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?

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    $\begingroup$ I'll leave it to someone more knowledgeable to expand this, but the answer to your final question is: tradition, unfortunately. $\endgroup$ – Matthew Drury Aug 18 '15 at 17:20

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