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An Approach to the Estimation of Growth Standards: The Univariate Case
Author(s) -
FRYER J. G.,
KARLBERG J.,
HAYES M.
Publication year - 1989
Publication title -
acta pædiatrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.772
H-Index - 115
eISSN - 1651-2227
pISSN - 0803-5253
DOI - 10.1111/j.1651-2227.1989.tb11195.x
Subject(s) - transformation (genetics) , univariate , invertible matrix , power transform , monotonic function , statistics , medicine , data transformation , gaussian , mathematics , proportional hazards model , estimation , econometrics , algorithm , data mining , computer science , multivariate statistics , mathematical analysis , discrete mathematics , pure mathematics , data warehouse , biochemistry , chemistry , physics , consistency (knowledge bases) , quantum mechanics , gene , management , economics
. This paper shows how reference values can be determined when the underlying characteristic (say, weight) follows a distribution that is not too distant from the Gaussian. Application of the normalizing Box‐Cox power transformation is the basis of our approach. This transformation is monotonic and hence invertible, so offering the choice of two scales of measurement on which to work—the original and the Gaussian. Modified versions of the procedure are provided allowing use of the basic transformation in the presence of certain deficiencies in the data, principally measurement error and misclassification. It is shown that application of Box‐Cox to a cohort at several points in time can be quite revealing. When the data are already symmetrical the Box‐Cox transformation has no effect: in this case the John‐Draper modulus transformation and modifications of it are shown to be helpful. All of this is illustrated by using data from the Swedish Longitudinal Growth Study.