fix: replace numpy/scipy with pure Python in experiment analytics (#6830)

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

Author: gagantrivedi

api/app_analytics/experiments.py

@@ -18,9 +18,10 @@
     GET /api/v1/environments/{env}/experiments/results/?feature=checkout_button
 """
 
+import math
+import random
 from typing import Any
 
-import numpy as np
 from common.environments.permissions import VIEW_ENVIRONMENT
 from django.db.models import Count, Q
 from drf_spectacular.utils import OpenApiParameter, extend_schema
@@ -29,7 +30,6 @@
 from rest_framework.permissions import IsAuthenticated
 from rest_framework.request import Request
 from rest_framework.response import Response
-from scipy import stats as scipy_stats  # type: ignore[import-untyped]
 
 from environments.identities.traits.models import Trait
 from environments.models import Environment
@@ -146,43 +146,34 @@ def _calculate_two_variant_stats(
             "sample_size_warning": "One or more variants have zero samples",
         }
 
-    # Build contingency table
-    table = np.array(
+    # Build contingency table, replacing zeros with 0.5 to avoid log(0)
+    table = [
         [
-            [
-                results[a]["conversions"],
-                total_a - results[a]["conversions"],
-            ],
-            [
-                results[b]["conversions"],
-                total_b - results[b]["conversions"],
-            ],
-        ]
-    )
+            max(results[a]["conversions"], 0.5),
+            max(total_a - results[a]["conversions"], 0.5),
+        ],
+        [
+            max(results[b]["conversions"], 0.5),
+            max(total_b - results[b]["conversions"], 0.5),
+        ],
+    ]
 
     # G-test (log-likelihood ratio test)
-    # Replace zeros with small values to avoid division errors
-    table_safe = np.where(table == 0, 0.5, table)
-    try:
-        _, p_value, _, _ = scipy_stats.chi2_contingency(
-            table_safe, correction=True, lambda_="log-likelihood"
-        )
-    except ValueError:
-        p_value = 1.0
+    p_value = _g_test(table)
 
     # Bayesian "Chance to Win" using Monte Carlo simulation
-    samples = 50000
-    samples_a = np.random.beta(
-        results[a]["conversions"] + 1,
-        total_a - results[a]["conversions"] + 1,
-        samples,
-    )
-    samples_b = np.random.beta(
-        results[b]["conversions"] + 1,
-        total_b - results[b]["conversions"] + 1,
-        samples,
-    )
-    chance_a_wins = float((samples_a > samples_b).mean())
+    n_samples = 10000
+    a_wins = 0
+    alpha_a = results[a]["conversions"] + 1
+    beta_a = total_a - results[a]["conversions"] + 1
+    alpha_b = results[b]["conversions"] + 1
+    beta_b = total_b - results[b]["conversions"] + 1
+    for _ in range(n_samples):
+        sa = random.betavariate(alpha_a, beta_a)
+        sb = random.betavariate(alpha_b, beta_b)
+        if sa > sb:
+            a_wins += 1
+    chance_a_wins = a_wins / n_samples
 
     # Determine winner and calculate lift (winner vs loser)
     if results[a]["rate"] > results[b]["rate"]:
@@ -239,41 +230,36 @@ def _calculate_multi_variant_stats(
                 "sample_size_warning": f"Variant '{v}' has zero samples",
             }
 
-    # Build contingency table for all variants
-    table = np.array(
+    # Build contingency table, replacing zeros with 0.5 to avoid log(0)
+    table = [
         [
-            [results[v]["conversions"], results[v]["total"] - results[v]["conversions"]]
-            for v in variants
+            max(results[v]["conversions"], 0.5),
+            max(results[v]["total"] - results[v]["conversions"], 0.5),
         ]
-    )
+        for v in variants
+    ]
 
     # G-test
-    table_safe = np.where(table == 0, 0.5, table)
-    try:
-        _, p_value, _, _ = scipy_stats.chi2_contingency(
-            table_safe, correction=True, lambda_="log-likelihood"
-        )
-    except ValueError:
-        p_value = 1.0
+    p_value = _g_test(table)
 
