Transform SPSS score to percentage
July 21, 2007 6:24 AM   Subscribe

SPSS / Stats question: Its Saturday morning and I'm working on my dissertation. I'm also pretty much of a dumbass in terms of stats, and some of my usual sources of help are unavailable. Anyway, I've got 400 student scores from a test. The test was out of 100 points. So a student that got an 85 got an 85/100, therefore their score seems to be in the 85th percentile.

However one of my dissertation committee members wants me to recode the scores to a percentage.

My first thought was 'Its already a percentage!'. However in doing some digging, I've found the 'Transform' section of SPSS, as well as discussion on 'Transform>Rank'. A lot of it makes sense and I've piddled around with transforming the date into a new variable through rank. However the new, transformed rank variable simply puts the students into a new rank that is close to the original.

If, instead I do a Transform>Different Variable, I'm not sure what transformation I should use.

Are the scores already a percentile, or should I look into transforming the student scores into a new variable either by rank or by some other computation?
posted by rryan to Education (10 answers total)
First off, there is a difference between a percentage and a percentile. In your case, the percentage is what % of the questions they got right, while the percentile is how they rank compared to the rest of their class. If it's a really dumb class, for example, a 66% may be in the 85th percentile.

I'm now thinking off the top of my head as to how you would do this in SPSS. You would first need to know the top score in the class. You could eyeball this. Then compute into different variable:

percentile = score/topscore * 100

I suppose it would be more elegant to use transform, but this is dirty, quick, and should work.

Usual disclaimers abound: IANAS, IANYS, but IAPHD.
posted by lleachie at 6:35 AM on July 21, 2007

Imagine that you gave your test to a million people. There would emerge from that, a distribution (think a histogram) of how common different scores were. The value at 85 would be the number of kids who got an 85. Next imagine that instead of a histogram you made a new plot where you added up all the people below a given number. So now, the value at 85 would be the number of kids who got an 85 or less. So the value at -1 would be 0 (you can't get that low) 0 would be the number that got a 0, and the number at 100 would be a million (since everyone got 100 or less by definition). Finally, divide the chart values by a million, so that instead of going from 0 to a million to goes from 0 to one. This is how you can think of the "population distribution" of your test scores.

When someone asks what your percentile on a test is, they're interested in that last plot (times 100). So if you got an 85, and 60% of the population would get an 85 or worse, your "percentile score" would be 60%.

The scores are already a "percentile" in that they are out of 100. However, when most people discuss "percentile" on a test, they mean your rank in the population. Since you don't have a population to start with, they want just the rank of each student in your sample divided by 4 (rank/400*100).
posted by a robot made out of meat at 6:36 AM on July 21, 2007

Also, I have to point out that score/max*100 is absolutely positively not a percentile score in the way that your committee member wants. They want ranks. I don't do SPSS (I'm an R person), and without knowing how you've got your data set up (hopefully a 400x2 matrix (ID, Score)?) I can't tell you exactly what commands to use.
posted by a robot made out of meat at 6:47 AM on July 21, 2007

percentile = score/topscore * 100

No! Percentiles are calculated on ranks, not scores.

The scores are already a "percentile" in that they are out of 100.

No, they aren't a percentile in any sense. Percentile has a specific meaning as both you and lleachie have alluded to.

The first link in a Google search for [spss percentile] seems to explain how to do it in SPSS.
posted by grouse at 6:56 AM on July 21, 2007

Thanks for the quick responses. The difference between percentage (85/100 or 85%) and rank within the population makes sense. Grouse: I had just found the Google return you linked to and am working through that right now- thanks for the page. Lleachie and 'a robot made out of meat'- thanks for the clarification as well. I'm now working through the spss calculations to get what my dissertation member needs.
posted by rryan at 7:07 AM on July 21, 2007

Percentile rank:

More SPSS-specific info (includes examples).
posted by charmston at 9:38 AM on July 21, 2007

Gah, I didn't know that it would strip my image. This image was originally embedded in the above post.
posted by charmston at 9:38 AM on July 21, 2007

I've got 400 student scores from a test. The test was out of 100 points. So a student that got an 85 got an 85/100, therefore their score seems to be in the 85th percentile.

My suspicion, reading these sentences, is that you're not going to be able to fix this yourself, even with the help from the above answerers. Does your university have a statistician you could pay to help you?

The first problem you have is not understanding what percentile means. If a student scores in the 85th percentile, that means that 85% of the other students scored worse than he did, and 15% scored better. Knowing someone's raw score (85/100) does not help in knowing what percentile they scored in; the percentile of an individual student is a function of the distribution of the scores.

For example, if the student scored 85 and all other students scored 100, he is in the 1st percentile. If the student scored 85 and all other students scored 15, he is in the 99th percentile. If 40% of the other students scored higher than 85 and 60% of the other students scored lower than 85, he is in the 60th percentile. I suggest that if you're starting from a place where you don't know about percentiles, you're not going to be immediately capable of using SPSS to give yourself reliable, useful analysis.

The second problem that you have is that you've not explained what the goal of your analysis is. "What hypothesis are you trying to disprove?" is the question that is usually asked by statisticians. Since the statistical analysis should generally be designed before the data is collected, you're already somewhat behind the 8-ball.

It's not possible to suggest helpful ways to analyze the data you have if we don't know what you're trying to do. Since you don't understand that we need to know what you're trying to do before we can suggest a method of statistical analysis, I suggest that you do not have enough of an understanding of the principles and practice of statistical analysis to be able to use it reliably for your purposes. You need professional help.

I don't mean this to be offensive or harsh. I think that the more time you spend trying to figure this out on your own, the more time - of your own and your committee's - you will waste, and maybe it's useful to you to know that.
posted by ikkyu2 at 12:23 PM on July 21, 2007

I am a statistician who helps PhD students with their analyses. Listen to ikkyu2 and get help.
posted by naturesgreatestmiracle at 3:00 PM on July 21, 2007

I could be reading the question wrong, but it sounds to me like you have a vocabulary problem, not a stats problem: You have a percentage, the 85%. You wrote that this percentage was a "percentile," which is the wrong word for describing what you had. Your committee member, thinking that the 85 was a percentile (since that's what you wrote) instead of a percentage (which is what it actually is), asked you to switch the numbers to percentages.

Which is what you have. You just used the wrong word. So it doesn't sound like you have to transform any data, just change the way you labeled that data so that it correctly describes the data you currently have.

(I could be totally wrong on this, so check it with someone else before assuming I know what I'm talking about.)
posted by occhiblu at 12:48 PM on July 22, 2007

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