(no subject)
BECKERW@ucs.indiana.edu
Mon, 28 Nov 94 18:39:38 EWT
In response to the inquiry about Gosset, the following is from
William E. Becker, Statistics for Business and Economics, South-
Western Publishing, 1995, pp. 309-310.
Few people think of the beer industry as employing path
breaking scientists. Yet, William S. Gosset (1877-1937)
invented the t distribution while working for Guinness
brewery in Ireland.
William Gosset recognized that in most applications
involving the estimation of the population mean, the value
of the population variance is unknown. In 1908 he published
"The Probable Error of a Mean" under the pseudonym of
"Student." Gosset's introduction of the t distribution
eventually revolutionized statistical work with small
samples. At first, however, the wide applicability of
"Student's t" was not recognized. It was not until 1925,
when Sir Ronald A. Fisher called attention to these
applications in his textbook that they became popular in
scientific inquiry.
Gosset was a student of both chemistry and mathematics.
He learned statistics from Karl Pearson (1857-1936), one of
a few distinguished English statisticians at the turn of the
century. Unlike most scientists of his time, however,
Gosset did not pursue a life in academe.
Gosset made his major scholarly contribution while
working for private industry. His employer, Guinness,
employed many university educated scientists but did not
encourage scholastic publishing. Thus, Gosset published
under his pseudonym. In the United States, Chemical Rubber
Co., a private firm in Cleveland, Ohio, assumed a key role
in the preparation, maintenance and dissemination of
probability tables for statistical research. Not all
contributions in statistics have come from academic
institutions and think tanks.
Although Gosset discovered the t distribution and
Fisher perfected and popularized it, it was Edward Paulson
(1942) who provided a convenient algorithm for approximating
probabilities based on "Student's t. Paulson showed that
the area more extreme than the absolute value of t, with n -
1 degrees of freedom, could be approximated with the area in
the upper tail of the standard normal distribution.
Provided that the degrees of freedom are greater than three
(n - 1 > 3), the approximate relationship between |t| and
the value of z is ...
...
Today inexpensive statistical computer programs can
calculate probabilities associated with the entire family of
t distributions regardless of the degrees of freedom
considered. W.I. Kennedy and J.E. Gentile (1980) review
some of the alternative algorithms that are used by
programmers to achieve extremely high accuracy.