feat(stats): add an SRM check to the price experiment report

The report now runs a chi-square sample-ratio-mismatch test of the arm counts
against the expected 50/50 split, on both the raw assigned counts and the matured
subset (to catch differential attrition), flagging a low p as an imbalance to
investigate before trusting results. Extract a shared Normal::cdf so the SRM and
Welch tests use one erf implementation.

app/Console/Commands/SendPriceExperimentFunnelReportCommand.php

@@ -7,6 +7,7 @@ use App\Services\Discord\DiscordWebhook;
 use App\Services\Stats\BinomialProportion;
 use App\Services\Stats\PriceExperimentFunnelCollector;
 use App\Services\Stats\ProportionSignificance;
+use App\Services\Stats\SampleRatioMismatch;
 use App\Services\Stats\WelchTTest;
 use App\Support\Money;
 use Carbon\CarbonImmutable;
@@ -29,6 +30,7 @@ class SendPriceExperimentFunnelReportCommand extends Command
         private PriceExperimentFunnelCollector $collector,
         private ProportionSignificance $significance,
         private WelchTTest $welch,
+        private SampleRatioMismatch $srm,
     ) {
         parent::__construct();
     }
@@ -44,7 +46,7 @@ class SendPriceExperimentFunnelReportCommand extends Command
             return self::SUCCESS;
         }
 
-        foreach ([...$this->tableLines($report), ...$this->significanceLines($report)] as $line) {
+        foreach ([...$this->tableLines($report), ...$this->srmLines($report), ...$this->significanceLines($report)] as $line) {
             $this->line($line);
         }
 
@@ -101,6 +103,39 @@ class SendPriceExperimentFunnelReportCommand extends Command
         return $lines;
     }
 
+    /**
+     * Sample-ratio-mismatch check: the split must be ~50/50. A low p means the
+     * assignment (or the pipeline that filters it) is broken, which invalidates
+     * every comparison below — so this is checked first, on the raw assigned counts
+     * and on the matured subset (to catch differential attrition).
+     *
+     * @param  array{variants: array<string, array<string, mixed>>}  $report
+     * @return list<string>
+     */
+    private function srmLines(array $report): array
+    {
+        $control = $report['variants'][PriceExperiment::CONTROL];
+        $high = $report['variants'][PriceExperiment::HIGH];
+        $lines = ['', 'SRM (assignment balance, expect 50/50 — a low p means the split is broken):'];
+
+        foreach (['assigned' => 'assigned', 'assignedMature' => 'matured'] as $field => $label) {
+            $c = (int) $control[$field];
+            $h = (int) $high[$field];
+
+            if ($c + $h === 0) {
+                $lines[] = sprintf('  %-8s control %d / high %d  (n=0)', $label, $c, $h);
+
+                continue;
+            }
+
+            $srm = $this->srm->evenSplit($c, $h);
+            $flag = $srm['p'] < 0.01 ? '  ⚠ IMBALANCE — investigate before trusting results' : '';
+            $lines[] = sprintf('  %-8s control %d / high %d  χ²=%.2f p=%.3f%s', $label, $c, $h, $srm['chiSq'], $srm['p'], $flag);
+        }
+
+        return $lines;
+    }
+
     /**
      * Primary decision test — Welch on contribution-margin-per-user (control vs
      * high), the metric we maximise — plus the conversion guardrail (Wilson CIs +
@@ -210,7 +245,7 @@ class SendPriceExperimentFunnelReportCommand extends Command
     {
         return [
             'title' => '💶 Price Experiment — Funnel (control vs high)',
-            'description' => "```\n".implode("\n", [...$this->tableLines($report), ...$this->significanceLines($report)])."\n```",
+            'description' => "```\n".implode("\n", [...$this->tableLines($report), ...$this->srmLines($report), ...$this->significanceLines($report)])."\n```",
             'color' => 0x57F287,
             'fields' => [
                 [

app/Services/Stats/Normal.php

@@ -0,0 +1,28 @@
+<?php
+
+namespace App\Services\Stats;
+
+/**
+ * Standard-normal cumulative distribution, shared by the significance tests that
+ * need a normal tail probability (Welch's t via the large-sample approximation,
+ * and the χ²₁ sample-ratio-mismatch check). One implementation so the erf
+ * approximation lives in a single place.
+ */
+final class Normal
+{
+    public static function cdf(float $x): float
+    {
+        return 0.5 * (1.0 + self::erf($x / sqrt(2.0)));
+    }
+
+    /** Abramowitz & Stegun 7.1.26 — |error| < 1.5e-7. */
+    private static function erf(float $x): float
+    {
+        $sign = $x < 0 ? -1.0 : 1.0;
+        $x = abs($x);
+        $t = 1.0 / (1.0 + 0.3275911 * $x);
+        $y = 1.0 - ((((1.061405429 * $t - 1.453152027) * $t + 1.421413741) * $t - 0.284496736) * $t + 0.254829592) * $t * exp(-$x * $x);
+
+        return $sign * $y;
+    }
+}

app/Services/Stats/SampleRatioMismatch.php

@@ -0,0 +1,35 @@
+<?php
+
+namespace App\Services\Stats;
+
+/**
+ * Sample-ratio-mismatch (SRM) check for a two-arm experiment: a χ² goodness-of-fit
+ * test (1 degree of freedom) of the observed arm counts against an even 1:1 split.
+ * A low p means the assignment is not really 50/50 — a data-pipeline or attrition
+ * bug that invalidates every downstream comparison, so it must be checked before
+ * trusting the funnel. Run it on the assigned counts AND on any filtered subset
+ * (matured / activated) to catch differential attrition a deterministic assignment
+ * can still produce.
+ */
+final class SampleRatioMismatch
+{
+    /**
+     * @return array{chiSq: float, p: float}
+     */
+    public function evenSplit(int $countA, int $countB): array
+    {
+        $total = $countA + $countB;
+
+        if ($total === 0) {
+            return ['chiSq' => 0.0, 'p' => 1.0];
+        }
+
+        $expected = $total / 2.0;
+        $chiSq = (($countA - $expected) ** 2 + ($countB - $expected) ** 2) / $expected;
+
+        // χ² with 1 df is Z²; its upper tail is P(|Z| > √χ²).
+        $p = 2.0 * (1.0 - Normal::cdf(sqrt($chiSq)));
+
+        return ['chiSq' => $chiSq, 'p' => $p];
+    }
+}

app/Services/Stats/WelchTTest.php

@@ -13,8 +13,8 @@ namespace App\Services\Stats;
  * returned for context.
  *
  * ponytail: normal-approx p-value, exact only for large n. If a future experiment
- * needs it at small n, swap normalCdf() for a Student-t CDF (regularised incomplete
- * beta) — the statistic and df here are already exact.
+ * needs it at small n, swap Normal::cdf() for a Student-t CDF (regularised
+ * incomplete beta) — the statistic and df here are already exact.
  */
 final class WelchTTest
 {
@@ -38,24 +38,8 @@ final class WelchTTest
             (($varA / $nA) ** 2) / ($nA - 1)
             + (($varB / $nB) ** 2) / ($nB - 1)
         );
-        $p = 2.0 * (1.0 - $this->normalCdf(abs($t)));
+        $p = 2.0 * (1.0 - Normal::cdf(abs($t)));
 
         return ['diff' => $diff, 'se' => $se, 't' => $t, 'df' => $df, 'p' => $p];
     }
-
-    private function normalCdf(float $x): float
-    {
-        return 0.5 * (1.0 + $this->erf($x / sqrt(2.0)));
-    }
-
-    /** Abramowitz & Stegun 7.1.26 — |error| < 1.5e-7. */
-    private function erf(float $x): float
-    {
-        $sign = $x < 0 ? -1.0 : 1.0;
-        $x = abs($x);
-        $t = 1.0 / (1.0 + 0.3275911 * $x);
-        $y = 1.0 - ((((1.061405429 * $t - 1.453152027) * $t + 1.421413741) * $t - 0.284496736) * $t + 0.254829592) * $t * exp(-$x * $x);
-
-        return $sign * $y;
-    }
 }

tests/Feature/SendPriceExperimentFunnelReportCommandTest.php

@@ -175,6 +175,34 @@ it('prints the primary CM/user (Welch) and conversion guardrail blocks', functio
         ->assertSuccessful();
 });
 
+it('flags a sample-ratio mismatch when the assignment split is lopsided', function () {
+    $signup = CarbonImmutable::parse('2026-06-05');
+
+    for ($i = 0; $i < 10; $i++) {
+        priceUser(PriceExperiment::CONTROL, $signup);
+    }
+    priceUser(PriceExperiment::HIGH, $signup);
+
+    artisan('stats:price-experiment-funnel', ['--no-discord' => true])
+        ->expectsOutputToContain('SRM')
+        ->expectsOutputToContain('IMBALANCE')
+        ->assertSuccessful();
+});
+
+it('does not flag SRM when the split is balanced', function () {
+    $signup = CarbonImmutable::parse('2026-06-05');
+
+    for ($i = 0; $i < 4; $i++) {
+        priceUser(PriceExperiment::CONTROL, $signup);
+        priceUser(PriceExperiment::HIGH, $signup);
+    }
+
+    artisan('stats:price-experiment-funnel', ['--no-discord' => true])
+        ->expectsOutputToContain('SRM')
+        ->doesntExpectOutputToContain('IMBALANCE')
+        ->assertSuccessful();
+});
+
 it('posts the price experiment embed to discord with the monitoring-only warning', function () {
     config(['services.discord.ai_cohort_webhook_url' => 'https://discord.test/hook']);
     Http::fake(['discord.test/*' => Http::response('', 204)]);

tests/Unit/SampleRatioMismatchTest.php

@@ -0,0 +1,32 @@
+<?php
+
+use App\Services\Stats\SampleRatioMismatch;
+
+it('reports p=1 for an exactly even split', function () {
+    $result = (new SampleRatioMismatch)->evenSplit(50, 50);
+
+    expect($result['chiSq'])->toBe(0.0)
+        ->and($result['p'])->toEqualWithDelta(1.0, 1e-6);
+});
+
+it('returns a neutral result for empty arms', function () {
+    $result = (new SampleRatioMismatch)->evenSplit(0, 0);
+
+    expect($result['chiSq'])->toBe(0.0)
+        ->and($result['p'])->toBe(1.0);
+});
+
+it('matches the known chi-square for a 60/40 split of 100', function () {
+    // χ² = ((60−50)² + (40−50)²)/50 = 4 → p = 2·(1 − Φ(2)) = 0.0455.
+    $result = (new SampleRatioMismatch)->evenSplit(60, 40);
+
+    expect($result['chiSq'])->toEqualWithDelta(4.0, 1e-9)
+        ->and($result['p'])->toEqualWithDelta(0.0455, 1e-3);
+});
+
+it('flags a badly lopsided split with a tiny p', function () {
+    $result = (new SampleRatioMismatch)->evenSplit(90, 10);
+
+    expect($result['chiSq'])->toEqualWithDelta(64.0, 1e-9)
+        ->and($result['p'])->toBeLessThan(0.001);
+});