Dear Statalist:
I am having trouble replicating the normal confidence
limits produced by -centile-. The manual states that
the standard error (Sq) of a given quantile, Cq, may
be computed under the assumption of normality using
the equation on p. 202 in the Stata Reference Manual
(Release 9, A-G). However, I have to multiply Sq by
sqrt(n) to get the same endpoints as Stata. My sample
code and output are provided below.
I am not sure why I cannot replicate Stata's results
using the equation presented in the manual. Given
that I can approximate the limits produced by
-centile, normal- using the bootstrap, I suspect that
the notation in the manual may be incorrect. I do not
have access to the original source (Kendall & Stuart)
and am therefore unable to verify whether or not this
is the case.
Regards,
Jim
. drawnorm y
. qui: summ y
. scalar sm1= r(mean)
. scalar sd1 = r(sd)
. scalar sn = r(N)
. qui: centile y, normal
. scalar smd2 = r(c_1)
. scalar stul = r(ub_1)
. scalar stll = r(lb_1)
. /* from Stata */
. scalar li smd2 stul stll
smd2 = .02788301
stul = .10364515
stll = -.04787914
. scalar sq =
sqrt(50*(100-50))/(100*sn*normalden(smd2,sm1,sd1))
. /* using formula given in manual */
. scalar ul11 = smd2 + sq*invnormal(.975)
. scalar ll11 = smd2 - sq*invnormal(.975)
. scalar li smd2 ul11 ll11
smd2 = .02788301
ul11 = .03027881
ll11 = .0254872
. /* multiplied by sqrt(n) */
. scalar ul12 = smd2 + sq*invnormal(.975)*sqrt(sn)
. scalar ll12 = smd2 - sq*invnormal(.975)*sqrt(sn)
. scalar li smd2 ul12 ll12
smd2 = .02788301
ul12 = .10364515
ll12 = -.04787914
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