Merge branch 'main' of github.com:statisticalbiotechnology/dsbook

Author: percolator

dsbook/statistics/multiple.ipynb

@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "1c634eaa",
+   "id": "0",
    "metadata": {},
    "source": [
     "# Multiple Hypothesis Corrections\n",
@@ -137,7 +137,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a6b0beaf",
+   "id": "1",
    "metadata": {
     "tags": [
      "hide-input"
@@ -189,7 +189,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "97c48585",
+   "id": "2",
    "metadata": {},
    "source": [
     "In the plot above, we simulate $p$ values for a large number of hypotheses (1,000 in this case). Half of these hypotheses represent **nulls** (meaning there is no effect), while the other half represent **alternative hypotheses** (meaning there is a true effect).\n",
@@ -217,7 +217,7 @@
     "\n",
     "When applying a significance threshold, we aim to find a balance between detecting true effects and minimizing errors. Specifically, we want to find a threshold that provides a good proportion of true findings while controlling the **False Discovery Rate (FDR)**.\n",
     "\n",
-    "The **FDR** is defined as the expected proportion of false positives among all rejected hypotheses. Mathematically, it is approximately:\n",
+    "The **FDR** is defined as the expected proportion of false positives among all rejected null hypotheses. This is approximately:\n",
     "\n",
     "```{math}\n",
     "\\text{FDR} \\approx \\frac{\\text{FP}}{\\text{TP + FP}}\n",

dsbook/statistics/multiple.md

@@ -209,7 +209,7 @@ In hypothesis testing, we want to determine a **threshold** that can help us ide
 
 When applying a significance threshold, we aim to find a balance between detecting true effects and minimizing errors. Specifically, we want to find a threshold that provides a good proportion of true findings while controlling the **False Discovery Rate (FDR)**.
 
-The **FDR** is defined as the expected proportion of false positives among all rejected hypotheses. Mathematically, it is approximately:
+The **FDR** is defined as the expected proportion of false positives among all rejected null hypotheses. This is approximately:
 
 ```{math}
 \text{FDR} \approx \frac{\text{FP}}{\text{TP + FP}}