Question 9.4: In the article “Review of Development and Application of CRS......
In the article “Review of Development and Application of CRSTER and MPTER Models” (R. Wilson, Atmospheric Environment, 1993:41–57), several measurements of the maximum hourly concentrations (in 𝜇g/m³) of SO_{2} are presented for each of four power plants. The results are as follows (two outliers have been deleted):
The following output (from MINITAB) presents results for a one-way ANOVA. Can you conclude that the maximum hourly concentrations differ among the plants?
| Plant 1: | 438 | 619 | 732 | 638 | ||
| Plant 2: | 857 | 1014 | 1153 | 883 | 1053 | |
| Plant 3: | 925 | 786 | 1179 | 786 | ||
| Plant 4: | 893 | 891 | 917 | 695 | 675 | 595 |
| One-way ANOVA: Plant 1, Plant 2, Plant 3, Plant 4 Source DF SS MS F P Plant 3 378610 126203 6.21 0.006 Error 15 304838 20323 Total 18 683449S = 142.6 R-Sq = 55.40% R-Sq(adj) = 46.48%Individual 95% CIs For Mean Based on Pooled StDevLevel N Mean StDev ——-+———+———+———+– 1 4 606.8 122.9 (——*——-) 2 5 992.0 122.7 (——*—–) 3 4 919.0 185.3 (——-*——-) 4 6 777.7 138.8 (—–*—–) ——-+———+———+———+– Pooled StDev = 142.6 |
In the ANOVA table, the P-value for the null hypothesis that all treatment means are equal is 0.006. Therefore, we conclude that not all the treatment means are equal.
| One-way ANOVA: Plant 1, Plant 2, Plant 3, Plant 4 Source DF SS MS F P Plant 3 378610 126203 6.21 0.006 Error 15 304838 20323 Total 18 683449S = 142.6 R-Sq = 55.40% R-Sq(adj) = 46.48% Individual 95% CIs For Mean Based on Level N Mean StDev ——-+———+———+———+– ——-+———+———+———+– Pooled StDev = 142.6 |