Next Page Previous Page Home Tools & Aids Search Handbook
7. Product and Process Comparisons
7.4. Comparisons based on data from more than two processes
7.4.3. Are the means equal?

7.4.3.5.

Confidence intervals for the difference of treatment means

Confidence intervals for the difference between two means This page shows how to construct a confidence interval around (mui- muj) for the one-way ANOVA by continuing the example shown on a previous page.
Formula for the confidence interval The formula for a (1-alpha) 100% confidence interval for the difference between two treatment means is:
    (muhat(i) - muhat(j)) +/-
 t(1-alpha/2;N-k)*SQRT{sigmahat(e)**2*(1/n(i) + 1/(n(j))}
where sigmahat(e)**2 = MSE.
Computation of the confidence interval for mu3 - mu1 For the example, we have the following quantities for the formula:
  • ybar3 = 8.56

  • ybar1 = 5.34
  • SQRT(1.454*(1/5 + 1/5)) = 0.763

  • t0.975, 12 = 2.179

Substituting these values yields (8.56 - 5.34) +/- 2.179(0.763) or 3.22 +/- 1.616.

That is, the confidence interval is from 1.604 to 4.836.

Additional 95% confidence intervals A 95% confidence interval for mu3 - mu2 is: from -1.787 to 3.467.

A 95% confidence interval for mu2 - mu1 is: from -0.247 to 5.007.

Contrasts discussed later Later on the topic of estimating more general linear combinations of means (primarily contrasts) will be discussed, including how to put confidence bounds around contrasts.
Home Tools & Aids Search Handbook Previous Page Next Page