Re: TDist Formula and Explanation
- From: Bruce Weaver <bweaver@xxxxxxxxxxxx>
- Date: Thu, 29 Mar 2007 08:33:20 -0400
Jack Tomsky wrote:
********Thanks for the post. It will certaintly serve as a
good source for
reference. However, I'm still struggling with
implementing the nuts
and bolts of the formula to come up with a valid
result. I've tried
to use the incomplete beta function to calculate the
p-value, but I'm
still getting skewed results. Using the results
listed below I find
that a = 0.5, b=9, x'=.894102 (using the formula:
(df_Regression * F
Statistic)/(df_Regression * F Statistic +
df_Residual). These values
should (I think) be my input to the incomplete beta
function.
However, when I put these inputs into the formula I
get results that
are consistently high. Is there something that you
see that I'm doing
incorrectly? If not, is there some guidance you
could provide on how
to use the formula?
X Y
28 5.2
26 5.1
32 5.6
24 4.6
54 11.3
59 8.1
44 7.8
30 5.8
40 5.1
82 18
42 4.9
58 11.8
28 5.2
20 4.8
42 7.9
47 6.4
112 20
85 13.7
31 5.1
26 2.9
I put your data into Minitab. I get y = -0.412 + 0.184*x as the fitted regression.
The standard error of beta is 0.1493 and t = 0.184/0.1493 = 12.3
That should 0.01493.
With 18 degrees of freedom, Excel calculates the right tail probability as 1.64E-10 if it's a one-sided test and 3.28E-10 if it's a two-sided test.
If your problem is to calculate small tails (i.e., large t), those expansions in A&S might turn out to be pretty accurate.
BTW, I had a problem downloading A&S online, but I still have the hard copy.
Jack
Re the OP's question about how to compute the p-value in Excel:
=TDIST(abs(t),df,tails)
--
Bruce Weaver
bweaver@xxxxxxxxxxxx
www.angelfire.com/wv/bwhomedir
.
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