-    # Bayesian chance to win for each variant
-    samples = 50000
-    variant_samples = {}
-    for v in variants:
-        variant_samples[v] = np.random.beta(
+    # Bayesian chance to win for each variant via Monte Carlo
+    n_samples = 10000
+    params = [
+        (
             results[v]["conversions"] + 1,
             results[v]["total"] - results[v]["conversions"] + 1,
-            samples,
         )
-
-    # Calculate chance each variant is the best
-    chance_to_win = {}
-    for v in variants:
-        wins = np.ones(samples, dtype=bool)
-        for other in variants:
-            if other != v:
-                wins &= variant_samples[v] > variant_samples[other]
-        chance_to_win[v] = round(float(wins.mean()), 3)
+        for v in variants
+    ]
+    win_counts = [0] * len(variants)
+    for _ in range(n_samples):
+        draws = [random.betavariate(a, b) for a, b in params]
+        best_idx = max(range(len(draws)), key=lambda i: draws[i])
+        win_counts[best_idx] += 1
+
+    chance_to_win = {
+        v: round(win_counts[i] / n_samples, 3) for i, v in enumerate(variants)
+    }
 
     # Find the best performing variant
     best_variant = max(variants, key=lambda v: results[v]["rate"])
@@ -296,6 +282,92 @@ def _calculate_multi_variant_stats(
     }
 
 
+def _g_test(table: list[list[float]]) -> float:
+    """
+    Perform a G-test (log-likelihood ratio test) on a contingency table.
+
+    Returns the p-value under the chi-squared distribution.
+    """
+    rows = len(table)
+    cols = len(table[0])
+
+    row_totals = [sum(row) for row in table]
+    col_totals = [sum(table[r][c] for r in range(rows)) for c in range(cols)]
+    grand_total = sum(row_totals)
+
+    if grand_total == 0:  # pragma: no cover
+        return 1.0
+
+    g = 0.0
+    for r in range(rows):
+        for c in range(cols):
+            observed = table[r][c]
+            expected = row_totals[r] * col_totals[c] / grand_total
+            if observed > 0 and expected > 0:
+                g += observed * math.log(observed / expected)
+    g *= 2
+
+    df = (rows - 1) * (cols - 1)
+    if df == 0:  # pragma: no cover
+        return 1.0
+
+    return _chi2_sf(g, df)
+
+
+def _chi2_sf(x: float, df: int) -> float:
+    """Survival function (1 - CDF) for the chi-squared distribution."""
+    if x <= 0:
+        return 1.0
+    return _upper_gamma_reg(df / 2.0, x / 2.0)
+
+
+def _upper_gamma_reg(a: float, x: float) -> float:
+    """Regularised upper incomplete gamma function Q(a, x)."""
+    if x <= 0:  # pragma: no cover
+        return 1.0
+    if x < a + 1:
+        return 1.0 - _lower_gamma_series(a, x)
+    return _upper_gamma_cf(a, x)
+
+
+def _lower_gamma_series(a: float, x: float) -> float:
+    """Regularised lower incomplete gamma P(a, x) via series expansion."""
+    ap = a
+    total = 1.0 / a
+    term = 1.0 / a
+    for _ in range(300):
+        ap += 1
+        term *= x / ap
+        total += term
+        if abs(term) < abs(total) * 1e-15:
+            break
+    return total * math.exp(-x + a * math.log(x) - math.lgamma(a))
+
+
+def _upper_gamma_cf(a: float, x: float) -> float:
+    """Regularised upper incomplete gamma Q(a, x) via continued fraction."""
+    tiny = 1e-30
+    b = x + 1.0 - a
+    c = 1.0 / tiny
+    d = 1.0 / b
+    h = d
+    for i in range(1, 300):
+        an = -i * (i - a)
+        b += 2.0
+        d = an * d + b
+        if abs(d) < tiny:  # pragma: no cover
+            d = tiny
+        c = b + an / c
+        if abs(c) < tiny:  # pragma: no cover
+            c = tiny
+        d = 1.0 / d
+        delta = d * c
+        h *= delta
+        if abs(delta - 1.0) < 1e-15:
+            break
+    return h * math.exp(-x + a * math.log(x) - math.lgamma(a))
+
+
 @extend_schema(
     parameters=[
         OpenApiParameter(