The Fisher Ratio Calculator is used in statistics and pattern recognition to evaluate how well two classes of data can be separated. It is particularly useful in feature selection and classification problems, especially in machine learning and data mining. By computing the ratio of between-class variance to within-class variance, the Fisher Ratio offers a clear measure of how distinct two groups are based on a specific feature.
A higher Fisher Ratio indicates that the classes are well-separated, making that feature more useful for classification. On the other hand, a lower ratio implies significant overlap between the two distributions, suggesting that the feature may not be very effective for distinguishing between the groups.
formula of Fisher Ratio Calculator
Where:
μ₁ = Mean of class 1
μ₂ = Mean of class 2
σ₁² = Variance of class 1
σ₂² = Variance of class 2
This formula calculates the square of the difference between the means, divided by the sum of the variances. It is a dimensionless number and provides a quick way to compare feature effectiveness in statistical models.
General Reference Table
| Feature Variable | Mean (Class 1) | Mean (Class 2) | Variance (Class 1) | Variance (Class 2) | Fisher Ratio |
|---|---|---|---|---|---|
| Height | 170 | 160 | 10 | 12 | 4.17 |
| Weight | 65 | 60 | 20 | 25 | 0.56 |
| Blood Pressure | 120 | 110 | 5 | 8 | 3.33 |
Use this table to estimate or compare the Fisher Ratios for different features before applying classification models.
Example of Fisher Ratio Calculator
Let’s compute the Fisher Ratio for two classes of test scores:
Class 1 (Group A):
Mean (μ₁) = 85
Variance (σ₁²) = 16
Class 2 (Group B):
Mean (μ₂) = 75
Variance (σ₂²) = 25
Fisher Ratio = ( (85 - 75)² ) / (16 + 25)
= (10²) / 41
= 100 / 41
≈ 2.44
Interpretation: A Fisher Ratio of 2.44 indicates that there is some degree of separation between the two groups based on their test scores. This feature may be useful in distinguishing between the two.
Most Common FAQs
A good Fisher Ratio is usually one that is significantly greater than 1. Higher values imply better separation between classes. However, the threshold depends on the context and how many features you are comparing.
The basic Fisher Ratio is designed for comparing two classes. For multiple classes, extensions like Fisher’s Linear Discriminant or generalized versions are used.
Yes. Fisher Ratio is commonly used for feature selection in classification tasks. Features with higher Fisher Ratios are considered more discriminative and are often selected for training machine learning models.