probable-error-of-a-mean.jpg

While looking up some papers on statistics I came across this freely-available copy of William Gosset’s March 1908 paper, almost a year before the its United States copyright expires and it becomes public domain. The paper is a very nice transcription of the original paper (available through JSTOR) which makes it much easier to read.

The point of the paper relates a statistical confidence limit and a set of bounds within which the mean of a set of measurements must lie. To be more specific, the paper addresses measurements whose distribution is Gaussian and goes on to specify how small a error bound you can place around the mean given a finite number of experiments with a finite certainty, say 95%. Furthermore, the usefulness of the paper comes from the fact that the limit is examined with a decreasing number of observations. This is useful since certain experiments cannot be performed many times and we need to be able to say how certain we are of the mean of the observed Gaussian random variable given the finite number of data points.

In a small side note, the p < 0.05 (or >95% “certainty”) is often considered to be a “good” value, but it may seem somewhat arbitrary. There are some people who attribute this to Karl Fisher, more specifically, his publication titled Statistical Tables for Agricultural, Biological and Medical Research (3.3MB). For those looking for Fisher’s historical papers, they can be found at the University of Adelaide.

( 1908student-the-probable-error-of-a-mean.pdf )

 
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