[R] difference percentile R vs SPSS

[Gerrit Eichner]

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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>
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---------------------------------------------------------------------
Dr. Gerrit Eichner                   Mathematical Institute, Room 212
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