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st: Why does -centile- provide different results compared to -sum- or -pctile-?

 From "Tiago V. Pereira" To statalist@hsphsun2.harvard.edu Subject st: Why does -centile- provide different results compared to -sum- or -pctile-? Date Fri, 16 Jul 2010 15:45:25 -0300 (BRT)

Thanks, Martin!

So, are both correct in statistical terms?

Sorry for taking your time for such apparently "easy-to-find" questions.
Our Stata is institutional, and we don't have access to the manuals at the
lab.

All the best,

Tiago

Dear statalister,

Am I misinterpreting the outpus or there is something wrong with
-centile-? For example, the values for percentile 10 differ in -centile-
(89.666) compard to -sum- and -pctile- (90.66666).

Cheers!

Tiago

(Stata 9 and 10.1 provide identical results).

*/ -------- start do ---------
clear
input X
223
104.3333
198.3333
126
95
101.3333
133
90.66666
38
91
101
36.5
101
203
92.5
149
142.3333
89.33334
105.6667
123.3333
136
240.6667
162.3333
98.66666
181.6667
261
206
251
339.3333
219.3333
114
end

sum X, detail

centile X , centile(1 5 10 25 50 75 90 95 99)

_pctile X, nq(10)

dis "P10 = " r(r1)
dis "P90 = " r(r9)

*/ ---------end do -----------------

My outputs:

sum X, detail

X
-------------------------------------------------------------
Percentiles      Smallest
1%         36.5           36.5
5%           38             38
10%     90.66666       89.33334       Obs                  31
25%     98.66666       90.66666       Sum of Wgt.          31

50%          126                      Mean            146.914
Largest       Std. Dev.       69.5917
75%          203       240.6667
90%     240.6667            251       Variance       4843.005
95%          261            261       Skewness       .7895009
99%     339.3333       339.3333       Kurtosis       3.214935

.
. centile X , centile(1 5 10 25 50 75 90 95 99)

-- Binom. Interp. --
Variable |     Obs  Percentile      Centile        [95% Conf. Interval]
-------------+-------------------------------------------------------------
X |      31          1          36.5            36.5    57.78294*
|                  5          37.4            36.5
90.95187* |                 10      89.60001            36.5
95.97249* |                 25      98.66666
90.32367     107.523 |                 50           126
101.1658     172.048 |                 75           203
140.9225    243.3249 |                 90      248.9333
205.2043    339.3333* |                 95      292.3333
225.5506    339.3333* |                 99      339.3333
257.1462    339.3333*

* Lower (upper) confidence limit held at minimum (maximum) of sample

.
. _pctile X, nq(10)

.
. dis "P10 = " r(r1)
P10 = 90.666656

. dis "P90 = " r(r9)
P90 = 240.6667

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