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I am writing a statistics text and I am not sure if I should either use "non-significant variables" or "not significant variables" (or anything else).

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It depends on the position of the adjective: You have to say "this is a non-significant variable," but you can say "this variable is not significant" or "... non-significant". (There may be a better technical term; if there is, hopefully somebody will give it in an answer.) – Peter Shor Jul 30 '13 at 17:34
There's not enough context to make a recommendation about the technical meaning. A common topic in statistics is a test of significance, or significance level, but these are applied to data sets (e.g. in view of an experimental hypothesis), and I'm having trouble conceiving of how it will be applied to a variable. – hardmath Jul 30 '13 at 18:04
In fact, I should probably refer to "non-significant variables". I just edited my question, thanks to @hardmath. – Costanza Jul 30 '13 at 18:51

@PeterShor's comment is also correct from a statistical point of view. Generally, though, we refer to the significance of a test statistic not a variable since there is no way to test whether a variable is significant, only a relationship, comparison, difference, etc. So, for example, in a regression model of y on x, the coefficient on x is non-significant | not significant. The x variable cannot be significant on its own.

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+1 for pointing out that a variable cannot be significant. – terdon Jul 30 '13 at 18:05
@terdon and Thomas, but if you have a significant correlation between vitamin deficiency and disease, is not this represented using a viariable? – user19148 Jul 30 '13 at 18:25
@Carlo_R. The correlation is significant, not either of the variables. – Thomas Jul 30 '13 at 18:28
@Carlo_R. I've never heard the word "significative". – Thomas Jul 30 '13 at 18:41
@Carlo_R. Try other dictionaries. ODO says significative is "rare: being a symbol or sign of something; having a meaning". Chambers & Longman don't list it. – TrevorD Jul 30 '13 at 19:40

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