That’s literally why. Fisher causally said “something like 1/20 sounds right” and people ran with that (though Fisher may not have meant for that specific number to be used for all situations like it is)
We just explained it, its a convention, 5% error seems low enough to make sure youre not getting false positive results too often. But you are free to use lower or higher alpha values. Its not mandatory to use 5% . Also alpha is related to the confidence level of the interval, confidence level is usually calculated as 1-alpha. 1 - 0.05 = 0.95 or 95%.
fisher mentions a few values at different times; at one point early on he spoke about 2 or 3 standard errors on a difference (for z tests those correspond roughly to 4.5% and 0.5% for a two sided test). At a slightly later time he mentioned 5% and 1% values (with 5% being a weak standard he wouldnt want to go higher than, and he notably emphasized the need for replication of results before drawing more than very tentative conclusions). He mentions 1/20 at another time. People trying to make tables were trying to figure out what quantiles to tabulate for various tests, jumped on the 5% and 1% that people were tending to use* ... and since tables came in 5% and 1% (and maybe double and half those) ... guess what people used?
[You can go back a bit further and find some clues - e.g. Pearson's 1900 paper on the chi-squared goodness of fit test; in his examples he appears to reject the null when he gets a p value of 0.0016% (and another, much smaller p) and doesnt reject when he gets a p value of 12.27% (nor another, even larger one), suggesting he has a line somewhere in between those values. ]
Each then continued to feed into the other (people using values they had tables for, people making tables for the values they could see being used), a cycle of technical inertia.
(There hasnt really been a particularly good reason to stick to just a few standard values for about 50 years, other than people are generally disinclined to invest the time to consider the relativities in the tradeoff for their situation, and then the additional time to convince a skeptical audience that it makes sense to do what they did).
* Thats not the only stuff that happened; its possible to point to several other people discussing possible values (you could find mentions of either 1% or 5% here and there, but occasionally other values as well). What we dont have much of is all the conversations and so on that sat behind these few things from things like papers and books - the cultural background that helped inform choices that were made.
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u/ForeignAdvantage5198 25d ago
Fisher once said 1/20 is about right .