Authors :
Chris Uchechi Onyemachi
Volume/Issue :
Volume 11 - 2026, Issue 10 - October
Google Scholar :
https://tinyurl.com/5xp6zsyy
DOI :
https://doi.org/10.38124/ijisrt/26Oct1280
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working days from the publication date to appear in PlumX Metrics, Semantic Scholar, and
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Abstract :
Models that specify a constant variance for the error terms perhaps form the “backbone” of statistical modeling as applied to much of scientific investigation. Error variance estimation is one of the most important issues in regression models. The estimation of the error variance is essential to assess the variability of the estimated mean of Yi given Xi. Therefore, the error variance plays an important role in regression analysis but uncorrelated in sense that errors in successive measurements cannot be forecast from a knowledge of errors in previous measurements. One of the central messages of this study is that (a) unequal variances may be more prevalent than typically recognized in statistical analysis, and (b) the usefulness of “Levene’s test when considering tests of equal variances, as test is actually a family of techniques. Depending on which of the Levene tests that are being implemented, and particularly the Levene’s test based on means which is found in widely used software like SPSS, one may be using a statistical technique that is as bad (if not worse) than the F test which the Levene test was intended to replace. The primary goals of this study are to (a) demonstrate that the current statistical practice of testing for equality of variances in hypothesis testing (as prescribed by textbooks and statistical software programs) is insufficient, hence data transformation is suggested.
Keywords :
Constant Variance, Error Variance, Estimation, Levene’s Test, F-Test, Transformation.
References :
- Alessandro, B. (2014). Data Transformation for Confidence Interval Improvement: An application to the Estimation of Stress-Strength Model Reliability. Available at http://digitalcommons.wayne.edu/jmasm/vol14/iss2/15
- Bartlett, M. S. (1947). The Use of Transformations. Biometrics. Vol. 3. Pp 39 - 52
- Box, G. E. P. and Cox, D. R (1964) An Analysis of Transformation. Journal of Royal Statistical Society, Series B (Methodological), Vol. 26, No. 2, pp. 211-252.
- Iwueze I.S (2007). Some Implications of Truncating the Distribution to the left at Zero. JASA, Vol 73, N0. 363, 536 - 544
- Johnson, A. C. and Thomopoulos, N. T. (2002). Use of the Left Truncated Normal Distribution for Improving Achieved Service Levels, Decisions Sciences Institute 2002 Annual Meeting. Journal of Applied Sciences. 2007;7(2):189-195.
- Wei, W. (1990) Time Series Analysis: Univariate and Multivariate Methods. Addison-Wesley Publishing Company, Inc., New York.
Models that specify a constant variance for the error terms perhaps form the “backbone” of statistical modeling as applied to much of scientific investigation. Error variance estimation is one of the most important issues in regression models. The estimation of the error variance is essential to assess the variability of the estimated mean of Yi given Xi. Therefore, the error variance plays an important role in regression analysis but uncorrelated in sense that errors in successive measurements cannot be forecast from a knowledge of errors in previous measurements. One of the central messages of this study is that (a) unequal variances may be more prevalent than typically recognized in statistical analysis, and (b) the usefulness of “Levene’s test when considering tests of equal variances, as test is actually a family of techniques. Depending on which of the Levene tests that are being implemented, and particularly the Levene’s test based on means which is found in widely used software like SPSS, one may be using a statistical technique that is as bad (if not worse) than the F test which the Levene test was intended to replace. The primary goals of this study are to (a) demonstrate that the current statistical practice of testing for equality of variances in hypothesis testing (as prescribed by textbooks and statistical software programs) is insufficient, hence data transformation is suggested.
Keywords :
Constant Variance, Error Variance, Estimation, Levene’s Test, F-Test, Transformation.
