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hotchpotch/-_mean_height.ipynb Secret

Created October 2, 2021 23:54
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平均身長の区間推定_mean_height.ipynb
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-_mean_height.ipynb
{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "平均身長の区間推定_mean_height.ipynb",
"provenance": [],
"collapsed_sections": [],
"authorship_tag": "ABX9TyNcd2puOTCB1fKc1Ont40Ex",
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/hotchpotch/7bf84a8e987f77bed5b100447a22c5cd/-_mean_height.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "code",
"metadata": {
"id": "kYD1Yct08ILd"
},
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"import scipy.stats\n",
"import math"
],
"execution_count": 4,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "08yQDcDUXtlH"
},
"source": [
""
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "exuvv6AYG9Vt",
"outputId": "a7478af0-e8f7-4f6e-c13a-0b27cd7dbee1"
},
"source": [
"%load_ext google.colab.data_table\n"
],
"execution_count": 5,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"The google.colab.data_table extension is already loaded. To reload it, use:\n",
" %reload_ext google.colab.data_table\n"
]
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "tuTk762W64WH"
},
"source": [
"# https://ja.wikipedia.org/wiki/%E8%BA%AB%E9%95%B7 より\n",
"# 日本人男性20歳以上の値\n",
"\n",
"base_mean = 168.0\n",
"base_var = 7.1\n",
"base_std = base_var ** 2\n"
],
"execution_count": 6,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "0J7E4-6C8UoR",
"outputId": "d8419d68-a920-475f-c69e-cb10e4465e46"
},
"source": [
"# それっぽい身長を作る\n",
"\n",
"def generate_standard_height():\n",
" return base_mean + np.random.randn() * base_var\n",
"\n",
"[generate_standard_height() for _ in range(20)]\n",
"\n"
],
"execution_count": 7,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"[161.0119632893179,\n",
" 149.34553275567944,\n",
" 171.41123243968028,\n",
" 157.15877203800517,\n",
" 174.3646412962626,\n",
" 170.0429266815561,\n",
" 149.6802701525633,\n",
" 168.87575845312182,\n",
" 177.12544396272065,\n",
" 166.67720970805055,\n",
" 173.83887919966634,\n",
" 166.5418718692225,\n",
" 161.66504338294095,\n",
" 164.83744972769992,\n",
" 171.57126091893915,\n",
" 187.5997740667393,\n",
" 174.21879737862844,\n",
" 157.49123005790062,\n",
" 170.2969980091891,\n",
" 175.51998644434286]"
]
},
"metadata": {},
"execution_count": 7
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 265
},
"id": "5rNcoRNu9XbE",
"outputId": "6c27dcae-12e2-42f4-beef-fe587abab6b8"
},
"source": [
"# 168 を中心に標準正規分布になってることを確認する。\n",
"\n",
"plt.hist([generate_standard_height() for _ in range(100000)], bins=50)\n",
"plt.show()\n"
],
"execution_count": 8,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "nVKDc2ygCrN7",
"outputId": "3787a11a-7092-4c82-cb24-4943ea2a464e"
},
"source": [
"# t分布 から値を取得する\n",
"\n",
"def calc_t_value(percent=0.95, n=10, ddof=1):\n",
" v = (1 - percent) / 2\n",
" upper = scipy.stats.t.ppf(1-v, n-ddof)\n",
" lower = scipy.stats.t.ppf(v, n-ddof)\n",
" return (lower, upper)\n",
"\n",
"# n = 10, 自由度 n - 1 (= 9) の値を求める。\n",
"# 信頼区間95%なら両端は0.025\n",
"# +-2.262 なら正しい\n",
"\n",
"print(calc_t_value(percent=0.95, n=10))"
],
