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I want to know what statistic should be used to investigate whether there is or not a correlation between specific sleep disorder and a certain personality trait.

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I depends on many things, such as: 1. What scale are yours measures on (ordinal, nominal...)? 2. Do you have any controls (e.g. gender, age)? – Nikita Samoylov Aug 1 '12 at 5:21
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I'll second @Nikita: you will need to provide more information for this answer to be answerable. You also need to specify whether you want to quantify such an association, or test its strength against a fixed (a priori) value. – chl♦ Aug 1 '12 at 9:58

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