Form simultaneous confidence intervals for the difference of the mean of lab 1 and those...

Form simultaneous confidence intervals for the difference of the mean of lab 1 and those of labs 4, 5, and 6 in Example A of Section 12.2.2.1.

Reference

We can illustrate Tukey’s method by applying it to the tablet data of Section 12.2.We list the labs in decreasing order of the mean of their measurements:

The mean from lab 1 is thus significantly different from those from labs 4, 5, and 6; The mean of lab 3 is significantly greater than that of lab 4. No other comparisons are significant at the .05 level.

At the 95% confidence level, the other differences in mean level that are seen in Figure 12.1 cannot be judged to be significantly different from zero. Although differences between these labs must certainly exist, we cannot reliably establish the signs of the differences.

It is interesting to note that a price is paid here for performing multiple comparisons simultaneously. If separate t tests had been conducted using the pooled sample variance, labs would have been declared significantly different if their means had differed by more than