Does Dividing the Range by Four Provide an Accurate Estimate of a Standard Deviation in Family Science Research? A Teaching Editorial

Abstract

Occasionally, scientific reports have omitted information on standard deviations, making estimates of effect sizes very difficult to impossible. In such situations, several scholars have recommended obtaining an estimate of the standard deviation of distributions by dividing the range of the distribution (highest value minus lowest value) by four. However, there appears to be little evidence to confirm the validity of this approach. Articles from 2012 to 2015 in the journal Marriage & Family Review were surveyed to find instances where demographic variables (age, education, duration of relationship, number of children) were reported with both standard deviations and ranges. Ratios between range and standard deviations were calculated by several rules of thumb or more complex formulas and compared with the actual ratios obtained. Results indicated that dividing by five in general provided a more accurate estimate of actual standard deviations but accuracy in predicting the true ratio between range and standard deviation was substantially related to the position of the mean score within the range of scores with larger divisors needed as the mean approached either the minimum or the maximum values of the demographic variable (skew). Other recent formulae for estimating the standard deviation were also evaluated, but the skew-based approach appeared to be more accurate than the others. However, further investigation in other samples is needed because the skew-based approach was derived from observation of the data here, which might not replicate in different sets of data.