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7. Product and Process Comparisons
7.3. Comparisons based on data from two processes
7.3.1. Do two processes have the same mean?

7.3.1.2.

Confidence intervals for differences between means

Definition of confidence interval for difference between population means Given two random samples,

Y1, ..., YN    and    Z1, ..., ZN

from two populations, two-sided confidence intervals with 100 (1-alpha)% coverage for the difference between the unknown population means, mu1 and mu2, are shown in the table below. Relevant statistics for paired observations and for unpaired observations are shown elsewhere.

Two-sided confidence intervals with 100(1-alpha)% coverage for mu1 - mu2:

Paired observations
mu1 - mu2 (where sigma(1) = sigma(2)) dbar +/- t(alpha/2;N-1)*s(d)/SQRT(N)

Unpaired observations
mu1 - mu2 (where sigma(1) = sigma(2)) Ybar - Zbar +/- t(alpha/2;N1+N2-2)*s*SQRT((1/N1) + (1/N2)
mu1 - mu2 (where sigma(1) <> sigma(2)) Ybar-Zbar+/-t(alpha/2;effective df)*s*SQRT((s1**2/N1) + (s2**2/N2)

Interpretation of confidence interval One interpretation of the confidence interval for means is that if zero is contained within the confidence interval, the two population means are equivalent.
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