From 576de4a2325efb25756c9b799b31b8dd712caac4 Mon Sep 17 00:00:00 2001
From: mmax3 <32703681+mmax3@users.noreply.github.com>
Date: Sun, 14 Dec 2025 21:16:16 +0100
Subject: [PATCH] Update hypothesis.md

Added didn't buy table and calculations for Chi-squared test example
---
 docs/stats/hypothesis.md | 10 +++++++++-
 1 file changed, 9 insertions(+), 1 deletion(-)

diff --git a/docs/stats/hypothesis.md b/docs/stats/hypothesis.md
index ec00955..5566ad0 100644
--- a/docs/stats/hypothesis.md
+++ b/docs/stats/hypothesis.md
@@ -380,11 +380,19 @@ $$ \chi^2 = \sum \frac{(O_i - E_i)^2}{E_i} $$
     If $H_0$ is true, both groups should convert at the Global Rate (15%).
     *   Blue Expected Buys: $100 \times 0.15 = 15$ ($E_1$).
     *   Red Expected Buys: $100 \times 0.15 = 15$ ($E_2$).
+  
+| Group | Bought (E) | Didn't Buy (E) | Total |
+| :--- | :--- | :--- | :--- |
+| **Blue** | 15 | 85 | 100 |
+| **Red** | 15 | 85 | 100 |
 
 4.  **Calculate $\chi^2$:**
     *   Blue Buys: $(10 - 15)^2 / 15 = 25/15 = 1.66$
     *   Red Buys: $(20 - 15)^2 / 15 = 25/15 = 1.66$
     *   *Do the same for "Didn't Buy" cells...*
+    *   Blue didn't buy: $(90−85)^2/85 = 0.29$
+    *   Red didn't buy: $(80−85)^2/85 = 0.29$
+    *   Sum it up
     *   $\chi^2 \approx 3.92$.
 
 5.  **Compute P-Value:**
@@ -486,4 +494,4 @@ We started with a promise: to learn the universal algorithm of inference.
     $$ \text{Score} = \frac{\text{Observed Signal}}{\text{Expected Noise}} $$
 4.  **The Decision:** If the Signal is much stronger than the Noise (High Score, Low P-value), we accept the new reality.
 
-**You have now graduated from "guessing" to "inference."**
\ No newline at end of file
+**You have now graduated from "guessing" to "inference."**