Applied Statistics and Probability for Engineers

0 5 10 15 20 25 psi

5% 10% 15% 20%

480 CHAPTER 13 DESIGN AND ANALYSIS OF SINGLE-FACTOR EXPERIMENTS: THE ANALYSIS OF VARIANCE

where LSD, the least significant difference,is

Figure 13-2 Results of Fisher’s LSD method in Example 13-2.

LSDt (13-16)

2,a^1 n^12 B

2 MSE

n

If the sample sizes are different in each treatment, the LSD is defined as

EXAMPLE 13-2 We will apply the Fisher LSD method to the hardwood concentration experiment. There are

a4 means, n6, MSE6.51, and t0.025,202.086. The treatment means are

The value of LSD is. Therefore, any

pair of treatment averages that differs by more than 3.07 implies that the corresponding pair

of treatment means are different.

The comparisons among the observed treatment averages are as follows:

From this analysis, we see that there are significant differences between all pairs of means

except 2 and 3. This implies that 10 and 15% hardwood concentration produce approximately

the same tensile strength and that all other concentration levels tested produce different tensile

strengths. It is often helpful to draw a graph of the treatment means, such as in Fig. 13-2, with

the means that are notdifferent underlined. This graph clearly reveals the results of the exper-

iment and shows that 20% hardwood produces the maximum tensile strength.

The Minitab output in Table 13-5 shows the Fisher LSD method under the heading

“Fisher’s pairwise comparisons.” The critical value reported is actually the value of t0.025,20

2 vs. 115.6710.00 5.67 3.07

3 vs. 217.0015.67 1.333.07

3 vs. 117.0010.00 7.00 3.07

4 vs. 321.1717.00 4.17 3.07

4 vs. 221.1715.67 5.50 3.07

4 vs. 121.1710.0011.17 3.07

LSDt0.025,20 12 MSE n2.086 121 6.51 2
6 3.07

y 4 .21.17 psi

y 3 .17.00 psi

y 2 .15.67 psi

y 1 .10.00 psi

LSDt 2,Na

B

MSE a

1

ni

1

njb

c 13 .qxd 5/8/02 9:20 PM Page 480 RK UL 6 RK UL 6:Desktop Folder:TEMP WORK:PQ220 MONT 8/5/2002:Ch 13: