Fix T21 PR number reference (#400 → #397) for yatchew_hr_test mean_independence

PR #397 added the `null="mean_independence"` mode; PR #400 was the
release-rollup that bundled it.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

Author: igerber

docs/tutorials/21_had_pretest_workflow.ipynb

@@ -2,7 +2,7 @@
  "cells": [
   {
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-   "id": "02f317b7",
+   "id": "6623db00",
    "metadata": {},
    "source": [
     "# Tutorial 21: HAD Pre-test Workflow - Did the Brand Campaign Satisfy the Identifying Assumptions?\n",
@@ -14,7 +14,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "47b10255",
+   "id": "baf69855",
    "metadata": {},
    "source": [
     "## 1. The Pre-test Battery\n",
@@ -31,7 +31,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b39cfcc4",
+   "id": "587dd5ae",
    "metadata": {},
    "source": [
     "## 2. The Panel\n",
@@ -42,13 +42,13 @@
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+   "id": "4169ccef",
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@@ -116,7 +116,7 @@
   },
   {
    "cell_type": "markdown",
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+   "id": "c21196bd",
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    "source": [
     "## 3. Step 1: The Overall Workflow (Two-Period Path)\n",
@@ -129,13 +129,13 @@
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    "outputs": [
@@ -188,7 +188,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8994fa7c",
+   "id": "a37bb4f5",
    "metadata": {},
    "source": [
     "**Reading the overall verdict.** Three things to note.\n",
@@ -203,13 +203,13 @@
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+   "id": "78aaa722",
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@@ -269,15 +269,15 @@
   },
   {
    "cell_type": "markdown",
-   "id": "892978cd",
+   "id": "aaa21a26",
    "metadata": {},
    "source": [
     "A note on the Yatchew row. The `T_hr` statistic is **very large and negative** (~-35,000). That looks alarming but is correct here: under perfectly linear dose-response with very heterogeneous doses (Uniform[\\$0.01K, \\$50K]) and 60 sorted-by-dose units, the differencing variance `sigma2_diff` (which captures the squared gap between adjacent-by-dose units' `dy` values) is much larger than the OLS residual variance `sigma2_lin`. The formula `T_hr = sqrt(G) * (sigma2_lin - sigma2_diff) / sigma2_W` then goes massively negative, p-value rounds to 1.0, and we comfortably fail to reject linearity. (For a different way to look at this same test, see the Yatchew side panel later in the notebook.)\n"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "461e877c",
+   "id": "09b0f2a3",
    "metadata": {},
    "source": [
     "## 4. Step 2: Upgrade to the Event-Study Workflow\n",
@@ -296,13 +296,13 @@
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-     "shell.execute_reply": "2026-05-09T23:26:37.759776Z"
+     "iopub.execute_input": "2026-05-09T23:37:57.414542Z",
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@@ -342,7 +342,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "78d6b00d",
+   "id": "ebb7378f",
    "metadata": {},
    "source": [
     "**Reading the event-study verdict.** Now the verdict reads `\"QUG, joint pre-trends, and joint linearity diagnostics fail-to-reject (TWFE admissible under Section 4 assumptions)\"`. The `\"deferred\"` caveat from the overall path is gone - all three paper steps closed jointly. The structural fields confirm: `pretrends_joint` and `homogeneity_joint` are both populated.\n",
@@ -353,13 +353,13 @@
   {
    "cell_type": "code",
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-   "id": "dfaf3133",
+   "id": "4c0f47d0",
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-     "shell.execute_reply": "2026-05-09T23:26:37.762905Z"
+     "iopub.execute_input": "2026-05-09T23:37:57.540476Z",
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    "outputs": [
@@ -432,7 +432,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "acab854c",
+   "id": "f28a7820",
    "metadata": {},
    "source": [
     "The pre-trends p-value (~0.07) sits close to the conventional alpha = 0.05 threshold - the test is not vacuous, it is informative. It is consistent with parallel pre-trends but not by a wide margin. In a real analysis this would warrant a closer look at the per-horizon CvM contributions (visible in `per_horizon_stats`) and possibly a Pierce-Schott-style linear-trend detrending via `trends_lin=True` (an extension we do not demonstrate here; see `did_had_pretest_workflow`'s docstring).\n",
@@ -444,29 +444,29 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ba3a0c3c",
+   "id": "b805e082",
    "metadata": {},
    "source": [
     "## 5. Side Panel: Yatchew-HR Null Modes\n",
     "\n",
     "The Yatchew-HR test exposes two `null=` modes (the second was added in 2026-04 for parity with the R `YatchewTest` package).\n",
     "\n",
     "- `null=\"linearity\"` (default; paper Theorem 7): tests `H0: E[dY | D]` is linear in `D`. Residuals come from OLS `dy ~ 1 + d`. This is what `did_had_pretest_workflow` calls under the hood.\n",
-    "- `null=\"mean_independence\"` (PR #400, 2026-04, Phase 4 R-parity): tests the stricter `H0: E[dY | D] = E[dY]`, i.e. `dY` is mean-independent of `D`. Residuals come from intercept-only OLS `dy ~ 1`. Mirrors R `YatchewTest::yatchew_test(order=0)`.\n",
+    "- `null=\"mean_independence\"` (added 2026-04-26 in PR #397, Phase 4 R-parity): tests the stricter `H0: E[dY | D] = E[dY]`, i.e. `dY` is mean-independent of `D`. Residuals come from intercept-only OLS `dy ~ 1`. Mirrors R `YatchewTest::yatchew_test(order=0)`.\n",
     "\n",
     "The mean-independence mode is typically used on **placebo (pre-treatment) data** to test parallel pre-trends as a non-parametric mean-independence assertion. Below we construct an illustrative input - the within-pre-period first-difference `dy = Y[week=4] - Y[week=3]` paired with each DMA's actual post-period dose - and run both modes side by side. Both should fail to reject on this clean linear DGP; the contrast is in the residual structure.\n"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 6,
-   "id": "319a1c0c",
+   "id": "63fa34db",
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-     "shell.execute_reply": "2026-05-09T23:26:37.768342Z"
+     "iopub.execute_input": "2026-05-09T23:37:57.543368Z",
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+     "shell.execute_reply": "2026-05-09T23:37:57.547551Z"
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    "outputs": [
@@ -528,7 +528,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d142244a",
+   "id": "da899c45",
    "metadata": {},
    "source": [
     "**Reading the side-panel comparison.**\n",
@@ -543,7 +543,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5c5d2b18",
+   "id": "c98e7202",
    "metadata": {},
    "source": [
     "## 6. Communicating the Validation to Leadership\n",
@@ -563,7 +563,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0d0c55b3",
+   "id": "56246bf2",
    "metadata": {},
    "source": [
     "## 7. Extensions\n",
@@ -585,7 +585,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "36453f8b",
+   "id": "ca588d0c",
    "metadata": {},
    "source": [
     "## 8. Summary Checklist\n",