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Standard Deviation Abstract

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Purpose: The purpose of this study is to propose an alternate, quick estimate of standard deviation, represented by s’, and compare its efficiency with the efficiency of other quick estimates of standard deviation, σ.

Research Questions: This study questions whether the proposed calculation of s’ is an efficient quick method of estimating standard deviation, and how s’ compares to past quick estimates of standard deviation.

Hypothesis: s’ can be used as a quick estimate of standard deviation by replacing the weighing of individuals by an estimated ranking of the individuals, with the weighing of groups of individuals. s’ is more efficient than other past quick estimates of standard deviation.

Main Findings: Except for sample sizes less than 10, s’ is shown to have an insignificant difference when compared with s. There is only a slight increase in bias as the number of groups increases. The use of s’ as an estimate for standard deviation is efficient and is a preferable method of estimating standard deviation when it is more convenient to rank the individuals than to measure them. However, it is probable that in most cases ranking is more difficult than using the standard method of finding standard deviation. The method of calculating s’ used here is more efficient than past recorded estimates of standard deviation. The disadvantages of this method are error due to subjective ranking and the assumption of normality. Non-normality may affect the efficiency of s’.

Mead, R. (1966). A quick method of estimating the standard deviation. Biometrika, 53 (3 & 4), 559-564.

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