I am conducting a Two-Way ANOVA test on a set of data, with replication; there are two variables, each with 3 different categories (thus, 9 different groups). Each group has 4 data points, bringing the total data set to 36 points. I conducted a Two-Way ANOVA test by hand (and confirmed the results with Minitab and Excel), and I am confident (pun not intended) with the accuracy of my $p$ values.
However, I am unsure of what an appropriate significance level is. All the literature I've read on introductory statistics assumes a 0.05 significance level; should I also assume the same? Is such a level based on personal preference? What justifies selecting 0.05?
