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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?

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