# Bias Study-Finding degree of freedom-P 92 of MSA manual 4th Ed.

#### kedarg6500

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Please help out to understand calculating degree of freedom for Bias Study -Page 92 of MSA manual 4th Edition.

I tried up to t-statistic

But I could not calculate
1. degrees of freedom
2. Significant t value (2-tailed)
3. 95% Confidence Interval of the Bias lower limit
4. 95% Confidence Interval of the Bias upper limit

Calculation Sheet & page 92 attached

Kedar

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#### Barbara B

Kedar,

the last four formulas in the table were wrong. Please see attached Excel sheet with corrections (and fortunately these values do match the MSA 4th manual).

Regards,

Barbara

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#### V5652

hello Barbara,
I have seen the excel sheet attached by you.
but i couldn't get that how can I calculate df=14 ? because i have seen it 10.8 as per 3rd manual.

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#### Barbara B

V5652,

with MSA3rd the test for a significant bias was based on the sample range as a measure for spread. With the range the df's for the t-test-statistic has to be taken from the d2*-table (MSA3rd, Appendix C). In a bias study with g=1 sample (=1 subgroup) and m=15 subgroup sample size Appendix C provides:
df=10.8 (and d2*=3.55333)

In MSA4th the standard deviation instead of the range is used in the t-test for bias. In this (more common) t-test-statistic the df are simply derived as
df = sample size - 1
So for a sample size of n=15, df = 15-1 = 14. No d2* table necessary anymore, and the t-value could easily be calculated Regards,

Barbara

#### kedarg6500

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Barbara

Thank you for guiding us correctly. Formula for df is "sample size - 1"

If sample size of n=20, we shall take df = 20-1 = 19. Is it right?

Where they have explained "Formula for df" in MSA V4?

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#### Barbara B

kedarg6500,

yes, you've got that right. For a T-test (independent one sample t-test) based on standard deviation as a measure of variation the df's are always given by
df = n-1
with n number of measurements taken (n=15 -> df = 15-1 = 14, n=20 -> df = 20-1 = 19, and so on).

The df's are notated as v (greek letter, spelled nu, see Nu_(letter)) in MSA4th which is a common notation for the degrees of freedom in statistics. You can find the formula for v on p.89 below the formula for the confidence interval for bias: v = n - 1.

Regards,

Barbara

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#### edwinzosef

Dear Barbara,
Actually I was in lot of confusions untill I refer ur post here,
Thanks a lot for sharing about 4th Ed & found out the correction on Bian xlsx sheet.

Can you advice me, if I'm going to do MSA for caliper ,Micrometers, I need to apply GRR,Bias,Linearity & Stablility?