Estimating the Standard Deviation From the Range: a Replication of Analysis of Demographic Data Reported in Marriage & Family Review, 2016-2017

Abstract

A major concern in the social sciences is lack of replication of previous studies. An important methodological concern in the social sciences is the ability to determine effect sizes in addition to statistical significance levels. Effect sizes cannot be easily calculated in the absence of sufficient data; usually standard deviations are needed. If standard deviations are not available, how can they be estimated? Various proposals have been offered to solve this question. One solution is to divide the range (maximum–minimum) by four; a variety of more complicated solutions, based on sample size or the skew of the variable’s distribution, have been suggested (Schumm, Higgins, et al., 2017). Here, 30 cases involving the demographic variable of age, from 23 articles published in Marriage & Family Review between 2016 and 2017, are assessed to replicate the previous report of Schumm, Higgins et al. (2017). Our results indicated that both linear and power functions significantly predicted the size of standard deviations, with larger samples featuring smaller standard deviations. Aside from sample size, the best solution appears to be to divide the range by 4.5–5.0; although for very small samples (N?<?50), it is probably better to divide by 3.5–4.0 whereas for larger samples, especially those that involve higher levels of skew, it may be better to divide by 5.0 or higher. The Wan et al. (2014) estimation procedure appears to be approximately a power function of sample size. For samples up to several thousand in size, the range of divisors appears to run between 3.0 and 8.0, extremes that could be used to determine the largest or smallest possible standard deviations, respectively. Values far below 3.0 or above 8.0 may reflect typographical errors in data reports or possibly be evidence of artificially generated data, if not scientific fraud. When a variable is split into subsamples, its standard deviations should usually increase for the subsamples compared with the total sample. Similar assessments remain in progress for non-demographic variables in social sciences.