That's fine, but then your power is low, and nearly every result you get will be an exaggeration. The more stringent your p value threshold, the more dramatic your results must be to be significant; if your sample size isn't adequate, you'll only get significance if you overestimate the effect.

This is an enormously common problem even with current p value thresholds. It's part of the reason why you see dramatic "A causes B!" results followed by replications saying "well, only a little."

http://www.statisticsdonewrong.com/regression.html#truth-inf...