In 1878, C. S. Peirce performed a calculation that (I think) would be better done using chi-squared testing — but Pearson hasn’t introduced that yet.
What exactly is Peirce doing here in the last sentence? Is it valid? almost valid? (When I did a chi-squared test, I got a different answer than he did.)
The first paragraph is straightforward enough. Where we would now say the probable error in the distribution of a sample is within +/- .6745 standard deviations, he has .477 * sqrt(2), and so on down his table.
In the next paragraph, he approximates p = 0.5 and then correctly calculates probable error on the two distributions.
But then what does he do in the last sentence?
(Once I figure that out, I’ll need to figure out if this was a common pre-Pearson approach.)