Type-I error: The mistake of rejecting a true null hypothesis. A maximum acceptable probability of Type-I error should be set during the design stage, before statistical analysis. Across much of the biological sciences, it is conventionally taken as α = 0.05, in which case the analysis will show significant effects if outputs yield P < 0.05.
The associated Type-II error is the mistake of accepting a false null hypothesis. A maximum acceptable probability of Type-II error should also be set during the design stage, before data collection, because the power of the design equals 1 - β. A probability β = 0.20 is often regarded as acceptable, meaning that the analysis will have a 0.8 chance of rejecting a false null hypothesis, and therefore a high probability of identifying pattern in the data if it exists.
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.