Are the raw scores of the NEO-PI-R normally distributed? Scoring the NEO-PI-R test results, as done for example in this document, involves converting an absolute score to a t-score. However, the conversion from absolute score to t-score (as can be seen in the document above and many others) seems to be always linear, i.e. $t=\alpha*raw+\beta$ for some values of $\alpha,\beta$. 

Since the t-scores are normally distributed, such a linear conversion only makes sense if the raw scores are also normally distributed (and not e.g. skew in either direction). In a limited sample that I took, I noticed that some of the facets are not normally distributed, in the sense that they have a significant amount of skewness. 

Is this not a flaw in the scoring system? Or is there a (psychological) reason why we should not worry about this?
Generally,  psychological scales that are the sum of forced-choice items exhibit skew as the mean approaches the floor or ceiling of the scale. 

The test manual for the NEO-PI shows the exact relationship between raw scores for domains and facets and corresponding percentiles. So if you want to be more precise and not assume normality, you can use that data.

Here's one table showing skewness values in an officer sample from Detrick &amp; Chibnall (2013). As is typical with this kind of data, there's a little bit of skew, but it's not huge. So the normal approximation wont be too bad.



Detrick, P., &amp; Chibnall, J. T. (2013). Revised NEO Personality Inventory normative data for police officer selection. Psychological Services, 10(4), 372.