Enter Confusion Matrix Counts
Provide the diagnostic test outcomes and generate a broad set of performance statistics instantly.
Example Data Table
This sample confusion matrix demonstrates how the calculator converts observed outcomes into a detailed diagnostic performance summary.
| Test Result | Condition Present | Condition Absent | Total |
|---|---|---|---|
| Positive | 48 (TP) | 12 (FP) | 60 |
| Negative | 7 (FN) | 133 (TN) | 140 |
| Total | 55 | 145 | 200 |
Formula Used
- Sensitivity = TP / (TP + FN)
- Specificity = TN / (TN + FP)
- PPV = TP / (TP + FP)
- NPV = TN / (TN + FN)
- Accuracy = (TP + TN) / (TP + FP + FN + TN)
- Balanced Accuracy = (Sensitivity + Specificity) / 2
- FPR = FP / (FP + TN)
- FNR = FN / (FN + TP)
- LR+ = Sensitivity / (1 − Specificity)
- LR− = (1 − Sensitivity) / Specificity
- DOR = LR+ / LR−
- Youden’s J = Sensitivity + Specificity − 1
- F1 Score = 2TP / (2TP + FP + FN)
- MCC = (TP×TN − FP×FN) / √[(TP+FP)(TP+FN)(TN+FP)(TN+FN)]
- 95% CI values use the Wilson score interval for key proportions.
How to Use This Calculator
- Enter the diagnostic test name and the target condition label.
- Provide counts for TP, FP, FN, and TN from your study or audit.
- Click Calculate Diagnostic Accuracy to display the result summary above the form.
- Review accuracy, predictive values, error rates, likelihood ratios, and confidence intervals together.
- Use the CSV export for spreadsheets or the PDF export for reports and presentations.
- Compare multiple thresholds by re-running the form with updated confusion matrix counts.
Interpretation Notes
Higher values reduce missed disease cases and improve screening value.
Higher values reduce false alarms and improve confirmatory usefulness.
These depend strongly on prevalence and can shift across populations.
LR+ above 10 and LR− below 0.1 often indicate strong evidence.
Useful for comparing thresholds because it combines sensitivity and specificity.
Helpful when classes are imbalanced because it uses all cells.
Why Diagnostic Accuracy Matters
Diagnostic accuracy shows how well a test separates people with a condition from those without it. A confusion matrix captures that performance through true positives, false positives, false negatives, and true negatives. These four counts drive every major measure in this calculator and provide a practical base for comparing screening tools, laboratory cutoffs, triage rules, and workflows.
Core Measures and Their Roles
Sensitivity measures the share of actual cases found by the test, while specificity measures the share of non-cases correctly excluded. Positive predictive value estimates how often a positive result is truly positive, and negative predictive value estimates how often a negative result is truly negative. Accuracy gives an overall correctness rate, while balanced accuracy helps when class sizes are uneven.
Worked Example from the Table
In the example matrix, TP equals 48, FP equals 12, FN equals 7, and TN equals 133. The total sample size is 200 and prevalence is 27.5%. Sensitivity is 87.27%, specificity is 91.72%, and accuracy is 90.50%. Positive predictive value is 80.00%, while negative predictive value is 95.00%. That pattern suggests reliable exclusion performance with relatively few missed cases.
Likelihood Ratios and Threshold Insight
Likelihood ratios show how strongly a result changes decision confidence. In the example, LR+ is high and LR− is low, supporting useful separation between positive and negative findings. Youden’s J is also strong, indicating favorable joint performance across sensitivity and specificity. These measures are valuable when teams compare thresholds and judge whether extra detection justifies more false alarms.
Confidence Intervals Improve Reporting
Point estimates alone can hide uncertainty. This calculator adds Wilson confidence intervals for key proportions so users can assess precision. Narrower intervals suggest stability, while wider intervals warn that sample size may limit confidence. Intervals become especially useful when two candidate tests have similar point estimates and small differences may not be meaningful.
Best Uses in Applied Settings
This calculator supports validation studies, audit reviews, and operational reporting. It can be used for medical diagnostics, fraud screening, defect detection, and binary classification tasks. CSV and PDF exports help with governance, documentation, and presentations. By combining confusion matrix counts, advanced statistics, and interval estimates, the tool supports clearer interpretation and better performance communication.
Frequently Asked Questions
1. What inputs are required for this calculator?
You need four confusion matrix counts: true positives, false positives, false negatives, and true negatives. Optional labels help name the test and target condition in the results.
2. Why can accuracy be misleading on its own?
Accuracy can look strong when one class dominates the sample. Sensitivity, specificity, balanced accuracy, and MCC provide a fuller picture when disease prevalence or class balance is uneven.
3. When should I focus on predictive values?
Use PPV and NPV when decisions depend on what a positive or negative result means in practice. Remember that both values change when prevalence changes.
4. What do likelihood ratios add?
Likelihood ratios show how much a test result shifts confidence in the condition being present or absent. They are especially helpful for comparing thresholds across different settings.
5. Why are confidence intervals included?
Confidence intervals show the precision of key estimates. They help you judge whether an apparently strong result is stable or whether sample size limitations may be influencing the estimate.
6. Can this calculator be used outside healthcare?
Yes. Any binary classification workflow can use these metrics, including fraud detection, defect screening, quality control, machine learning validation, and risk rule evaluation.