False Discovery rate Calculator

A False Discovery Rate (FDR) calculator is a statistical tool used in hypothesis testing, particularly in multiple comparisons, to control the rate of false positives or Type I errors. It helps researchers identify statistically significant results while minimizing the chances of incorrectly claiming significance. FDR control is often used in fields like genomics, where researchers test thousands or even millions of hypotheses simultaneously.

FDR calculator works

Here, I’ll explain how an FDR calculator works, provide its formula, and break down the process into headings for clarity:

Hypothesis Testing:

• In hypothesis testing, researchers typically have a set of null hypotheses (H0) and alternative hypotheses (H1).

P-Values:

• After conducting experiments or statistical tests, researchers calculate p-values for each hypothesis. The p-value represents the probability of observing results as extreme as the ones obtained, assuming the null hypothesis is true.

Sorting P-Values:

• Sort the p-values in ascending order. The lowest p-value corresponds to the most significant result.

FDR Calculation:

• The FDR calculator employs the Benjamini-Hochberg procedure, a common method for controlling the False Discovery Rate.

Formula for FDR Calculation:

The formula for the Benjamini-Hochberg procedure is as follows:

FDR = (m / n) * q

• FDR: False Discovery Rate (the desired level of controlling false positives)
• m: Rank of the p-value being tested (in the sorted list)
• n: Total number of hypotheses tested
• q: The desired level of FDR control (usually set by researchers, e.g., 0.05 for a 5% FDR)

Implementation Steps:

Here are the steps to implement the Benjamini-Hochberg procedure:

a. Start with the sorted list of p-values.

b. Set a significance level, q, often 0.05 for a 5% FDR.

c. For each p-value (p_i), calculate FDR_i = (i / n) * q.

d. Find the largest p-value (p_j) for which FDR_j <= q.

e. Reject all null hypotheses corresponding to p-values p_1, p_2, …, p_j.

Interpretation:

• The hypotheses corresponding to the p-values p_1, p_2, …, p_j are considered statistically significant while controlling the FDR at the desired level (q).
• Any hypothesis with a p-value greater than p_j is not considered statistically significant under this FDR control.

Benefits of FDR:

• FDR control is more permissive than strict familywise error rate (FWER) control (e.g., Bonferroni correction), making it suitable for situations with a large number of comparisons.
• It balances the trade-off between finding true positives and limiting false positives