0033/0 of 15 and 2 of 2.ipynb

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   "id": "d607511d-8b51-4f22-bd7e-d848ab296a05",
   "metadata": {},
   "outputs": [],
   "source": [
    "using Distributions\n",
    "using StatsPlots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "720143aa-4def-4890-bac2-9d592f54850c",
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      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function logtick(; xlim=(0.03, 30))\n",
    "    xmin, xmax = xlim\n",
    "    a = floor(Int, log10(xmin))\n",
    "    b = ceil(Int, log10(xmax))\n",
    "    nums =     [1, 2, 3, 4, 5, 6, 7, 8, 9]\n",
    "    mask = Bool[1, 1, 0, 0, 1, 0, 0, 0, 0]\n",
    "    \n",
    "    logtick = foldl(vcat, ([10.0^k*x for x in nums if xmin ≤ 10.0^k*x ≤ xmax] for k in a:b))\n",
    "    logticklabel_a = foldl(vcat,\n",
    "        ([mask[i] ? string(round(10.0^k*x; digits=-k)) : \"\"\n",
    "                for (i, x) in enumerate(nums) if xmin ≤ 10.0^k*x ≤ xmax]\n",
    "            for k in a:-1))\n",
    "    logticklabel_b = foldl(vcat,\n",
    "        ([mask[i] ? string(10^k*x) : \"\"\n",
    "                for (i, x) in enumerate(nums) if xmin ≤ 10.0^k*x ≤ xmax]\n",
    "            for k in 0:b))\n",
    "    logticklabel = vcat(logticklabel_a, logticklabel_b)\n",
    "    (logtick, logticklabel)\n",
    "end\n",
    "\n",
    "logtick()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "807f0054-23de-4073-85ba-c3ded7ab64df",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "pvalue_fisher_sterne (generic function with 1 method)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function pvalue_clopper_pearson(model::DiscreteUnivariateDistribution, data)\n",
    "    min(1, 2cdf(model, data), 2ccdf(model, data-1))\n",
    "end\n",
    "\n",
    "function pvalue_fisher_clopper_pearson(a, b, c, d; ω = 1)\n",
    "    if ω == 1\n",
    "        model = Hypergeometric(a+b, c+d, a+c)\n",
    "    else\n",
    "        model = FisherNoncentralHypergeometric(a+b, c+d, a+c, ω)\n",
    "    end\n",
    "    pvalue_clopper_pearson(model, a)\n",
    "end \n",
    "\n",
    "x ⪅ y = x < y || x ≈ y\n",
    "\n",
    "function pvalue_sterne(model::DiscreteUnivariateDistribution, data)\n",
    "    p0 = pdf(model, data)\n",
    "    p0 == 0 && return 0.0\n",
    "    p0 == 1 && return 1.0\n",
    "    m = mode(model)\n",
    "    pdf(model, m) ≈ p0 && return 1.0\n",
    "    if data > m\n",
    "        i = m - 1\n",
    "        while !(pdf(model, i) ⪅ p0) i -= 1 end\n",
    "        return cdf(model, i) + ccdf(model, data-1)\n",
    "    else # data < m\n",
    "        i = m + 1\n",
    "        while !(pdf(model, i) ⪅ p0) i += 1 end\n",
    "        return cdf(model, data) + ccdf(model, i-1)\n",
    "    end\n",
    "end\n",
    "\n",
    "function pvalue_fisher_sterne(a, b, c, d; ω = 1)\n",
    "    if ω == 1\n",
    "        model = Hypergeometric(a+b, c+d, a+c)\n",
    "    else\n",
    "        model = FisherNoncentralHypergeometric(a+b, c+d, a+c, ω)\n",
    "    end\n",
    "    pvalue_sterne(model, a)\n",
    "end "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9cc436cf-9297-48d8-85b3-bab84e68f957",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "confint_or_pearson_chisq (generic function with 1 method)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "safemul(x, y) = x == 0 ? x : isinf(x) ? typeof(x)(Inf) : x*y\n",
