Title: Usually it is advisable to avoid "usually" in statistics
Other Titles: rapid response
Authors: Goedhuys, Jo # ×
Issue Date: 21-Oct-2005
Publisher: B M J Group
Series Title: BMJ Open vol:331
Article number: 903
Abstract: Altman and Bland state that "about 95% of observations of any distribution usually fall within the 2 standard deviation limits". However, using the Chebyshev Inequality, we know that only 75% (or more) of observations fall between these limits. To be sure of 95% or more of the observations we need 4.5 standard deviations.

In line with the attempt to explain difficult statistics in a simple way, as the authors always do in an excellent manner, I see no problem with the following sentence. "If you don't know what your distribution really looks like, whether it is unimodal or not, symmetric or not, ... you can use the following rule: there is always at least 1-(1/k square) percent of observations between k standard deviation limits. Thus for values of k = 2, 3 and 4 we know that at least 1 - 1/4 = 75%, 1 - 1/9 = 89% and 1 - 1/16 = 93% of observations respectively, can be found in the area between 2, 3 and 4 standard deviation limits."
ISSN: 2044-6055
VABB publication type: VABB-1
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Academic Center for General Practice
× corresponding author
# (joint) last author

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