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TDIST and TINV
For some reason the developers of Excel wrote the TDIST and
TINV
functions to act differently than NORSDIST and NORSINV and
other
similar functions in Excel!
TDIST
NORSDIST"#$ %ives the pro&a&ility "area$ to the left of
#!
TDIST %ives the area to the ri%ht of t' and on top of that it
only wor(s for
positive values of t ) you have to tric( Excel to ma(e it wor(
for ne%ative
values of t! *nd+ of course+ if you do want the area to the left
of t it will
e,ual - ) "area to the ri%ht of t$!
The %eneral form of TDIST is . TDIST"t+ de%rees of freedom+ - or
/$!
The last ar%ument+ the - or /+ states whether you are doin% a
-0tail or a /0tail
hypothesis test! This is &ecause that+ in %eneral+ TDIST is
used to %et the p0
values for t0tests!
Now remem&er for 123 tests the p0value is the area to the
ri%ht of t! *nd+
usually when you have a 12 test3 you will %et a positive value
of t! So+ for
example if you %et t . /!45 and have /6 de%rees of freedom+ the
p0value for
the 12 test3 would &e %otten &y7 . TDIST"t+df+-$ .
TDIST"/!45+/6+-$!
For a 183 test+ the p0value is the area to the left of t! *nd+
usually when you
have a 18 test3 you will %et a ne%ative value of t! Now
&ecause the t0
distri&ution if symmetric+ everythin% to the left of a
ne%ative value of t is
everythin% to the ri%ht of the correspondin% positive value of
t! So+ for
example if you %et t . 0-!95 and have -/ de%rees of freedom+ the
p0value for
the 18 test3 would &e %otten &y7 . TDIST"0t+DF+-$ .
TDIST"-!95+-/+-$!
For 1:3 or /0tailed test the p0value is %otten &y
TDIST"t+DF+/$ if t is positive
and TDIST"0t+DF+/$ if t is ne%ative!
Now if t is ne%ative for a 123 test+ the p0value will &e 2
!; since it is the area
to the ri%ht of a ne%ative t0value! This is - ) "area to the
left of the ne%ative t0
value$ . - ) "area to the ri%ht of the correspondin% positive
t0value$ .
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- ) TDIST"0t+df+-$! Similarly if t is positive for a 183 test+
the p0value . -0
TDIST"t+DF+-$!
So the followin% chart summari#es the p0values for t0tests!
*ssume t has &een calculated and is cell E4 of the
spreadsheet!
TEST t p0value Example
TEST t DF
"in cell E4$
p0value
2 2< TDIST"t+DF+-$ 2 /!45 /6 .TDIST"E4+/6+-$
8 8< TDIST"0t+DF+-$ 8 0-!95 -/ .TDIST"0E4+-/+-$
: 2< TDIST"t+DF+/$ : -! 9 .TDIST"0E4+9+/$
2 8< .-0TDIST"0t+DF+-$ 2 0
