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pseudonym, and in 1908 published a paper in
Biometrika
that introduced
the
t
test.
The sampling distribution of
t,
as is true for
F,
depends on degrees
of freedom. The
t
distribution is
leptokurtic
-comparedtothenormal
curve, its tails are higher and the middle portion is a bit more compressed.
Gosset actually used
z
for his leptokurtic distribution, but, because that
letter came to be associated with the normal distribution, textbook writers
began referring to the leptokurtic distribution as “Student's
t
” (taking the
last letter from “Student”). It is by this name assigned by the textbook
writers that it has become known to generations of students.
4.8.2 THE RELATIONSHIP OF
t
AND
F
Gosset's
t
test and Fisher's ANOVA are algebraically equivalent, and thus
lead researchers to the same conclusions regarding a two-group com-
parison when the groups have met the assumption of homogeneity of
variance (i.e., that the groups have comparable variances). The relation-
ship between the two techniques becomes more obvious when we note
that the square of the
t
statistic is equal to the
F
value and, conversely, the
square root of
F
is equal to the
t
statistic. Thus,
t
2
=
F
and
=
√
F
t
.
(4.5)
Because of the interchangeability of
t
and
F
, Keppel, Saufley, and
Tokunaga (1992, p. 129) have suggested that it is useful for students to
learn the
t
test primarily “ . . . as an aid in understanding references to
the
t
test...[in]...the research literature and as a touchstone with the
past. . . . ”
