Hi, David,
I think you're confusing the q-th percentile of your data, i. e., the
empirical q-th percentile, which is -- roughly -- the value x_q for which
q * 100 % of the data are less than or equal to x_q, with the q-th
percentile of a distribution (here the normal distribution) that has as
population mean the arithmetic mean of the data and as population standard
deviation the standard deviation of the data. Those are different things.
Your SPSS code seems to compute the empirical quantile, but you R code
produces the other quantile. To get empirical quantiles of your data in R
see
?quantile
Hth -- Gerrit
On Thu, 8 Nov 2012, David A. wrote:
Dear list,
I am calculating the 95th percentile of a set of values with R and with SPSS
In R:
normal200<-rnorm(200,0,1)
qnorm(0.95,mean=mean(normal200),sd=sd(normal200),lower.tail =TRUE)
[1] 1.84191
In SPSS, if I use the same 200 values and select Analyze -> Descriptive Statistics
-> Frequencies
and under "Statistics", I type in '95' under Percentiles, then the output is
Percentile 95 1.9720
I think the main difference is that SPSS only calculates critical values within
the range of values in the data, while R fits a normal and calculates the
critical value using the fitted distribution. This is more obvious if the size
of the data is much lower:
normal20
[1] 0.27549020 0.87994304 -0.23737370 0.04565484 -1.10207183 -0.68035949
0.01698773 -2.15812038 0.26296513 0.21873981 0.03266598 -0.01318572
[13] 0.83492830 0.54652613 0.73993948 -0.31937556 -0.03060194 -0.96028421
0.27745331 -1.01292410
max(normal20)
[1] 0.879943
qnorm(0.95,mean=mean(normal20),sd=sd(normal20),lower.tail =TRUE)
[1] 1.118065
And in SPSS
Percentile 95 0.8777
Can anyone comment on my statement? and thus, is R more exact? The differences
are quite large and this is important for setting thresholds.
Cheers,
Dave
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Dr. Gerrit Eichner Mathematical Institute, Room 212
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