Calculator Inputs
Example Data Table
| Sample | pH | Absorbance | Conductivity | Logistic Probability | Logistic Class | Discriminant Score | Discriminant Class |
|---|---|---|---|---|---|---|---|
| CHEM-001 | 6.80 | 0.74 | 1.25 | 0.7114 | Contaminated Sample | 1.3360 | Contaminated Sample |
| CHEM-002 | 7.10 | 0.22 | 0.90 | 0.2916 | Acceptable Sample | -0.5720 | Acceptable Sample |
| CHEM-003 | 5.90 | 0.61 | 1.48 | 0.6532 | Contaminated Sample | 0.9730 | Contaminated Sample |
Formula Used
Logistic regression: z = b0 + b1x1 + b2x2 + b3x3
Probability of Class 1: P = 1 / (1 + e-z)
Logistic decision rule: If P is greater than or equal to the logistic threshold, assign Class 1. Otherwise, assign Class 0.
Linear discriminant score: D = d0 + d1x1 + d2x2 + d3x3
Discriminant decision rule: If D is greater than or equal to the discriminant threshold, assign Class 1. Otherwise, assign Class 0.
This calculator uses a linear discriminant score for fast chemistry screening and quick model comparison.
How to Use This Calculator
- Enter a sample ID for your chemistry record.
- Input three predictor values such as pH, absorbance, and conductivity.
- Enter logistic intercept, coefficients, and the decision threshold.
- Enter discriminant intercept, coefficients, and the score threshold.
- Set labels for Class 0 and Class 1.
- Optionally select the actual class to check each model.
- Press Compare Models to view results above the form.
- Use the export buttons to save a CSV file or PDF report.
Why This Chemistry Model Comparison Matters
Discriminant analysis and logistic regression are both used for classification. Chemistry teams use them to separate acceptable and unacceptable samples. They also help with impurity checks, batch release, spectral screening, and stability decisions. This calculator makes the comparison simple. You enter three predictors and two model structures. Then you see probabilities, scores, agreement, and class decisions in one place.
Logistic Regression in Laboratory Decisions
Logistic regression is useful when you want a direct probability for Class 1. That helps when a chemist needs a clear risk estimate. The model handles binary outcomes well. It is practical for pass or fail rules, contamination alerts, and quality flags. In analytical chemistry, that probability can support better reporting. It also works well when assumptions behind classical discriminant methods are not fully satisfied.
Discriminant Analysis in Chemical Classification
Discriminant analysis is strong when class separation is driven by measured chemical features. It is often used in chemometrics, assay grouping, and instrumental data interpretation. A discriminant score can show how far a sample sits from the decision boundary. That is useful for rapid screening. When covariance patterns are stable and training data are well prepared, discriminant methods can provide very clear separation.
How to Interpret Both Models Together
Neither model should be chosen from one sample alone. Use validation data from real chemistry experiments. Compare sensitivity, specificity, and misclassification cost across a holdout set. This page is still useful for fast sample review. It helps you inspect coefficient effects, threshold changes, and decision shifts. That makes it a practical learning tool for laboratory analysts, students, and process quality teams.
Frequently Asked Questions
1. What does this calculator compare?
It compares one logistic model and one linear discriminant score using the same chemistry inputs. You can inspect predicted class, probability, score, agreement, and optional correctness.
2. Why use chemistry variables like pH and absorbance?
Those values are common laboratory predictors. They make the calculator practical for batch screening, assay checks, contamination review, and simple chemometric demonstrations.
3. Is the discriminant score a full LDA implementation?
This page uses a linear discriminant score form for quick comparison. It is a practical calculator, not a full matrix-based training system.
4. What is the logistic threshold for?
The threshold controls when the probability becomes a Class 1 decision. A higher threshold makes the model more conservative for positive classification.
5. What does agreement mean here?
Agreement shows whether both models assign the same class to the current chemistry sample. It does not prove either model is better overall.
6. Should I trust the model with the larger margin?
Not by itself. A larger margin may show stronger separation for that sample, but real model choice needs validation data and domain testing.
7. Can I export the result?
Yes. The calculator includes CSV export for spreadsheet work and PDF export for a simple report you can save or share.
8. What is the best way to choose between both models?
Evaluate both on historical chemistry data. Compare accuracy, sensitivity, specificity, interpretability, and how each model fits your laboratory assumptions.