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Note: Im not sure Im using the proper "Math" term here in deviation, it is what google translate gives me for the dutch "Afwijking"

I got this question from my father in law who took a personality test to take a look at how his scores were calculated. In this test his personality traits and such are displayed as graphs/bars , to be read from the "middle", but give a result from 0 to 100 later in the test. (or -50 to + 50)

The test (in dutch) claims these values are calculated as "the difference between you and the "norm" (the dutch working population)

Q1 I was wondering how one would get such a value? Given the norm (1-100) and a score (1-100) how do you get a deviation from average on a +50/-50 scale

Q2 Say the average person has a score of 30 in a competence, and you have 15, would you get a score of 25%//25? and what if you get 60? does that give you 100%? and > 60?

example of "bars"

Durielblood
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  • I think this is a good question, but I'm still not sure what the actual question is. You mention it's a personality test, but then you talk about it measuring "competence" which doesn't seem to be a personality trait to me. Could you maybe give some links that tell more about the test, and/or pictures of the report? Also note professing to be bad at math(s) does not usually generate sympathy from those who are good at it. Just do your best to ask a coherent question. – Matthew Leingang Dec 30 '16 at 16:38
  • Removed the being bad at part. But yes appearantly your personality influences your competence. For example a salesperson is likely to be more competent if he/she s got an extravert personality and a mathamatician would likely do well to be pay attention to be organisized rather than disorganized. – Durielblood Dec 30 '16 at 16:44
  • I expect they make use of percentiles - https://en.wikipedia.org/wiki/Percentile . – Jens Dec 30 '16 at 19:39
  • @jens, having read that Wikipedia page I agree that your comment is likely correct , though if my understanding is correct that would neccecitate having a vast database of (sorted) anwers per question for each person in the dutch population for their claim to be true?. Could you make your comment into an answer and maybe add an example? – Durielblood Jan 04 '17 at 11:19

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Per your request, here's an answer.

Q1:

They presumably use percentiles as I said in my comment. Basically, you take a sorted list of $N$ values and see how many of those values (as a percentage of $N$) are less than a given value $V$. If, for example, $80$% of the values in the list are less than $V$, then $V$ is at the $80$th percentile.

It should be mentioned that there is no universally agreed upon definition of percentile (the Wiki link has several variants), but these variants are only really of interest for small $N$.

Q2:

If the "average" person had a score of $30$ in a competence, that would just mean that the $50$th percentile was $30$. Theoretically, all values in the list could be $30$ and thus the $100$th percentile would also be $30$.

However, talk about an "average" person implies a very large $N$ and furthermore implies a normal distribution. Which leads me to an answer to your question in the comments, namely: "Would this neccecitate having a vast database of (sorted) anwers per question for each person in the dutch population for their claim to be true?"

The answer is no. If they had a sufficiently large database of answers, and therefore a sufficient sample size, they could make reasonable assertions regarding the population as a whole.

I, of course, have no idea if this is how they do it. But it is a way that a reputable company could do it.

Jens
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