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Estimating the sample variance from the sample size and range
Author(s) -
Rychtář Jan,
T. Taylor Dewey
Publication year - 2020
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.8747
Subject(s) - estimator , sample size determination , statistics , mathematics , range (aeronautics) , bounded function , sample (material) , set (abstract data type) , variance (accounting) , exponential function , data set , computer science , mathematical analysis , materials science , chemistry , accounting , chromatography , business , composite material , programming language
For meta‐analysis studies and systematic reviews, it is important to pool the data from a set of similar clinical trials. To pool the data, one needs to know their SD. Many trial reports, however, contain only the median, the minimum and maximum values, and the sample size. It is therefore important to be able to estimate the SD S from the sample size n and range r . For small n ≤ 100 , we improve existing estimators of r / S , the “divisor,” denoted by ξ ( n ) . This in turn yields improved estimators of the SD in the formS ^ = r / ξ ^ ( n ) on simulated as well as real datasets. We provide numerical values of the proposed estimator as well as approximation by a simple formula 3 ln ( n ) − 1 . 4025 . Furthermore, for large n , we provide estimatorsξ ^ ( n ) of the divisor ξ ( n ) for the normal, exponential, and other bounded and unbounded distributions.