Re: Who first used the T-score?

naught@xxxxxxx wrote in news:e9d6de$u8j$1@xxxxxxxxxxxxxxxxxxxxx:

Did the OP mean t-score or t-test? What David ably provides is a
description of what is commonly called the t-test. T-scores, OTOH,
are one of many ways of standardizing scores, in this case, setting
the mean = 50 and sd = 10, as in the intelligence and psychometric
literature. I don't know it's origins but my money would be on one of
the early intelligence testing people.

I provided information regarding the development of the t distribution.
You do not appear to understand that both the t-test and t-scores derive
from that common source. Gosset's breakthrough was in recognizing that a
different (from the Normal) distribution was needed when small samples
were taken and inference was desired on the basis of the sample mean and
variance.

Standardizing to a mean of <some_big_number> and a variance of
<some_other_number> does not require the use of a t distribution, since
that could just as easily result in a z-score. The process you describe
is more accurately called standardization. If the "true" mean and
variance is unknown and the sample mean and variance are used in their
place, then your suggested implementation would be one of many possible
T-scores.

My understanding (though I do very little psychometrics) is the more
commonly used convention in intelligence testing standardizes to a mean
at 100 and standard deviation at 10. The numbers are arbitrary. The SAT
uses 800 and 100.

--
DW


tennisfan <butlerme@xxxxxxxx> wrote:
David, thanks for the interesting info.

David Winsemius wrote:
"tennisfan" <butlerme@xxxxxxxx> wrote in
news:1152904077.713401.155840 @h48g2000cwc.googlegroups.com:

I was explaining what a T-score is to my boss this morning and he
said 'why is it that formula'? Does anyone know who first
introduced the T-score and why? Thanks in advance.


I think most would give the credit to Gosset. It was developed to
predict small-sample properties for continuous random variables.

http://en.wikipedia.org/wiki/William_Sealey_Gosset
http://www.mrs.umn.edu/~sungurea/introstat/history/w98/gosset.html

...but the anonymous author of the current Wikipedia entry says
Fisher modified Gosset's results to derive what we today call the
t-distribution:

"Gosset's statistic was z = t/sqrt(n - 1). Fisher introduced the
t-form because it fitted in with his theory of degrees of freedom.
Fisher was also responsible for the applications of the
t-distribution to regression."

--
David Winsemius



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