Jupyter notebooks

These jupyter notebooks are licensed as follows:

===============================================================================
 nb — notebooks
 Copyright (C) 2025 — Erwann Rogard
 Released under GPL 3.0
 See https://www.gnu.org/licenses/gpl-3.0.en.html
===============================================================================

HHS false negative controversy

This relates to a post on X that states:

4 out of 5 doctors at Harvard cannot answer a question from introductory statistics.

"If a test to detect a disease whose prevalence is 1/1000 has a false positive rate of 5%, what is the chance that a person found to have a positive result actually has the disease?"

I claim one cannot solve the stated problem due to the unspecified false negative rate. I've provided a Mathematica notebook where state, outcome, and ppv should read as "has the disease", "result of the test", and "chance that a person found to have a positive result actually has the disease", respectively.

$$ \text{ppv} = \frac{(1 - \text{falsenegrate}) \cdot \text{prevalence}}{\text{falseposrate} \cdot (1 - \text{prevalence}) + (1 - \text{falsenegrate}) \cdot \text{prevalence}} $$

However, the derivative of ppv with respect to falsenegrate (for short, p) is negative, such that the max is attained at p=0, which yields around 2%.