Comparing variances and means when distributions have non-identical shapes

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The paper compares several methods for computing robust 1-α confidence intervals for σ 1 2-σ 2 2, or σ 1 2/σ 2 2, where σ 1 2 and σ 2 2 are the population variances corresponding to two independent treatment groups. The emphasis is on a Box-Scheffe approach when distributions have different shapes, and so the results reported here have implications about comparing means. The main result is that for unequal sample sizes, a Box-Scheffe approach can be considerably less robust than indicated by past investigations. Several other procedures for comparing variances, not based on a Box-Scheffe approach, were also examined and found to be highly unsatisfactory although previously published papers found them to be robust when the distributions have identical shapes. Included is a new result on why the procedures examined here are not robust, and an illustration that increasing σ 1 2-σ 2 2 can reduce power in certain situations. Constants needed to apply Dunnett’s robust comparison of means are included.