Applied Statistics and Probability for Engineers

13-5

Table S13-2 Minitab Output Illustrating Tukey’s Method

One-way ANOVA: Tensile Str versus Conc

Analysis of Variance for Tensile

Source DF SS MS F P

Conc 3 382.79 127.60 19.61 0.000

Error 20 130.17 6.51

Total 23 512.96

Individual 95% CIs For Mean

Based on Pooled StDev

Level N Mean StDev -----+----------+----------+----------+-

5 6 10.000 2.828 (---*---)

10 6 15.667 2.805 (---*----)

15 6 17.000 1.789 (---*----)

20 6 21.167 2.639 (---*----)

-----+----------+----------+----------+-

Pooled StDev 2.551 10.0 15.0 20.0 25.0

Tu k ey’s pairwise comparisons

Family error rate 0.0500

Individual error rate0.0111

Critical value3.96

Intervals for (column level mean) (row level mean)

510 15

10 9.791

1.542

15 11.124 5.458

2.876 2.791

20 15.291 9.624 8.291

7.042 1.376 0.042

widely available; for example, see Montgomery (2001). Equivalently, we could construct a set

of 100(1    )% confidence intervals for all pairs of mean using

For unequal sample sizes, use

The Tukey confidence intervals are a set of simultaneous confidence intervals that hold with prob-

ability 1 . Tukey’s method is a very conservative procedure relative to Fisher’s LSD because

it requires a larger observed difference in treatment averages to declair the pair of means different.

Minitab implements the Tukey procedure and reports the results in terms of the confi-

dence interval. Table S13-2 is the Minitab output for the hardwood concentration experiment

of Example S13-1. Notice that, like Fisher’s LSD, Tukey’s method indicates that all pairs of

means are different except at 10% and 15% concentrations.

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