Table 2.
Calculation worksheet of the effects of the three-variable system and magnitude of effects and error limits of Set I.
| Experimental Conditions | Calculation of Effects | |
|---|---|---|
| Temperature | 1/4(a13 + a14 + a21 + a23 − a11 − a12 − a22 − a24) | −1.1363 |
| Time | 1/4(a12 + a14 + a21 + a24 − a11 − a13 − a22 − a23) | −0.4213 |
| Ethanol concentration | 1/4(a12 + a13 + a21 + a22− a11 − a14 − a23 − a24) | −0.1263 |
| Temperature × time | 1/4(a11 + a14 + a21 + a22 − a12 − a13 − a23 − a24) | −0.1113 |
| Temperature × ethanol concentration | 1/4(a11 + a13 + a21 + a24 − a12 − a14 − a22 − a23) | 0.0188 |
| Time × ethanol concentration | 1/4(a11 + a12 + a21 + a23 − a13 − a14 − a22 − a24) | −0.1013 |
| Temperature × time × ethanol concentration | 1/4(a21 + a22 + a23 + a24 − a11 − a12 − a13 − a14) | −0.0213 |
| Change in mean effect | 1/10(a11 + a12 + a13 + a14 + a21 + a22 + a23 + a24 − 4a10 − 4a20) | −0.2105 |
| Standard deviation (σ) | 1/2(σ1 + σ2)=1/2(R1 × fk,n + R2 × fk,n) (1) | 0.1230 |
| Error limits: | ||
| for average | ±1.414σ (±2σ/√n) | 0.1739 |
| for effects | ±1.004σ (±0.71 × 2σ/√n) | 0.1235 |
| for change in mean | ±0.891σ (±0.63 × 2σ/√n) | 0.1096 |
R1: (largest difference − smallest difference) in block 1; R2: (largest difference − smallest difference) in block 2; fk,n = constant depending on number of replications (n) and number of experiments (k) per cycle = 0.3 for n = 2 and k = 5.