    "safediv(x, y) = x == 0 ? x : isinf(y) ? zero(y) : x/y\n",
    "\n",
    "function delta(a, b, c, d; ω=1)\n",
    "    A, B, C = 1-ω, a+d+ω*(b+c), a*d-ω*b*c\n",
    "    isinf(ω) ? typeof(ω)(-min(b, c)) : safediv(2C, B + √(B^2 - 4A*C))\n",
    "end\n",
    "\n",
    "# correction = 0.5 は連続性補正を与える.\n",
    "function _chisqstat_or(a, b, c, d, δ; correction=0.0)\n",
    "    ã, b̃, c̃, d̃ = a-δ, b+δ, c+δ, d-δ\n",
    "    safemul(max(0, abs(δ)-correction)^2, 1/ã + 1/b̃ + 1/c̃ + 1/d̃)\n",
    "end\n",
    "\n",
    "function chisqstat_or(a, b, c, d; ω=1, correction=0.0)\n",
    "    δ = delta(a, b, c, d; ω)\n",
    "    _chisqstat_or(a, b, c, d, δ; correction)\n",
    "end\n",
    "\n",
    "function pvalue_or_pearson_chisq(a, b, c, d; ω=1, correction=0.0)\n",
    "    χ² = chisqstat_or(a, b, c, d; ω, correction)\n",
    "    ccdf(Chisq(1), χ²)\n",
    "end\n",
    "\n",
    "function confint_or_pearson_chisq(a, b, c, d; α=0.05, correction=0.0)\n",
    "    (a+b==0 || c+d==0 || a+c==0 || b+d==0) && return [0, Inf]\n",
    "    f(logω) = logit(pvalue_or_pearson_chisq(a, b, c, d; ω=exp(logω), correction)) - logit(α)\n",
    "    ps = if a == 0 || d == 0\n",
    "        [0, exp(find_zero(f, 0.0))]\n",
    "    elseif b == 0 || c == 0\n",
    "        [exp(find_zero(f, 0.0)), Inf]\n",
    "    else\n",
    "        ORhat = oddsratiohat(a, b, c, d)\n",
    "        ω_L, ω_U = ORhat/2, 2ORhat\n",
    "        [exp(find_zero(f, log(ω_L))), exp(find_zero(f, log(ω_U)))]\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "02c578b0-1c0c-4caf-a1fa-79e062ea0d64",
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     "text": [
      "pvalue_fisher_clopper_pearson(0, 15, 2, 0) = 0.014705882352941168\n",
      "pvalue_fisher_sterne(0, 15, 2, 0) = 0.007352941176470584\n",
      "pvalue_or_pearson_chisq(0, 15, 2, 0) = 3.737981840170161e-5\n"
     ]
    }
   ],
   "source": [
    "@show pvalue_fisher_clopper_pearson(0, 15, 2, 0)\n",
    "@show pvalue_fisher_sterne(0, 15, 2, 0)\n",
    "@show pvalue_or_pearson_chisq(0, 15, 2, 0);"
   ]
  },
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   "execution_count": 6,
   "id": "3c53e7d8-ae7e-4e75-8ad9-d77673d454f9",
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      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot()\n",
    "plot!(ω -> pvalue_fisher_clopper_pearson(0, 15, 2, 0; ω), 0.001, 3; label=\"CP\")\n",
    "plot!(ω -> pvalue_fisher_sterne(0, 15, 2, 0; ω); label=\"S\")\n",
    "plot!(ω -> pvalue_or_pearson_chisq(0, 15, 2, 0; ω); label=\"χ²\")\n",
    "plot!(ytick=0:0.1:1)\n",
    "plot!(xscale=:log10, xtick=logtick(xlim=(0.001, 10)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "736d4109-c766-4789-a8d4-f3a58e86ddcc",
   "metadata": {},
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      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(legend=:topleft)\n",
    "plot!(ω -> pvalue_fisher_clopper_pearson(15, 0, 0, 2; ω), 0.3, 1000; label=\"CP\")\n",
    "plot!(ω -> pvalue_fisher_sterne(15, 0, 0, 2; ω), 0.3, 35; label=\"S\")\n",
    "plot!(ω -> pvalue_or_pearson_chisq(15, 0, 0, 2; ω); label=\"χ²\")\n",
    "plot!(ytick=0:0.1:1)\n",
    "plot!(xscale=:log10, xtick=logtick(xlim=(0.3, 1000)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b81ac2e1-7220-497b-a1a1-1bce81db67e7",
   "metadata": {},
   "source": [
    "https://mobile.twitter.com/subsub99999/status/1548293633623064576"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "bdf837a6-b22f-4214-9211-ec9df2642dca",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(a, b, c, d) = (7, 1182, 2, 811)\n",
      "pvalue_fisher_clopper_pearson(a, b, c, d) = 0.4398562959899008\n",
      "pvalue_fisher_sterne(a, b, c, d) = 0.3257190127661149\n",
      "pvalue_or_pearson_chisq(a, b, c, d) = 0.26027090050066687\n"
     ]
    },
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      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m, a, n, c = 1189, 7, 813, 2\n",
    "b, d = m-a, n-c\n",
    "@show a, b, c, d\n",
    "@show pvalue_fisher_clopper_pearson(a, b, c, d)\n",
    "@show pvalue_fisher_sterne(a, b, c, d)\n",
    "@show pvalue_or_pearson_chisq(a, b, c, d)\n",
    "\n",
    "plot()\n",
    "plot!(ω -> pvalue_fisher_clopper_pearson(a, b, c, d; ω), 0.2, 50; label=\"CP\")\n",
    "plot!(ω -> pvalue_fisher_sterne(a, b, c, d; ω); label=\"S\")\n",
    "plot!(ω -> pvalue_or_pearson_chisq(a, b, c, d; ω); label=\"χ²\")\n",
    "plot!(ytick=0:0.1:1)\n",
    "plot!(xscale=:log10, xtick=logtick(xlim=(0.2, 50)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "3806ef79-009d-49d8-8548-1cccf1c6e4e7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(a, b, c, d) = (1, 3365, 2, 811)\n",
      "pvalue_fisher_clopper_pearson(a, b, c, d) = 0.19749505692255276\n",
      "pvalue_fisher_sterne(a, b, c, d) = 0.09874752846127638\n",
      "pvalue_or_pearson_chisq(a, b, c, d) = 0.03877863766475411\n"
     ]
    },
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      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m, a, n, c = 3366, 1, 813, 2\n",
    "b, d = m-a, n-c\n",
    "@show a, b, c, d\n",
    "@show pvalue_fisher_clopper_pearson(a, b, c, d)\n",
    "@show pvalue_fisher_sterne(a, b, c, d)\n",
    "@show pvalue_or_pearson_chisq(a, b, c, d)\n",
    "\n",
    "plot()\n",
    "plot!(ω -> pvalue_fisher_clopper_pearson(a, b, c, d; ω), 0.0001, 20; label=\"CP\")\n",
    "plot!(ω -> pvalue_fisher_sterne(a, b, c, d; ω); label=\"S\")\n",
    "plot!(ω -> pvalue_or_pearson_chisq(a, b, c, d; ω); label=\"χ²\")\n",
    "plot!(ytick=0:0.1:1)\n",
    "plot!(xscale=:log10, xtick=logtick(xlim=(0.0001, 20)), xrotation=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "db055b08-b506-4ade-bfcf-1782ec9e246a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(a, b, c, d) = (1, 2943, 0, 207)\n",
      "pvalue_fisher_clopper_pearson(a, b, c, d) = 1.0\n",
      "pvalue_fisher_sterne(a, b, c, d) = 1.0\n",
      "pvalue_or_pearson_chisq(a, b, c, d) = 0.7908499031109096\n"
     ]
    },
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      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m, a, n, c = 2944, 1, 207, 0\n",
    "b, d = m-a, n-c\n",
    "@show a, b, c, d\n",
    "@show pvalue_fisher_clopper_pearson(a, b, c, d)\n",
    "@show pvalue_fisher_sterne(a, b, c, d)\n",
    "@show pvalue_or_pearson_chisq(a, b, c, d)\n",
    "\n",
    "plot(legend=:topleft)\n",
