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Title:
Testing homogeneity of variances with unequal sample sizes | Computational Statistics
Description:
When sample sizes are unequal, problems of heteroscedasticity of the variables given by the absolute deviation from the median arise. This paper studies how the best known heteroscedastic alternatives to the ANOVA F test perform when they are applied to these variables. This procedure leads to testing homoscedasticity in a similar manner to Levene’s (1960) test. The difference is that the ANOVA method used by Levene’s test is non-robust against unequal variances of the parent populations and Levene’s variables may be heteroscedastic. The adjustment proposed by O’Neil and Mathews (Aust Nz J Stat 42:81–100, 2000) is approximated by the Keyes and Levy (J Educ Behav Stat 22:227–236, 1997) adjustment and used to ensure the correct null hypothesis of homoscedasticity. Structural zeros, as defined by Hines and O’Hara Hines (Biometrics 56:451–454, 2000), are eliminated. To reduce the error introduced by the approximate distribution of test statistics, estimated critical values are used. Simulation results show that after applying the Keyes–Levy adjustment, including estimated critical values and removing structural zeros the heteroscedastic tests perform better than Levene’s test. In particular, Brown–Forsythe’s test controls the Type I error rate in all situations considered, although it is slightly less powerful than Welch’s, James’s, and Alexander and Govern’s tests, which perform well, except in highly asymmetric distributions where they are moderately liberal.
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Keywords {🔍}

article, google, scholar, stat, math, test, mathscinet, variances, tests, variance, anova, educ, levenes, equality, data, comput, analysis, unequal, testing, wilcox, statistics, homogeneity, robust, means, simul, keselman, privacy, cookies, content, sample, sizes, parrafrutos, heteroscedasticity, alternatives, comparison, assoc, heterogeneity, comparing, psychol, publish, research, search, august, heteroscedastic, method, structural, hines, error, estimated, values,

Topics {✒️}

month download article/chapter estimated critical values full article pdf generalizied behrens-fisher problem removing structural zeros monte carlo results robust large-sample tests unequal sample sizes simulation results show small sample behavior robust i-sample analysis structural zeros table 1 type article parra-frutos weighted linear regression privacy choices/manage cookies effect size fixed effects analyses samples sizes hara hines rj sample sizes anova f-test robust alexander-govern anova method crossed effects model wilcox test statistic wilcox rr commun stat-simul 26 commun stat simul european economic area scope submit manuscript correct null hypothesis highly asymmetric distributions meet assumptions underlying feir-walsh bj asymmetric trimming strategies finite-intersection method statistical tests brown-forsythe solution bus eco stat assumption violations revisited rogan jc accepting optional cookies related subjects stanford university press check access methodological research instant access increased power location-scale low power

Questions {❓}

Bradley JV (1978) Robustness?
Rogan JC, Keselman HJ (1977) Is the ANOVA F-test robust to variance heterogeneity when samples sizes are equal?
Wilcox RR (1995) ANOVA: a paradigm for low power and misleading measures of effect size?

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