The effect of non-normality on the use of the range in estimating the population standard deviation

Abstract

The relative efficiency and biasedness of using the standardized mean range to estimate σ is discussed. The effect σ parental non-normality on the relative efficiency of the range estimator of σ is found to be minimal for n≦20. This further establishes the robustness of using this method of estimating σ in quality control analysis. For larger sample sizes and non-normal distributions, the use of the standardized mean range often results in extremely biased estimates of σ. This can be problematic when selecting proper sample sizes. With populations which are grossly leptokurtic, sample sizes which are too large occur, and an extra cost may be incurred. With platykurtic distributions, sample sizes which are too small occur, and additional sampling may be necessary to obtain a proper sample size.