# Attribute Gage RR- Correct Confidence Intervals?

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• #34825

One calculation, which I came across has made me post this question.
I need to know the way to get the 95% upper and lower confidence limits on the calculated score during attribute gage RR study. This 95% CI represents the range within which the true Calculated Score lies given the uncertainty associated with limited sample size.
Lets assume that calculated score of one operator is 96.7%.
Sample size is 30. Number of matches = 29. There is one mismatch.
Distribution – Binomial.
What I observed in published article was:
Sample Size = 30
# Matches = 29
95% UCL = 99.9 % ???
Calculated score = 96.7 %
95% LCL = 82.8 % ???
This does not match with my calculations.
I got proportion mismatches = p-hat= 0.033 (propor. that matched = 0.967, i.e. 96.7% of the time the operator could match the Attr. value)
Z_alpha/2 = Z_0.025 = 1.96.
Using formula for 95% 2-sided CI  for p-hat, i.e.
p-hat – Z_0.025*SQRT(p-hat(1-(p-hat))/n) < p < p-hat + Z_0.025*SQRT(p-hat(1-(p-hat))/n)
Using the results from the above equation I got CI as follows:
LCL = 90.2 %
UCL = 100 %
Would appreciate the correct method to arrive at published LCL= 82.8 % and UCL= 99.9 %. Or are these CIs false?
Thanks

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#96571

SSBB,
You are using a normal approxamation to calculate the confidence intervals for a binomial distribution.  The published article has used the exact calculations from a binomial.
When  np and n(1-p) are both greater than or equal to five and n is greater than 30, then the normal approximation is pretty good.  If not, as in your case (n(1-p) =0.987), the approxamation is not so good.
Minitab will calculate the exact binomial CIs for you in the 1-proportions test.
Statman

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