Well, I guess to be fair we have to remember that Gosset originally
used z instead of t for his formulas in 1908. It was later that
Fisher came along and changed Gosset's z to t (and added the df
concept in I believe) because he wanted to use z for something
else... I believe it was Gosset though that, when introducing the
concept of his z (now t) in 1908 referred to it as the difference
between a sample mean and the population mean divided by the standard
deviation of the sample, so that z was a measure in terms of standard
deviations (of the sample)... it could be that Fisher took this
concept and made z equal the mean difference divided by the SD of the
population instead of the SD of the sample while at the same time
arbitrarily renaming Gosset's z to t and changing it to be divided by
the DF instead of just the sample size. There was a "feud" between
Fisher and Pearson, whom Gosset thanks a lot in his work, so it
easily could be that Fisher chose to use z just to irritate Pearson
and Gosset... though he might have given a reason somewhere later. I
haven't had a chance to go back and re-read everything related to
this to figure out the exact details, but most of these original
works are available on-the web, just not all in one spot... I'm not
sure what it says about me that I find the history of statistics so
interesting...
- Marc
PS- For others who are (or might be) interested in the history of
statistics , I do recommend "The Lady Tasting Tea: How Statistics
Revolutionized Science in the Twentieth Century" by Salsburg if you
haven't read it already... and I welcome other recommendations people
might have on the topic :)
At 06:10 PM 10/3/2007, you wrote:
In that case, since Fisher didn't bother to enlighten us as to the
meaning of z, I have a perfectly logical (which, in all things
etymological, is synonymous with "wrong") explanation you can feel
free to hand out to anyone who asks (please don't give me credit).
It is called the z-distribution, short for the "zero distribution",
since 0 is the mean, median and mode of the distribution. This
explanation has the advantage of being face valid and, evidently,
unless deeper research finds additional information, irrefutable.
=============================================
G. Marc Turner, PhD, MEd, Network+, MCP
Senior Lecturer & Technology Coordinator
Department of Psychology
Texas State University-San Marcos
San Marcos, TX 78666
phone: (512)245-2526
email: [EMAIL PROTECTED]
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