¿Por qué 0.05?

¿Por qué usamos p=0.05 como umbral de significancia? ¿Cuáles son los motivos históricos detrás de dicha decisión? ¿Tiene ventajas? ¿Inconvenientes?

Quien quiera conocer en qué contexto dijo R.A. Fischer que

[…] for in fact no scientific worker has a fixed level of significance at which from year to year, and in all circumstances, he rejects hypotheses; he rather gives his mind to each particular case in the light of his evidence and his ideas. Further, the calculation is based solely on a hypothesis, which, in the light of the evidence, is often not believed to be true at all, so that the actual probability of erroneous decision, supposing such a phrase to have any meaning, may be much less than the frequency specifying the level of significance.

o cómo aceptaba hipótesis con p-valores de 0.089 o las rechazaba con otros de 0.088 podrá satisfacer su curiosidad leyendo el capítulo Why P=0.05? del libro The Little Handbook of Statistical Practice de Gerard E. Dallal.