Difficulty with calculated t-value for Linearity

[I_am_the_Derp]

Hello Everyone,

I am currently creating a Stability, Bias and Linearity spreadsheet for some method validation work I am doing in the lab. Creating the stabilty and bias portion were quite simple; however, the linearity portion gave me some trouble. I have been using the raw data from spcforexcel.com newletter on Variable Measurement Systems: Part 3 - Linearity as a reference. I have been using MSA 3 and 4 manuals for the creation of my spreadsheet.

The calculated t-value at the bottom of page 93 in the MSA 3 is where my trouble began. If I solve the equation as written I get a value of 3.299. Not the expected value of 10.433. Using this site I discovered that I had to multiply (Sum(xi-xbar)^2) by the number of trials (m=10) in the experiment. Now I am able to get the correct values.

I could not find anywhere where this was written and since it is not part of the equation I would have never figured it out on my own.

I know I have to do this but I would like to know why? To me it seems like this is assumed knowledge, like an unwritten rule. I know this is not the case. Any enlightenment would be greatly appreciated.

Cheers.

[Stijloor]

A Quick Bump!

Can someone help?

Thank you very much!!

[Barbara B]

It's quite difficult to detect the gap if we can't take a look at the data and formulas you're using. It would be appreciated if you attach the data and spreadsheet.

The example which you're using is taken from this page: http://www.spcforexcel.com/variable-...rt-3-linearity

10.433 is the t_b1-value for the test with the assumption H0: slope=0. The slope is called "b1" on spcforexcel.com and "a" in the MSA 3 and 4 manual, so the t-value is t_b1 or t_a respectively.

What values did you fill in for "b1", "s" and "sum of squares (xi-bar(x))" to calculate 3.299? And how did you alter your formula to achieve 10.433?

[I_am_the_Derp]

Hello Barbara_B,

On the attached spreadsheet I have included how I was originally calculating the t-value (labeled 'Wrong Way') along with the corrected calculation (labeled 'Right Way').

Thank you for taking a look

[Barbara B]

The definition in the formula of x_j for the t-score in the slope test in MSA 4 is a little bit misleading. x_j is not the same as x_i (reference value of part i). To explain this and the multiplication with the number of trials, please take a look at the attached paper.

Hope this answers your question

Barbara

[I_am_the_Derp]

Thank you so much for the detailed explanation Barbara, you went above and beyond

[Stijloor]

In Reply to Parent Post by I_am_the_Derp

Thank you so much for the detailed explanation Barbara, you went above and beyond

I am one of the Moderators.

Please tell others about this great resource.

Glad you're happy!!

Stijloor, Forum Moderator.

[erinmcclure]

ah-ha - Clarity !!!

Thanks Barbara