Table 1 Inadequate and Quenouille-Addelman solutions for the data presented in Fig. 1a, b
Inadequate | Quenouille-Addelman solution | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
Source of variation | df | SS | MS | F | P | Source of variation | df | SS | MS | F | P |
Fixed-effect solution for a completely randomized design based on the data presented in Fig. 1a | |||||||||||
Qualitative variable (A) | 2 | 101.77 | 50.89 | 208.40 | > 0.01 | Qualitative variable (A) | 2 | 136.60 | 68.30 | 326.35 | > 0.01 |
Quantitative variable (Z) | 3 | 156.66 | 52.22 | 213.87 | > 0.01 | Quantitative variable (Z) | 3 | 156.66 | 52.22 | 249.52 | > 0.01 |
A × Z | 6 | 60.59 | 10.10 | 41.36 | > 0.01 | A × Z | 4 | 25.76 | 6.44 | 30.77 | > 0.01 |
Error | 12 | 2.93 | 0.24 | Error | 14 | 2.93 | 0.21 | ||||
Total | 23 | 321.95 | Total | 23 | 321.95 | ||||||
Fixed effect solutions for a completely randomized design based on the data presented in Fig. 1b | |||||||||||
Qualitative variable (A) | 2 | 64.48 | 32.24 | 179.94 | > 0.01 | Qualitative variable (A) | 2 | 84.20 | 42.10 | 274.14 | > 0.01 |
Quantitative variable (Z) | 3 | 255.79 | 85.26 | 475.89 | > 0.01 | Quantitative variable (Z) | 3 | 255.79 | 85.26 | 555.20 | > 0.01 |
A × Z | 6 | 19.87 | 3.31 | 18.48 | > 0.01 | A × Z | 4 | 0.10 | 0.03 | 0.16 | 0.95 |
Error | 12 | 2.15 | 0.18 | Error | 14 | 2.15 | 0.15 | ||||
Total | 23 | 342.29 | Total | 23 | 342.24 | ||||||
Polynomial fixed effect solution for a completely randomized design based on the data presented in Fig. 1b | |||||||||||
Qualitative variable (A) | 2 | 64.48 | 32.24 | 179.94 | > 0.01 | Qualitative variable (A) | 2 | 84.20 | 42.10 | 274.14 | > 0.01 |
Quantitative variable (Z) | Quantitative variable (Z) | ||||||||||
Linear | 1 | 206.66 | 206.66 | 1153.45 | > 0.01 | Linear | 1 | 206.66 | 206.66 | 1345.69 | > 0.01 |
Quadratic | 1 | 39.58 | 39.58 | 220.91 | > 0.01 | Quadratic | 1 | 39.58 | 39.58 | 257.73 | > 0.01 |
Cubic | 1 | 9.54 | 9.54 | 53.25 | > 0.01 | Cubic | 1 | 9.54 | 9.54 | 62.12 | > 0.01 |
A × Z | A × Z | ||||||||||
Linear | 2 | 12.16 | 6.08 | 33.93 | > 0.01 | Linear | 2 | 0.01 | 0.01 | 0.03 | 0.97 |
Quadratic | 2 | 5.71 | 2.86 | 15.93 | > 0.01 | Quadratic | 2 | 0.10 | 0.05 | 0.33 | 0.73 |
Cubic | 2 | 2.00 | 1.00 | 5.58 | 0.02 | Error | 14 | 2.15 | 0.15 | ||
Error | 12 | 2.15 | 0.18 | Total | 23 | 342.24 | |||||
Total | 23 | 342.28 | |||||||||