Manual Formula for p-value Calculation for MSA Analysis

Rameshwar25

Quite Involved in Discussions
#1
I use excel's tinv function to calculate p-value for msa analysis. I want to know whether I can manually calculate p-value. Are there some reference tables? or there is a direct formula?
 
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Statistical Steven

Statistician
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Super Moderator
#2
I use excel's tinv function to calculate p-value for msa analysis. I want to know whether I can manually calculate p-value. Are there some reference tables? or there is a direct formula?
There are tables for the p-value of the t-distribution available in almost all statistical textbooks. If you want to caclulate it manually you would need to integrate the probability density function of the t-distribution. Not something I would recommend. :)
 

Miner

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#6
Miner, Please explain how to refer these tables for following values:
T-static=.1224
df=14
alpha=0.05

Thanks in advance
First decide whether it is a one or two-tailed test.

I will illustrate using the University of Missouri's table and a two-tailed test.

Use the Tail Probability, 2-tailed column on the left side and follow it down to the row marked 0.05. This is the alpha value. Follow this row across to the right until it intersects the two columns marked 12 and 15 degrees of freedom.

The critical value of t for 12 df is 2.179 and for 15 df is 2.131. You can interpolate the critical t-value for 14 as follows.

(15-14)/(15-12) = (t - 2.131)/(2.179 - 2.131)
1/3 = (t-2.131)/0.048
0.048/3 = t - 2.131
0.016 + 2.131 = t
t = 2.147; If the t - statistic is >= 2.147, then Ho is rejected.

In your case t = 0.1224. This is << the critical value of t (2.147), so you fail to reject Ho.

Ho: there is no difference (because this is a 2 - tailed test)
Ha: there is a difference
 

Rameshwar25

Quite Involved in Discussions
#7
Miner, Thanks for reply. But my query was regarding p-value instead of t-value.

for t=0.1224, df=14 and tails=2 , excel's tdist function returns p-value=.904322. Can i get this p-value using tables. If yes, how?
 

Miner

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Staff member
Admin
#8
You have to work the table in reverse.

Find the 15 df column and follow it down until you bracket the t - value of 0.1224. In this case it is between the 1st and 2nd rows.

Next, interpolate both table t - values for 14 df. The method is the same as I illustrated in the previous post.

Go over to the two-sided tail probability and interpolate the probability for a t-value of 0.1224 using the two values that you just interpolate.
 
P

p_tww

#9
You have to work the table in reverse.

Find the 15 df column and follow it down until you bracket the t - value of 0.1224. In this case it is between the 1st and 2nd rows.

Next, interpolate both table t - values for 14 df. The method is the same as I illustrated in the previous post.

Go over to the two-sided tail probability and interpolate the probability for a t-value of 0.1224 using the two values that you just interpolate.
Hi, Miner

could you please kindly show the detailed calculation steps, thanks
 

Rameshwar25

Quite Involved in Discussions
#10
Miner, i too tried a lot but could not calculate. Request you to tell me which table to be used and how?
for example
bias=.0067
std dev=.210
std error of mean= std dev/sqrt(n)=.0547
n=15
df=14
t-static=bias/std error of mean=.1224

using excel function =tdist(.1224,14,2) we get pvalue=.9042

how can we get the same value using tables which you have suggested.
 
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