    "plot!(ω -> pvalue_fisher_clopper_pearson(a, b, c, d; ω), 0.0001, 20; label=\"CP\")\n",
    "plot!(ω -> pvalue_fisher_sterne(a, b, c, d; ω); label=\"S\")\n",
    "plot!(ω -> pvalue_or_pearson_chisq(a, b, c, d; ω); label=\"χ²\")\n",
    "plot!(ytick=0:0.1:1)\n",
    "plot!(xscale=:log10, xtick=logtick(xlim=(0.0001, 20)), xrotation=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "4154087f-fea5-43a9-b652-f27c5aca255c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(a, b, c, d) = (3, 3423, 0, 207)\n",
      "pvalue_fisher_clopper_pearson(a, b, c, d) = 1.0\n",
      "pvalue_fisher_sterne(a, b, c, d) = 1.0\n",
      "pvalue_or_pearson_chisq(a, b, c, d) = 0.6701636586351863\n"
     ]
    },
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      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m, a, n, c = 3426, 3, 207, 0\n",
    "b, d = m-a, n-c\n",
    "@show a, b, c, d\n",
    "@show pvalue_fisher_clopper_pearson(a, b, c, d)\n",
    "@show pvalue_fisher_sterne(a, b, c, d)\n",
    "@show pvalue_or_pearson_chisq(a, b, c, d)\n",
    "\n",
    "plot(legend=:topleft)\n",
    "plot!(ω -> pvalue_fisher_clopper_pearson(a, b, c, d; ω), 0.005, 100; label=\"CP\")\n",
    "plot!(ω -> pvalue_fisher_sterne(a, b, c, d; ω); label=\"S\")\n",
    "plot!(ω -> pvalue_or_pearson_chisq(a, b, c, d; ω); label=\"χ²\")\n",
    "plot!(ytick=0:0.1:1)\n",
    "plot!(xscale=:log10, xtick=logtick(xlim=(0.005, 100)), xrotation=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "836ed6cf-1b2b-41e9-afb8-df21655e4aea",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(a, b, c, d) = (5, 1148, 1, 1163)\n",
      "pvalue_fisher_clopper_pearson(a, b, c, d) = 0.21372727242346493\n",
      "pvalue_fisher_sterne(a, b, c, d) = 0.12283603212607436\n",
      "pvalue_or_pearson_chisq(a, b, c, d) = 0.09960444930607301\n"
     ]
    },
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      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m, a, n, c = 1153, 5, 1164, 1\n",
    "b, d = m-a, n-c\n",
    "@show a, b, c, d\n",
    "@show pvalue_fisher_clopper_pearson(a, b, c, d)\n",
    "@show pvalue_fisher_sterne(a, b, c, d)\n",
    "@show pvalue_or_pearson_chisq(a, b, c, d)\n",
    "\n",
    "plot(legend=:topleft)\n",
    "plot!(ω -> pvalue_fisher_clopper_pearson(a, b, c, d; ω), 0.2, 500; label=\"CP\")\n",
    "plot!(ω -> pvalue_fisher_sterne(a, b, c, d; ω); label=\"S\")\n",
    "plot!(ω -> pvalue_or_pearson_chisq(a, b, c, d; ω); label=\"χ²\")\n",
    "plot!(ytick=0:0.1:1)\n",
    "plot!(xscale=:log10, xtick=logtick(xlim=(0.2, 500)), xrotation=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "81b15980-3b1e-49ca-b7ba-30d5b268d188",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(a, b, c, d) = (7, 3708, 1, 1163)\n",
      "pvalue_fisher_clopper_pearson(a, b, c, d) = 0.7920332409663169\n",
      "pvalue_fisher_sterne(a, b, c, d) = 0.689160413826347\n",
      "pvalue_or_pearson_chisq(a, b, c, d) = 0.4506596398383987\n"
     ]
    },
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     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m, a, n, c = 3715, 7, 1164, 1\n",
    "b, d = m-a, n-c\n",
    "@show a, b, c, d\n",
    "@show pvalue_fisher_clopper_pearson(a, b, c, d)\n",
    "@show pvalue_fisher_sterne(a, b, c, d)\n",
