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   "source": [
    "# Fisher exact tests\n",
    "\n",
    "<br>\n",
    "Author: Martin Horvat, March 2026\n",
    "\n",
    "Ref:\n",
    "* https://en.wikipedia.org/wiki/Fisher%27s_exact_test\n",
    "* https://mathworld.wolfram.com/FishersExactTest.html"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b24f6f9-4bf2-4751-8312-f011afd3422c",
   "metadata": {},
   "source": [
    "## Common"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "362e9a29-2caf-4155-8d90-a591005b4b25",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.special import gammaln\n",
    "\n",
    "def _log_table_prob(a, b, c, d):\n",
    "    r1, r2 = a + b, c + d\n",
    "    c1, c2 = a + c, b + d\n",
    "    n = r1 + r2\n",
    "    return (\n",
    "        gammaln(r1 + 1) + gammaln(r2 + 1) + gammaln(c1 + 1) + gammaln(c2 + 1)\n",
    "        - (gammaln(a + 1) + gammaln(b + 1) + gammaln(c + 1) + gammaln(d + 1) + gammaln(n + 1))\n",
    "    )\n",
    "\n",
    "def calculate_table_prob(a, b, c, d):\n",
    "    return float(np.exp(_log_table_prob(int(a), int(b), int(c), int(d))))\n",
    "\n",
    "def arange_at_margins(r, c):\n",
    "    amin = max(0, r[0] - c[1])\n",
    "    amax = min(r[0], c[0])\n",
    "    return np.arange(amin, amax + 1, dtype=np.int64)\n",
    "\n",
    "def fisher_p_value(table, eps: float = 1e-12):\n",
    "    mat = np.asarray(table, dtype=np.int64)\n",
    "    if mat.shape != (2, 2) or np.any(mat < 0):\n",
    "        raise ValueError(\"table must be a 2x2 array of nonnegative counts\")\n",
    "\n",
    "    a, b, c_, d = map(int, mat.ravel())\n",
    "    r = mat.sum(axis=1)  # [r1, r2]\n",
    "    c = mat.sum(axis=0)  # [c1, c2]\n",
    "\n",
    "    a_vals = arange_at_margins(r, c)\n",
    "\n",
    "    n = int(r[0] + r[1])\n",
    "    const = (\n",
    "        gammaln(int(r[0]) + 1) + gammaln(int(r[1]) + 1)\n",
    "        + gammaln(int(c[0]) + 1) + gammaln(int(c[1]) + 1)\n",
    "        - gammaln(n + 1)\n",
    "    )\n",
    "\n",
    "    b_vals = r[0] - a_vals\n",
    "    c_vals = c[0] - a_vals\n",
    "    d_vals = r[1] - c_vals\n",
    "\n",
    "    logp = const - (\n",
    "        gammaln(a_vals + 1) + gammaln(b_vals + 1)\n",
    "        + gammaln(c_vals + 1) + gammaln(d_vals + 1)\n",
    "    )\n",
    "\n",
    "    logp_obs = _log_table_prob(a, b, c_, d)\n",
    "    observed_p = float(np.exp(logp_obs))\n",
    "\n",
    "    mask = logp <= (logp_obs + np.log1p(eps))\n",
    "    two_sided_p = float(np.exp(logp[mask]).sum())\n",
    "\n",
    "    return observed_p, two_sided_p"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b5109a3-acf0-4285-8cfd-227074cfb015",
   "metadata": {},
   "source": [
    "## Check"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "9d0b1232-ff1a-41da-965e-7f27ed61cd77",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.01048951048951043, 0.11013986013986005, 0.33041958041957936, 0.3671328671328668, 0.1573426573426565, 0.023601398601398604, 0.0008741258741258679]\n",
      "0.9999999999999976\n"
     ]
    }
   ],
   "source": [
    "# Check \n",
    "table = [[8, 2], [1, 5]]\n",
    "\n",
    "# margins\n",
    "r = np.sum(table, axis = 1)\n",
    "c = np.sum(table, axis = 0)\n",
    "\n",
    "# values of a\n",
    "avals = arange_mat_margins(r, c)\n",
    "\n",
    "probs = [prob_mat_margins(x, r, c) for x in avals]\n",
    "\n",
    "print(probs)\n",
    "print(sum(probs))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "218076bd-89d8-4305-8656-41cde67de1b4",
   "metadata": {},
   "source": [
    "## Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "5b861593-4786-4b00-bdce-da1710b68af1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Odds Ratio: 20.0000\n",
      "P-value: 0.0350\n",
      "\n",
      "Result is statistically significant (Reject H0)\n",
      "\n",
      "Observed Table Probability: 0.0236\n",
      "Two-Sided P-Value: 0.0350\n"
     ]
    }
   ],
   "source": [
    "# 2x2 Contingency Table\n",
    "#             Success | Failure\n",
    "# Treatment A:   8    |    2\n",
    "# Treatment B:   1    |    5\n",
    "table = [[8, 2], [1, 5]]\n",
    "\n",
    "# Perform the test\n",
    "# returns the odds ratio and the p-value\n",
    "odds_ratio, p_value = scipy.stats.fisher_exact(table)\n",
    "\n",
    "print(f\"Odds Ratio: {odds_ratio:.4f}\")\n",
    "print(f\"P-value: {p_value:.4f}\")\n",
    "\n",
    "# Interpretation\n",
    "alpha = 0.05\n",
    "if p_value < alpha:\n",
    "    print(\"\\nResult is statistically significant (Reject H0)\")\n",
    "else:\n",
    "    print(\"\\nResult is not statistically significant (Fail to reject H0)\")\n",
    "\n",
    "obs_p, final_p = fisher_p_value(table)\n",
    "print(f\"\\nObserved Table Probability: {obs_p:.4f}\")\n",
    "print(f\"Two-Sided P-Value: {final_p:.4f}\")\n"
   ]
  }
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