Skip to main content
SpringerLink
Log in

Testing independence in two-way contingency tables with data subject to misclassification

  • Published:
Psychometrika Aims and scope Submit manuscript

Abstract

The misclassification process is represented by a stochastic matrix containing the probabilities that an individual who belongs in one cell is counted as belonging to another (or perhaps the same) cell. These probabilities are supposed known. If misclassification in the row direction is independent of that along the column variable then the size of the usual chi-square test is unchanged. It is shown how to calculate loss of power in this case and also how to calculate the change in size of the test if the errors are not independent. A modified test criterion is suggested when errors are not independent and a numerical example is included.

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

  1. Assakul, K. Testing hypotheses with categorical data subject to misclassification. Mimeo. Series No. 448, Institute of Statistics, Raleigh, N. C., 1965.

    Google Scholar 

  2. Barnard, G. A. Significance tests for 2 × 2 tables.Biometrika, 1947,34, 248–252.

    Google Scholar 

  3. Bross, I. Misclassification in 2 × 2 tables.Biometrics, 1954,10, 478–486.

    Google Scholar 

  4. Cramer, H.Mathematical methods of statistics. Princeton: Princeton University Press, 1946.

    Google Scholar 

  5. Diamond, E. L. The limiting power of categorical data chi-square tests analogous to normal analysis of variance.Ann. Math. Stat., 1963,34, 1432–1441.

    Google Scholar 

  6. Fix, E. Tables of non-centralx 2.Univ. Calif. Publication in Statistics, 1949,1, 15–19.

    Google Scholar 

  7. Mitra, S. K. On the limiting power function of the frequency chi-square test.Ann. Math. Stat., 1958,29, 1221–1233.

    Google Scholar 

  8. Mote, V. L. and Anderson, R. L. The effect of misclassification on the properties ofx 2-tests.Biometrika, 1965,52, 95–109.

    Google Scholar 

  9. Neyman, J. Contributions to the theory of thex 2-tests. In theProceedings of the Berkeley Symposium on Mathematical Statistics and Probability. University of California Press, 1949.

  10. Pitman, E. J. G. Notes on non-parametric statistical inference. Mimeo. Series No. 27, Institute of Statistics, Raleigh, N. C., 1948.

    Google Scholar 

  11. Roy, S. N. and Mitra, S. K. An introduction to some non-parametric generalizations of analysis of variance and multivariate analysis. Mimeo. Series No. 139, Institute of Statistics, Raleigh, N. C., 1955.

    Google Scholar 

  12. U. S. Bureau of Census.Evaluation and Research Program of the U. S. Censuses of Population and Housing, 1960—Accuracy of Data on Housing Characteristics. Series ER60, No. 3, Washington, D. C., 1964.

  13. U. S. Bureau of the Census.U. S. Census of Housing: 1960. Washington, D. C., 1963, VI.

Download references

Author information

Authors and Affiliations

  1. Chulalongkorn University, Bangkok, Thailand

    Kwanchai Assakul

  2. North Carolina State University, USA

    Charles H. Proctor

Authors
  1. Kwanchai Assakul
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Charles H. Proctor
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Assakul, K., Proctor, C.H. Testing independence in two-way contingency tables with data subject to misclassification. Psychometrika 32, 67–76 (1967). https://doi.org/10.1007/BF02289405

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02289405

Keywords

Search

Navigation