Simulation and comparison of five estimators of variability in units of standard deviation for small samples drawn from normally distributed data

It is convenient to measure or estimate variation in samples or distributions in units of standard deviations. There are alternative methods of estimation of standard deviation aside from the conventional and well-known definition. Estimation of standard deviation for very small samples (as small as two), whereas not always ideal, might be useful in certain practical circumstances. A simulation study of five standard deviation estimation methods and the effects of small sample sizes 2 through 6 is made through description of sampling variations and biases. Consideration of the unbiased mean, small median biases, and algorithmic simplicity, show logically that Gini mean difference estimation is a competitive method.