Centile estimation                                                 (STB-8: sg7)
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	^centile^ [varlist] [^if^ exp] [^in^ range] [^, c^entile^(# [# ...]^)^
		^cc^i ^n^ormal ^m^eansd ^l^evel^(^#^)^


Description
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^centile^ calculates the centiles of varlist specified by the list in ^centile()^.
If varlist is not specified, all variables are used.  If ^centile()^ is not
specified, medians (^centile(50)^) are reported.

By default, centile uses a binomial method for obtaining confidence intervals
that makes no assumptions as to the underlying distribution of the variable.
If the data contains many ties, however, the the intervals may not be valid.


Options
-------

^centile(^# [#...]^)^ specifies the centiles to be reported and defualts to
    centile(50) if not specified.  Specifying ^centile(5)^ would report the 
    5th (per)centile.  Specifying ^centile(5 50 95)^ would report the 5th, 50th,
    and 95th centiles.

^cci^ prevents centile from interpolating when calculating the distribution-free
    (binomial-based) confidence limits.  ^cci^ stands for conservative confi-
    dence interval.  The resulting intervals are generaly wider than the 
    default (interpolated) intervals.

^normal^ specifies that confidence intervals are to be obtained assuming that
    both the data and the centiles are normally distributed.  Also see the
    ^meansd^ alternative, below.  

^meansd^ specifies that the data are again to be assumed to be normally distri-
    buted.  Centiles are calculated as the sample mean plus k standard devia-
    tions, where k is determined from the centiles of the standard normal 
    distribution (e.g., k=1.645 for the 95th centile).  Confidence intervals
    are calculated assuming that the estimated centiles themslves are normally
    distributed.  For example, with ^meansd^, the 50th centile (median) is taken
    as the sample mean and a 95% confidence interval is the mean plus or minus
    1.96 times the estimated standard error of the mean.

^level(^#^)^ specifies the significance level, in percent, for the confidence 
    interval and defaults to 95 or the value set by ^set level^; see ^help level^.



Examples
--------

 . ^centile x, centile(5 50 95)^
		calculates the 5th, 50th (median) and 95th centiles for x,
		not assuming normality.

 . ^centile x y, centile(2.5 97.5) meansd^
		calculates 2.5th and 97.5th centiles for x and y from their
		means and standard deviations, assuming normality.

 . ^centile x, centile(10) normal^
		calculates the 10th centile for x, assuming normality.


In each case 95% confidence intervals for the specified centiles are provided.


Warning
-------

The formulas used for obtaining centiles are slightly different than those
used by ^summarize, detail^.  See sg7 (STB-8) for technical details.


Saved Results
-------------

^centile^ saves in the ^$S_^# macros:

	^S_1^   number of observations
	^S_2^   number of centiles requested
	^S_3^   last centile requested
	^S_4^   last estimated centile
	^S_5^   last estimated lower confidence limit
	^S_6^   last estimated upper confidence limit
	^S_7^   first requested centile of final variable in varlist
	^S_8^.. 2nd,... requested centile of final variable in varlist, if any


Author
------

Patrick Royston, Royal Postgraduate Medical School, London.


Also see
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    STB:  sg7 (STB-8)
On-line:  ^help^ for ^ci^, ^lv^, ^summarize^