the application of probability theory to agricultural experiments. Essay on principles. Section 9. (In Polish) Roczniki Nauk Roiniczych, Tom X, pp. 1–51

    Google Scholar 

  • Reprinted in Statistical Science 1990, 5, 463–480, with discussion by T. Speed and D. Rubin.

    MathSciNet  MATH  Google Scholar 

  • Neyman, J. (1935) Statistical problems in agricultural experimentation. Supplement to the Journal of the Royal Statistical Society, 2, 107–180.

    Article  MATH  Google Scholar 

  • Pagano, M. and Tritchler, D. (1983) Obtaining permutation distributions in polynomial time. Journal of the American Statistical Association, 78, 435–440.

    Article  MathSciNet  MATH  Google Scholar 

  • Robinson, J. (1973) The large sample power of permutation tests for randomization models. Annals of Statistics, 1, 291–296.

    Article  MathSciNet  MATH  Google Scholar 

  • Rosenbaum, P. R. (1988) Sensitivity analysis for matching with multiple controls. Biometrika, 75, 577–581.

    Article  MathSciNet  MATH  Google Scholar 

  • Rosenbaum, P. R. (1989) On permutation tests for hidden biases in observational studies: An application of Holley’s inequality to the Savage lattice. Annals of Statistics, 17, 643–653.

    Article  MathSciNet  MATH  Google Scholar 

  • Rosenbaum, P. R. (1991) Some poset statistics. Annals of Statistics, 19, 1091–1097.

    Article  MathSciNet  MATH  Google Scholar 

  • Rosenbaum, P. R. (1994) Coherence in observational studies. Biometrics, 50, 368–374.

    Article  MATH  Google Scholar 

  • Rosenbaum, P. R. (1995) Quantiles in nonrandom samples and observational studies. Journal of the American Statistical Association, 90, 1424–1431.

    Article  MathSciNet  MATH  Google Scholar 

  • Rosenbaum, P. R. (1999) Holley’s inequality. Encyclopedia of Statistical Sciences, Update Volume 3, S. Kotz, C. B. Read, D. L. Banks, eds., New York: Wiley, pp. 328–331.

    Google Scholar 

  • Rubin, D. B. (1974) Estimating the causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology, 66, 688–701.

    Article  Google Scholar 

  • Rubin, D. B. (1977) Assignment to treatment group on the basis of a covariate. Journal of Educational Statistics, 2, 1–26.

    Article  Google Scholar 

  • Rubin, D. B. (1986) Which ifs have causal answers? Journal of the American Statistical Association, 81, 961–962.

    Google Scholar 

  • Savage, I. R. (1957) Contributions to the theory of rank order statistics: The trend case. Annals of Mathematical Statistics, 28, 968–977.

    Article  MathSciNet  MATH  Google Scholar 

  • Savage, I. R. (1964) Contributions to the theory of rank order statistics: Applications of lattice theory. Review of the International Statistical Institute, 32, 52–63.

    Article  MathSciNet  MATH  Google Scholar 

  • Tukey, J. W. (1985) Improving crucial randomized experiments-especially in weather modification-by double randomization and rank combination. In: Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer, L. Le Cam and R. Olshen, eds., Volume 1, Belmont, CA: Wadsworth, pp. 79–108.

    Google Scholar 

  • Welch, B. L. (1937) On the z-test in randomized blocks and Latin squares. Biometrika, 29, 21–52.

    MATH  Google Scholar 

  • Wilcoxon, F. (1945) Individual comparisons by ranking methods. Biometrics, 1, 8083.

    Google Scholar 

  • Wilk, M. B. (1955) The randomization analysis of a generalized randomized block design. Biometrika, 42, 70–79.

    MathSciNet  MATH  Google Scholar 

  • Wittgenstein, L. (1958) Philosophical Investigations (Third Edition) . Englewood Cliffs, NJ: Prentice-Hall.

    Google Scholar 

  • Zelen, M. (1974) The randomization and stratification of patients to clinical trials. Journal of Chronic Diseases, 27, 365–375.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer Science+Business Media New York

About this chapter

Cite this chapter

Rosenbaum, P.R. (2002). Randomized Experiments. In: Observational Studies. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3692-2_2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-3692-2_2

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4419-3191-7

  • Online ISBN: 978-1-4757-3692-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics