Advertisement

On an Approximate Test for Homogeneity of Coefficients of Variation

  • B. M. Bennett
Part of the Experientia Supplementum book series (EXS, volume 22)

Summary

The coefficient of variation (c. v.) ζ = σ/ξ, or ratio of standard deviation to mean (ξ > 0), is a useful parameter and measure of variability in certain situations since it is expressed in absolute units. Thus in comparing results on repeated clinical data when k (≥ 2) different measurement techniques are utilized in analyzing the same or paired specimens, it is of interest to compare the corresponding sample c. v.’s z 1, ... , z k respectively for the k techniques. For this situation the following note presents a test which is based on McKay’s approximation [4] to the distribution of the sample c. v. for the normal distribution, and utilizes Pitman’s method [5] for the hypothesis of equality of scale parameters of Gamma variates.

Key Words

Coefficients of variation in independent samples McKay’s approximation Pitman’s test for scale parameters. 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Iglewicz, B., Myers, R. H. and Howe, R. B. (1968): On the percentage points of the sample coefficient of variation. Biometrika 56, 580–581.CrossRefGoogle Scholar
  2. [2]
    Iglewicz, B. and Myers, R. H. (1970): Comparisons of approximations to the percentage points of the sample coefficient of variation. Technometrics 12, 166–169.Google Scholar
  3. [3]
    Koopmans, L. H., Owens, D. B. and Rosenblatt, J. I. (1964): Confidence intervals for the coefficient of variation for the normal and log-normal distributions. Biometrika 51, 25–32.Google Scholar
  4. [4]
    Mckay, A. T. (1932): Distribution of the coefficient of variation and the extended t distribution. J. R. Statist. Sec. 95, 695–698.CrossRefGoogle Scholar
  5. [5]
    Pitman, E. J. G. (1939): Tests of hypotheses concerning location and scale parameters. Biometrika 31, 200–215.Google Scholar
  6. [6]
    Tang, P. C. (1938): The power function of the analysis of variance tests with tables and illustrations of their use. Stat. Res. Mem. 2, 126–149.Google Scholar

Copyright information

© Springer Basel AG 1976

Authors and Affiliations

  • B. M. Bennett
    • 1
  1. 1.School of Public HealthUniversity of HawaiiHonoluluUSA

Personalised recommendations