Estimation and statistical inference of univariate non-sequential signal-to-noise ratios
C.-L. Huynh (2002). Estimation and statistical inference of univariate non-sequential signal-to-noise ratios. Journal of Statistical Research, Vol. 36, No. 2, pp. 201-213.
Abstract
The exact and asymptotic distributions of the biased and unbiased estimators of the univariate mean-to-standard-deviation ratio are studied. Normalizing and variance stabilizing transformations of these estimators are derived. Monte Carlo studies show that the Rao transformation of the exact distribution performs better than other procedures for $\alpha=05, .01$ with samples as small as five. Statistical inferences on single ratios and ratio comparisons are discussed. Standard normal tests are recommended for $n>5$. Methods and tables for statistical tests using exact distributions for small samples are also provided.