The Elsmar Cove Forum Difficulty with calculated t-value for Linearity
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#1
2nd August 2012, 12:08 PM
 I_am_the_Derp Shy Poster (1 to 5 Posts)   Registration Date: Jul 2012 Location: Canada Posts: 3 Thanks Given to Others: 1 Thanked 0 Times in 0 Posts Karma Power: 4 Karma: 10
Difficulty with calculated t-value for Linearity

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.

#2
3rd August 2012, 02:47 AM
 Stijloor Cross Forum Moderator   Registration Date: May 2003 Location: Charlotte, North Carolina. Posts: 13,422 Thanks Given to Others: 2,947 Thanked 4,268 Times in 3,025 Posts Karma Power: 1430 Karma: 23887
Re: Difficulty with calculated t-value for Linearity

A Quick Bump!

Can someone help?

Thank you very much!!
 Thanks to Stijloor for your informative Post and/or Attachment!
#3
9th August 2012, 05:20 AM
 Barbara B Number Cruncher   Registration Date: May 2005 Location: Germany Posts: 390 Thanks Given to Others: 95 Thanked 270 Times in 173 Posts Karma Power: 79 Karma: 3799
Re: Difficulty with calculated t-value for Linearity

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?
#4
9th August 2012, 09:39 AM
 I_am_the_Derp Shy Poster (1 to 5 Posts)   Registration Date: Jul 2012 Location: Canada Posts: 3 Thanks Given to Others: 1 Thanked 0 Times in 0 Posts Karma Power: 4 Karma: 10
Re: Difficulty with calculated t-value for Linearity

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
Attached Files: 1. Scan for viruses before using, 2. Please report any 'bad' files by Reporting this post, 3. Use at your Own Risk.
 linearity.xlsx (19.3 KB, 43 views)
#5
10th August 2012, 10:04 AM
 Barbara B Number Cruncher   Registration Date: May 2005 Location: Germany Posts: 390 Thanks Given to Others: 95 Thanked 270 Times in 173 Posts Karma Power: 79 Karma: 3799
Re: Difficulty with calculated t-value for Linearity

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.

Barbara
Attached Files: 1. Scan for viruses before using, 2. Please report any 'bad' files by Reporting this post, 3. Use at your Own Risk.
 MSA test slope=0.pdf (221.5 KB, 16 views)
 Thanks to Barbara B for your informative Post and/or Attachment!
#6
10th August 2012, 10:21 AM
 I_am_the_Derp Shy Poster (1 to 5 Posts)   Registration Date: Jul 2012 Location: Canada Posts: 3 Thanks Given to Others: 1 Thanked 0 Times in 0 Posts Karma Power: 4 Karma: 10
Re: Difficulty with calculated t-value for Linearity

Thank you so much for the detailed explanation Barbara, you went above and beyond
#7
10th August 2012, 10:42 AM
 Stijloor Cross Forum Moderator   Registration Date: May 2003 Location: Charlotte, North Carolina. Posts: 13,422 Thanks Given to Others: 2,947 Thanked 4,268 Times in 3,025 Posts Karma Power: 1430 Karma: 23887
Re: Difficulty with calculated t-value for Linearity

Quote:
 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.

Stijloor, Forum Moderator.
#8
10th August 2012, 03:39 PM
 erinmcclure Involved in Discussions   Registration Date: Aug 2009 Posts: 10 Thanks Given to Others: 0 Thanked 0 Times in 0 Posts Karma Power: 17 Karma: 10
Re: Difficulty with calculated t-value for Linearity

ah-ha - Clarity !!!

Thanks Barbara

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