Significance Test Cutoff: Is .05 Result Significant?

[BigPappa]

In any significance test, if the result is greater than the cutoff it is not significant, if the result is less than the cutoff it is significant. What if it is exactly equal to the cutoff (.05) is it significant or not?

 

[SW VandeCarr]

In any significance test, if the result is greater than the cutoff it is not significant, if the result is less than the cutoff it is significant. What if it is exactly equal to the cutoff (.05) is it significant or not?

Significance levels are really matters of choice and convention. As far as the matter of whether alpha is an open or closed upper bounded interval; I'm not aware of any general rule. For most research in which I've been involved, journals and regulatory agencies require a two sided alpha of p=0.05 which means p=0.025 is the significance level in each tail. A value in the closed upper bounded interval of alpha=0.025 in the right tail is considered significant for rejecting the null hypothesis in typical cases. However there are many cases where more stringent criteria are set.

(A closed bound includes the bounding value, so a right sided value of exactly p=0.025 would be significant given that alpha level. In practice, I've never seen the issue come up because the alpha cut off is a point on a continuum and therefore an exact value occurs with probability zero).