Significance: The strength of evidence for an effect, measured by a P-value associated with the F-ratio from analysis of variance. A significant effect has a small P-value indicating a small chance of making a Type I error. For example, P < 0.05 means a less than 5% chance of mistakenly rejecting a true null hypothesis. For many tests this would be considered a reasonable level of safety for rejecting the null hypothesis of no effect, in favour of the model hypothesis of a significant effect on the response. The significance of an effect is not directly informative about the size of the effect. Thus an effect may be statistically highly significant as a result of low residual variation, yet have little biological significance as a result of a small effect size in terms of the amount of variation between sample means or the slope of a regression. A non significant effect should be interpreted with reference to the Type II error rate, which depends on the power of the test to detect significant effects.
Doncaster, C. P. & Davey, A. J. H. (2007) Analysis of Variance and Covariance: How to Choose and Construct Models for the Life Sciences. Cambridge: Cambridge University Press.