1. Analysis of Variance (ANOVA) (Ronald Fisher)
ANOVA compares means across multiple groups to determine if observed differences are statistically significant.
Formula:
F = (SSB / (k - 1)) / (SSW / (N - k))
Where:
F: F-statistic
SSB: Sum of squares between groups (variance explained by group differences)
SSW: Sum of squares within groups (variance within each group)
k: Number of groups
N: Total number of observations
2. Categorization and Subjective Weights
This example illustrates how subjective weighting of variables can affect group comparisons using ANOVA.
Groups:
- Group A: Productivity = 90, Education = 85
- Group B: Productivity = 70, Education = 65
- Group C: Productivity = 40, Education = 45
Subjective Weights:
- Productivity weight: 0.6
- Education weight: 0.4
Weighted Scores:
- Group A: R = (0.6 × 90) + (0.4 × 85) = 54 + 34 = 88
- Group B: R = (0.6 × 70) + (0.4 × 65) = 42 + 26 = 68
- Group C: R = (0.6 × 40) + (0.4 × 45) = 24 + 18 = 42
SSB Calculation:
Overall Mean = (88 + 68 + 42) / 3 = 66
SSB = Σ(GroupSize × (GroupMean - OverallMean)²)
SSB = (1 × (88 - 66)²) + (1 × (68 - 66)²) + (1 × (42 - 66)²)
= 484 + 4 + 576 = 1064
This example demonstrates how subjective weights can influence group rankings and justify resource allocation decisions.