False Discovery Rate Calculator

Measure false discoveries in physics experiments quickly. Enter counts, p values, and rates for checks. See q results before interpreting significant signals carefully today.

Advanced Calculator

Example Data Table

Input Example Value Use
True Positives 42 Verified real physics signals.
False Positives 8 Positive calls later found false.
Alpha 0.05 Maximum target discovery error rate.
P Values 0.001, 0.008, 0.021, 0.044 Multiple tested detector or model signals.

Formula Used

Count FDR: FDR = FP / (TP + FP)

Precision: Precision = TP / (TP + FP)

False Positive Rate: FPR = FP / (FP + TN)

False Negative Rate: FNR = FN / (FN + TP)

Bayesian FDR: FDR = [(1 - Specificity) × (1 - Prevalence)] / {[Sensitivity × Prevalence] + [(1 - Specificity) × (1 - Prevalence)]}

Benjamini Hochberg: Critical value = (rank / number of tests) × alpha

Adjusted Q Value: q = minimum adjusted value after ranking p values from smallest to largest.

How to Use This Calculator

  1. Enter true positives, false positives, true negatives, and false negatives.
  2. Add prevalence, sensitivity, and specificity for Bayesian interpretation.
  3. Paste p values from physics tests, one per line or separated by commas.
  4. Add labels for each p value when you need a readable table.
  5. Set alpha, such as 0.05, for the target discovery threshold.
  6. Press the calculate button and read the result above the form.
  7. Download CSV or PDF for notes, reports, or lab records.

False Discovery Rate in Physics

Physics research often tests many signals at once. A detector may scan many energy bins. A simulation may compare many parameters. A lab may review many candidate peaks. Some results will look significant by chance. The false discovery rate helps measure that risk.

Why It Matters

A single p value can be useful. It can also mislead. When hundreds of tests are made, random noise can create apparent discoveries. This calculator gives a practical check. It estimates the share of positive findings that may be false. It also applies the Benjamini Hochberg rule to p values. That rule controls expected false discoveries across many tests.

What The Calculator Does

The tool supports three views. The count method uses true positives and false positives. It returns FDR, precision, and related error rates. The Bayesian method uses prevalence, sensitivity, and specificity. It estimates the chance that a positive test is actually false. The p value method sorts results and finds q values. It then marks discoveries that pass a selected threshold.

Practical Interpretation

A lower rate is usually better. Yet context matters. Early searches may tolerate more false positives. Final claims should use stricter limits. Physics teams often combine statistical evidence with calibration checks. They also review systematic uncertainty, detector effects, and replication. This calculator cannot replace a full analysis plan. It helps organize the numbers before deeper review.

Example Workflow

Start with your observed positives. Enter expected or verified false positives when known. Add p values from candidate tests when using multiple comparison control. Pick an alpha value, such as 0.05. Read the adjusted q values. Results below the selected limit are stronger candidates. Export the table for documentation.

Good Reporting Habits

Always describe the method used. State the number of tests. Report the chosen threshold before interpreting results. Mention limitations clearly. If assumptions are uncertain, run several scenarios. Compare optimistic and conservative settings. This reduces overconfidence. It also makes your physics conclusion easier to audit.

Use In Class

Teachers can use it during data analysis lessons. Students can compare raw significance with adjusted evidence. The side by side outputs show why repeated testing needs care. That lesson is important in modern physics lab work.

FAQs

What is false discovery rate?

False discovery rate is the expected share of positive findings that are false. It is useful when many tests are performed together.

Why is FDR important in physics?

Physics experiments often scan many channels, bins, or models. FDR helps reduce accidental claims caused by repeated testing.

What does a lower FDR mean?

A lower FDR means fewer positive findings are expected to be false. It does not prove every accepted result is true.

What is the Benjamini Hochberg method?

It ranks p values and compares them with increasing critical values. It is commonly used to control false discoveries.

What is a q value?

A q value is an adjusted p value. It shows the minimum false discovery threshold at which a test may pass.

Can this replace expert review?

No. It supports analysis only. Physics claims still need calibration checks, uncertainty review, replication, and domain judgment.

What alpha value should I use?

Many studies use 0.05. Exploratory work may use a looser value. Final claims usually need stricter control.

Can I export my results?

Yes. Use the CSV button for spreadsheet records. Use the PDF button for a readable report copy.

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