# MSA Manual Bias Calculation - Why is the d2* correction factor needed

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#### Glenn

In the automotive MSA Manual the confidence bounds about the bias are calculated using a standard t-test except that the formulae are multiplied by d2/d2*.

I'm curious as to why this correction factor is needed.

The repeatability standard deviation was calculated by dividing the range by d2*, which is fair enough. The bias standard deviation is then the standard error of the repeatability, fair enough.

The manual then uses the bias divided by this bias standard deviation as the t statistic, yet again no problem.

But then it introduces this correction factor into the calculation of the confidence bounds, and I'm stumped as to why.

It won't make much difference because d2 and d2* are almost equal for the fairly large (>10) sample sizes involved, but why do it?

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#### Atul Khandekar

Glenn said:
In the automotive MSA Manual the confidence bounds about the bias are calculated using a standard t-test except that the formulae are multiplied by d2/d2*.

I'm curious as to why this correction factor is needed.

....but why do it?
Why, indeed (since a correction factor d2* has already been used)?

I found one article on AIAG website which deals with derivation of d2* factor:
Stat Expose´ The d-two-star tables uncovered
Unfortunately, not being a trained statistician, there are limitations to my understanding all the stuff it says.

For larger samples, I think you can use the standard one sample t-test.

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#### Atul Khandekar

Oops...
Glenn, Welcome to the Cove!

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