    "@show pvalue_or_pearson_chisq(a, b, c, d)\n",
    "\n",
    "plot(legend=:topleft)\n",
    "plot!(ω -> pvalue_fisher_clopper_pearson(a, b, c, d; ω), 0.2, 500; label=\"CP\")\n",
    "plot!(ω -> pvalue_fisher_sterne(a, b, c, d; ω); label=\"S\")\n",
    "plot!(ω -> pvalue_or_pearson_chisq(a, b, c, d; ω); label=\"χ²\")\n",
    "plot!(ytick=0:0.1:1)\n",
    "plot!(xscale=:log10, xtick=logtick(xlim=(0.2, 500)), xrotation=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "aac541dd-3c0a-4856-99cd-8662555a463f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(a, b, c, d) = (70, 13640, 65, 6143)\n",
      "pvalue_fisher_clopper_pearson(a, b, c, d) = 5.24884029653111e-5\n",
      "pvalue_fisher_sterne(a, b, c, d) = 3.562440333991962e-5\n",
      "pvalue_or_pearson_chisq(a, b, c, d) = 1.9193599037140927e-5\n"
     ]
    },
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     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m, a, n, c = 13710, 70, 6208, 65\n",
    "b, d = m-a, n-c\n",
    "@show a, b, c, d\n",
    "@show pvalue_fisher_clopper_pearson(a, b, c, d)\n",
    "@show pvalue_fisher_sterne(a, b, c, d)\n",
    "@show pvalue_or_pearson_chisq(a, b, c, d)\n",
    "\n",
    "plot(legend=:topleft)\n",
    "plot!(ω -> pvalue_fisher_clopper_pearson(a, b, c, d; ω), 0.2, 1.5; label=\"CP\")\n",
    "plot!(ω -> pvalue_fisher_sterne(a, b, c, d; ω); label=\"S\")\n",
    "plot!(ω -> pvalue_or_pearson_chisq(a, b, c, d; ω); label=\"χ²\")\n",
    "plot!(ytick=0:0.1:1)\n",
    "plot!(xscale=:log10, xtick=logtick(xlim=(0.2, 5)), xrotation=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "d927a105-3435-4cdd-937c-45a2e77c6ee8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(a, b, c, d) = (99, 17657, 65, 6143)\n",
      "pvalue_fisher_clopper_pearson(a, b, c, d) = 0.00015769080075413985\n",
      "pvalue_fisher_sterne(a, b, c, d) = 0.00010937380058293333\n",
      "pvalue_or_pearson_chisq(a, b, c, d) = 5.6561464800920445e-5\n"
     ]
    },
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       "  1546.1,1356.02 1548.16,1356.24 1550.22,1356.42 1550.73,1356.46 1551.25,1356.49 1551.76,1356.52 1552.27,1356.55 1552.79,1368.47 1553.3,1368.56 1553.81,1368.65 \n",
       "  1554.32,1368.74 1556.37,1369.07 1558.41,1369.36 1560.45,1369.61 1562.49,1369.82 1578.62,1381.36 1594.51,1390.94 1609.4,1398.78 1624.08,1405.16 1638.55,1410.3 \n",
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      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m, a, n, c = 17756, 99, 6208, 65\n",
    "b, d = m-a, n-c\n",
    "@show a, b, c, d\n",
    "@show pvalue_fisher_clopper_pearson(a, b, c, d)\n",
    "@show pvalue_fisher_sterne(a, b, c, d)\n",
    "@show pvalue_or_pearson_chisq(a, b, c, d)\n",
    "\n",
    "plot(legend=:topleft)\n",
    "plot!(ω -> pvalue_fisher_clopper_pearson(a, b, c, d; ω), 0.2, 1.5; label=\"CP\")\n",
    "plot!(ω -> pvalue_fisher_sterne(a, b, c, d; ω); label=\"S\")\n",
    "plot!(ω -> pvalue_or_pearson_chisq(a, b, c, d; ω); label=\"χ²\")\n",
    "plot!(ytick=0:0.1:1)\n",
    "plot!(xscale=:log10, xtick=logtick(xlim=(0.2, 5)), xrotation=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f4dad74e-bb0a-4f9e-8e40-be3d22cce776",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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