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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@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.