Λεπτομέρειες βιβλιογραφικής εγγραφής
| Τίτλος: |
Characterizing the back-transformed standard deviation and closely related quantities. |
| Συγγραφείς: |
Chatfield, Mark D.1 (AUTHOR) m.chatfield@uq.edu.au, Dobson, Annette J.1 (AUTHOR), Marquart-Wilson, Louise1 (AUTHOR), Farewell, Daniel M.2 (AUTHOR) |
| Πηγή: |
Communications in Statistics: Theory & Methods. 2026, Vol. 55 Issue 17, p5663-5668. 6p. |
| Θεματικοί όροι: |
*Standard deviations, Inverse functions, Arithmetic mean, Lognormal distribution, Data transformations (Statistics), Statistical measurement |
| Περίληψη: |
The standard deviation of a random variable is the quadratic mean absolute deviation. We consider whether similar statements can be made for back-transformed standard deviations of transformed variables and closely related quantities. We show f − 1 (SD (f (X))) is a quasi-arithmetic mean of the back-transformed absolute (transformed scale) deviation, subject to some conditions. In the special case where the log transformation is used on a positive-valued random variable, the geometric standard deviation arises. It is a quasi-arithmetic mean of the multiplier or divisor that describes how the random variable is higher or lower than its geometric mean, respectively. Corresponding statements are also provided for the coefficient of variation, standard error, root mean square error and their geometric counterparts. [ABSTRACT FROM AUTHOR] |
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