Skip to main content
SpringerLink
Log in

Confidence Interval Estimation for a Difference Between Two Dependent Intraclass Correlation Coefficients With Variable Class Sizes

  • Published:
Journal of Statistical Theory and Practice Aims and scope Submit manuscript

Abstract

Four confidence intervals for a difference between two dependent intraclass correlation coefficients (ICCs) are developed, focusing on applications to family studies. The basic idea adopted here is that confidence intervals for a difference between two parameters can be obtained from confidence limits for each parameter. Among the four confidence procedures considered, the one based on the inverse hyperbolic tangent transformation for a single ICC performed best. Francis Galton’s data on human stature are used to illustrate the methodology.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bartko, J.J., 1966. The intraclass correlation coefficient as a measure of reliability. Psychological Reports, 19, 3–11.

    Article  Google Scholar 

  • Bartlett, M.S., 1953. Approximate confidence intervals. Biometrika, 40, 12–19.

    Article  MathSciNet  Google Scholar 

  • Bhandary, M., Fujiwara, K., 2008. Confidence interval estimation for a linear contrast in intraclass correlation coefficients under unequal family sizes for several populations. Journal of Statistical Computation and Simulation, 78, 609–621.

    Article  MathSciNet  Google Scholar 

  • Brass, W., 1958. Models of birth distribution in human populations. Bulletin of International Statistical Institute, 36, 165–179.

    MATH  Google Scholar 

  • Donner, A., 1986. A review of inference procedures for the intraclass correlation coefficient in the one-way random effects model. International Statistical Review, 54, 67–82.

    Article  MathSciNet  Google Scholar 

  • Donner, A., Klar, N., 2000. Design and Analysis of Cluster Randomization Trials in Health Research. Arnold, New York.

    Google Scholar 

  • Donner, A., Koval, J.J., 1980. The estimation of intraclass correlation in the analysis of family data. Biometrics, 36, 19–25.

    Article  Google Scholar 

  • Donner, A., Koval, J.J., Bull, S., 1984. Testing the effect of sex differences on sib-sib correlations. Biometrics, 40, 349–356.

    Article  Google Scholar 

  • Donner, A., Wells, G., 1986. A comparison of confidence interval methods for the intraclass correlation coefficient. Biometrics, 42, 401–412.

    Article  MathSciNet  Google Scholar 

  • Donner, A., Zou, G., 2002. Testing the equality of dependent intraclass correlation coefficients. Statistician, 51, 367–379.

    MathSciNet  Google Scholar 

  • Eliasziw, M., Donner, A., 1991. A generalized non-iterative approach to the analysis of family data. Annals of Human Genetics, 55, 77–90.

    Article  Google Scholar 

  • Elston, R.C., 1975. On the correlation between correlations. Biometrika, 62, 133–140.

    Article  MathSciNet  Google Scholar 

  • Fisher, R.A., 1925. Statistical Methods for Research Workers. Oliver and Boyd, Edinburgh.

    MATH  Google Scholar 

  • Giraudeau, B., Porcher, R., Mary, J., 2005. Power calculation for the likelihood ratio-test when comparing two dependent intraclass correlation coefficients. Computer Methods and Programs in Biomedicine, 77, 165–173.

    Article  Google Scholar 

  • Haggard, E.A., 1958. Intraclass Correlation and the Analysis of Variance. Dryden Press, New York.

    MATH  Google Scholar 

  • Hanley, J.A., 2004. Transmuting women into men: Galton’s family data on human stature. American Statistician, 58, 237–243.

    Article  MathSciNet  Google Scholar 

  • McGraw, K.O., Wong, S., 1996. Forming inference about some intraclass correlation coefficients. Psychological Methods, 1, 30–46.

    Article  Google Scholar 

  • Naik, D.N., Helu, A., 2007. On testing equality of intraclass correlations under unequal family sizes. Computational Statistics and Data Analysis, 51, 6498–6510.

    Article  MathSciNet  Google Scholar 

  • Ramasundarahettige, C.F., Donner, A., Zou, G.Y., 2009. Confidence interval construction for a difference between two dependent intraclass correlation coefficients. Statistics in Medicine, 28, 1041–1053.

    Article  MathSciNet  Google Scholar 

  • Rao, C.R., 1948. Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation. Mathematical Proceedings of the Cambridge Philosophical Society, 44, 50–57.

    Article  MathSciNet  Google Scholar 

  • Rosner, B., 1982. On the estimation and testing of intraclass correlations: The general case of multiple replicates for each variable. American Journal of Epidemiology, 116, 722–730.

    Article  Google Scholar 

  • Smith, C.A.B., 1957. On the estimation of intraclass correlation. Annals of Human Genetics, 21, 363–373.

    Article  MathSciNet  Google Scholar 

  • Swiger, L.A., Harvey, W.R., Everson, D.O., Gregory, K.E., 1991. The variance of intraclass correlation involving groups with one observation. Biometrics, 20, 818–826.

    Article  Google Scholar 

  • Thomas, J.D., Hultquist, R.A., 1978. Interval estimation for the unbalanced case of the one-way random effects model. Annals of Statistics, 6, 582–587.

    Article  MathSciNet  Google Scholar 

  • Ukoumunne, O.C., Davison, A.C., Gulliford, M.C., Chinn, S., 2003. Non-parametric bootstrap confidence intervals for the intraclass correlation coefficient. Statistics in Medicine, 22, 3805–3821.

    Article  Google Scholar 

  • Weinber, R., Patel, Y.C., 1981. Simulated intraclass correlation coefficients and their z-transformations. Journal of Satatistical Computation and Simulation, 13, 13–26.

    Article  Google Scholar 

  • Zou, G.Y., 2008. On the estimation of additive interaction by use of the four-by-two tables and beyond. American Journal of Epidemiology, 168, 212–224.

    Article  Google Scholar 

  • Zou, G.Y., Donner, A., 2008. Construction of confidence limits about effect measures: A general approach. Statistics in Medicine, 27, 1693–1702.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Epidemiology and Biostatistics, University of Western Ontario, London, Ontario, Canada, N6A 5C1

    Danuta Kowalik

  2. Robarts Clinical Trials, Robarts Research Institute, University of Western Ontario, London, Ontario, Canada, N6A 5K8 &

    Yun-Hee Choi

  3. Department of Epidemiology and Biostatistics, School of Public Health, Southeast University, Nanjing, Jiangsu Province, PR China

    G. Y. Zou

Authors
  1. Danuta Kowalik
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yun-Hee Choi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. Y. Zou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Danuta Kowalik.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kowalik, D., Choi, YH. & Zou, G.Y. Confidence Interval Estimation for a Difference Between Two Dependent Intraclass Correlation Coefficients With Variable Class Sizes. J Stat Theory Pract 5, 613–625 (2011). https://doi.org/10.1080/15598608.2011.10483734

Download citation

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1080/15598608.2011.10483734

AMS Subject Classification

Key-words

Search

Navigation