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Which Significance Test?

I have a population of 4,780 users who answer 50 questions from a personality test. The responses are tabulated into a score for each of the four personality types that all add up to 50.

Given that I have statistics for an individual and statistics for the 4,780 user population is there a significance test that I can apply to determine whether the difference between the scores for different traits is significant for an individual?

Example:

Thinker (20), Feeler (15), Risk taker (10), Conservative (5)

I'm guessing that I could show that the preceding example has a significant difference between Thinker and Feeler and Risk taker and Conservative, but that the following example would not show significance:

Thinker (13), Feeler (13), Risk taker (12), Conservative (12)

The population has the following mean() and std deviation[]:

Thinker (12.98) [4.06], Feeler (11.91) [3.76], Risk taker (12.70) [3.50], Conservative (12.40) [3.69]

What test can I use and how can I apply it?

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    $\begingroup$ Thinker (20). Is 20 a score on the numerical scale or ordinal scale? $\endgroup$
    – SmallChess
    Commented Mar 6, 2017 at 3:44
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    $\begingroup$ You need to explain the problem more clearly. $\endgroup$
    – Michael R. Chernick
    Commented Mar 6, 2017 at 5:17

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It doesn't make sense to talk about the differences across variables being significant 'for an individual' - when you are doing significance testing you are trying to reject the null hypothesis that, in the population that your sample is drawn from, the value of the parameter in question is zero (given sampling variation) - as the logic of drawing a sample and then trying to make inference back to the population doesn't apply to a single case, you can't say that bob is 'significantly' more 'thinker' than sam.

So the answer is none - the whole framework of significance testing doesn't apply to individual differences.

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  • $\begingroup$ But I'm trying to say that Bob is more of a thinker than a feeler with some statistical significance. It seems like one should be able to do something like this. $\endgroup$
    – user3654387
    Commented Mar 6, 2017 at 4:15
  • $\begingroup$ If you have repeated measures on bob, then yes it may be reasonable, under the assumption that the test scores vary over time and you're trying to estimate bob's 'true' score for thinking or feeling - with a single observation I don't think so. $\endgroup$
    – MartinQLD
    Commented Mar 6, 2017 at 4:17

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