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# Interpreting Level of Confidence - Round Robin for Tensile Testing - Help needed

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#### Sorin

Performing Round Robin for tensile testing (required for Nadcap cert)

I have 3 operators. Each one processed 4 tests.

Population 12
Level of confidence required is 95%
Standard deviation (for tensile values only) is 0.51.
Required tensile range (for acceptance) is 280-300 ksi. All results were in the upper range - lowest 295.7, highest 297.4.
Average: 296.67
Calculating level of confidence using "confidence" function in Excel is giving me a result of 0.289.

How do I interpret this?

Detailed explanations would be very, very appreciated.

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#### NumberCruncher

Re: Need help interpreting level of confidence

Hi sorin

Take your standard deviation (0.51) and divide by [square root(12)]=3.1641
This gives you 0.1472, which is the estimated standard deviation of your mean (remember sigma/(root n) ?)

Multiply by 3.1641 x 1.96 (ie 95% range for standard normal distribution) to give 0.2885596, or about 0.289.

So for your mean, the 95% confidence interval is between (mean - 0.289) and (mean +0.289) in whatever units you used to measure the tensile strength. So the 95% c.i. will be about 296.7 +/- 0.289 (in tensile strength units).

NC

Last edited by a moderator:
S

#### Sorin

Re: Need help interpreting level of confidence

Hi sorin

Take your standard deviation (0.51) and divide by [square root(12)]=3.1641
This gives you 0.1472, which is the estimated standard deviation of your mean (remember sigma/(root n) ?)

Multiply by 3.1641 x 1.96 (ie 95% range for standard normal distribution) to give 0.2885596, or about 0.289.

So for your mean, the 95% confidence interval is between (mean - 0.289) and (mean +0.289) in whatever units you used to measure the tensile strength. So the 95% c.i. will be about 296.7 +/- 0.289 (in tensile strength units).

NC
Would that mean that in order to have a 95% confidence, only individual results and/or only avg results (for each operator) shall be between 296.381 and 296.959 ?

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
Re: Need help interpreting level of confidence

the method NumberCruncher applied is for the MEANS and not for the individual values. If you need 95% confidence on the spread of the individual values you need a different formula. You could use an assumption of a Normal distribution of the individual values (mean + 1.96*sample SD/c4), tolerance intervals or prediction intervals. with such a small sample size, tolerance intervals will be very large.

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#### NumberCruncher

Re: Need help interpreting level of confidence

Hi sorin

Have a look at the Excel help file for "confidence". You should be able to follow the calculation.

As Bev has so concisely explained, the calculation gives the confidence interval of your single, mean result, of 296.67. This will be rather smaller than the interval for individual measurements.

The calculation used by Excel is simply the application of the central limit theorem. Look it up on the net.

NC