Dear colleagues
Can anyone tell the formulas used by SPSS to calculate the Percentile and the percentile ranks?
Hello Sabry,
Here's a simplified explanation:
Assume scores are in ascending order, and there are N cases.
The value corresponding to the k-th percentile would be found by linking the value, (N + 1) * k/100 to the corresponding value of cases.
For example, if you have scores 1, 2, 3...20 (N = 20) and wanted to estimate the 10th percentile, then: (a) the target case value is: (20 +1) * 10/100 = 21 * 0.10 = 2.1.
As there is no specific "2.1-th" case, you need to interpolate 1/10 of the distance between the 2nd and 3rd cases (here, having values of 2 and 3, respectively). Thus, the value for the 10th percentile would be 2.1.
The 25th percentile would be 5.25, the 50th percentile would be 10.5, and so on.
Finally, it appears that IBM SPSS no longer posts their algorithms online. Too bad; that hardly makes for a transparent system.
Good luck with your work.
I assume you are asking of the several different ways of calculating percentiles (or quantiles more generally), which does SPSS use. https://www.jstor.org/stable/2684934?origin=crossref is often used for discussing several of these measures, and in recent R help for quantiles it says Minitab and SPSS used #6. I don't have SPSS, but you could put together a few variables with lots of ties, go through the different R options for this, and see which corresponds with the SPSS values, and that would give you a good idea which it uses (if it uses one of those).
In Frequencies when specifying statistics you can be asked to identify the percentiles for the values of the variable. The example is asking you to identify the 20th, 40th, 60th, and 80th percentiles. Figure 1 attached.
Another procedure is to transform the original values into percentiles. This generates a new variable with the position in terms of percentiles for each case. This is done from the Transform - Categorize variables option. Figure 2 attached.
Many thanks for you all for your reply.
There are two definitions of percentiles: A score below which a given percentage k of scores in its frequency distribution falls ("exclusive" definition) or a score at or below which a given percentage fall.
What definition should be used when interpreting the percentile score in SPSS? Does SPSS uses different definitions of percentiles for different methods of calculating percentiles?
Also, what definition should be used when interpreting percentile rank in SPSS?
Thanks
Dear Carlos Albarracin
thank your for your reply and explanation. unfortunately, I could not locate the second screen shot in SPSS 25.0. Could you please guide me to find this window in recent versions of SPSS?
Regards
Sabry Abd-El-Fattah , you say "there are two definitions" meaning either you disagree with the paper I note (where more are noted, and you could use others), or you didn't bother looking at the paper. For either of these, more explanation would be useful. As I said, it may be what they call Type 6 that is used by SPSS, but as I said there, it is fairly easy to check.
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