# Re: st: RE: Quantile question

 From Maarten buis To stata list Subject Re: st: RE: Quantile question Date Mon, 3 Mar 2008 14:42:36 +0000 (GMT)

```--- Ronan Conroy wrote:
> I was involved in looking at the effect of a number of measures of
> the patient's response to illness as predictors of depression - work
> and social adjustment, symptom frequency, symptom bother, and so on.
> These were measured using standardised scales, but each scale had
> its own theoretical range, its own empirical score distribution and,
> most important, each scale was measured in arbitrary units.
>
> It was useful for the reader to be able to see the odds ratios (and
> confidence intervals) associated with a 1-decile increase in each of

> these predictors, as it gave them a way of comparing their effects
> and of judging their practical importance as well as their
> statistical significance.
>
> There are times, then, when quantiles do not lose information but
> increase it, by converting unfamiliar and arbitrary measurement
> scales to a definable measurement unit.

I think the issue is terminology here. Say we have a variable with an
arbitrary unit, say, symptom bother. The the 9th percentile is the
value of the arbitrarily scaled variable sympton bother which has 9% of
the observations below it. (http://en.wikipedia.org/wiki/Quantile)

What you seem to mean is the percentile rank, which in the example
above would be the number 9, and is a useful way of standardizing
variables: you can create a new variable with now range (0 to 100),
mean (50), standard deviation (approx. 28.6, depending on the number of
knots) and distribution (uniform distribution).

If that is the case than I agree with you. The more common alternative
(in my discipline anyhow) is z-scores (the variable minus the mean
devided by the standard deviation), and is often implicitly interpreted
in terms of these percentile ranks: a value of 1.96 is large because if
the variable is from a normal (Gaussian) distribution, 97.5 % of the
respondents will have a value less than that. Notice that you now need
scores don't make.

However, Nick is right when he points out that this is a non-linear
transformation. In particular, you will only retain information about
the ordering of values and loose information about the distances
between values.

-- Maarten

-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------

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