"execution_count": 9,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"(-2.2621571627409915, 2.2621571627409915)\n"
]
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "yZcAGENYFtAD",
"outputId": "e2b9357a-5261-408c-d651-17406cfd63cf"
},
"source": [
"# 信頼区間の値を求める\n",
"\n",
"def calc_confident_value(percent, n, mean, std, ddof=1):\n",
" v = std / math.sqrt(n) \n",
" lower, upper = calc_t_value(percent, n, ddof)\n",
" return (mean + lower*v, mean + upper*v)\n",
"\n",
"# 確認。2538.78 < mean < 2648.62 であれば正しい。\n",
"calc_confident_value(percent=0.95, n=10, mean=2593.20, std=77.48)\n"
],
"execution_count": 10,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"(2537.7741469267944, 2648.6258530732052)"
]
},
"metadata": {},
"execution_count": 10
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "FqVMBKAA-MA0",
"outputId": "7605a2a5-d232-4e21-9da0-976451daab94"
},
"source": [
"def generate_sample(n, group, mean, var, seed=42):\n",
" np.random.seed(seed)\n",
" ary = np.random.standard_normal((group, n))\n",
" ary = ary * var + mean\n",
" return ary\n",
"\n",
"def generate_sample_height(n, group, seed=42):\n",
" return generate_sample(n, group, base_mean, base_var)\n",
"\n",
"generate_sample_height(4, 10)"
],
"execution_count": 11,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([[171.52667049, 167.01832346, 172.59858862, 178.81351198],\n",
" [166.33751104, 166.33762761, 179.21241099, 173.44878658],\n",
" [164.66673186, 171.85217631, 164.70973438, 164.69331875],\n",
" [169.71793213, 154.41571026, 155.75308339, 164.00775854],\n",
" [160.80889905, 170.23115606, 161.55302906, 157.97264372],\n",
" [178.40610626, 166.39698827, 168.47945025, 157.88428788],\n",
" [164.13488266, 168.78755039, 159.8279456 , 170.66745593],\n",
" [163.7354653 , 165.92897438, 163.72788305, 181.15117511],\n",
" [167.9041697 , 160.4902524 , 173.84006888, 159.33201009],\n",
" [169.48293152, 154.08634212, 158.56987905, 169.39771477]])"
]
},
"metadata": {},
"execution_count": 11
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 655
},
"id": "39oBaCAI_wYD",
"outputId": "f651ee72-e68f-46fc-8a06-3fb7c2a50608"
},
"source": [
"# 標本数が4で、信頼区間95%の平均値を求める区間を推定する。\n",
"\n",
"n = 4\n",
"group = 10000\n",
"percent = 0.95\n",
"\n",
"samples = generate_sample_height(n, group)\n",
"s_mean = samples.mean(axis=1)\n",
"s_var = samples.var(axis=1)\n",
"s_std = np.sqrt(s_var)\n",
"\n",
"rows = []\n",
"for (m, s) in np.stack([s_mean, s_std], axis=1):\n",
" (lower, upper) = calc_confident_value(percent=percent, n=n, mean=m, std=s, ddof=1)\n",
" valid = lower < base_mean < upper\n",
" rows.append([m, s ,lower, upper, valid])\n",
"\n",
"df = pd.DataFrame(data=rows, columns=['mean', 'std', 'lower', 'upper', 'valid'])\n",
"df_invalid = df[df['valid'] == False]\n",
"# 標本数が4だと、区間推定に収まっているものは92.86%。以外と悪いなぁ。\n",
"print(len(df), len(df_invalid), f\"per: {1 - len(df_invalid) / len(df)}\")\n",
"df"
],
"execution_count": 33,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"10000 714 per: 0.9286\n"
]
},
{
"output_type": "execute_result",
"data": {
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\"178.82680150173522\",\n },\ntrue],\n [{\n 'v': 1984,\n 'f': \"1984\",\n },\n{\n 'v': 170.50459698397418,\n 'f': \"170.50459698397418\",\n },\n{\n 'v': 12.597342354077503,\n 'f': \"12.597342354077503\",\n },\n{\n 'v': 150.45941416840674,\n 'f': \"150.45941416840674\",\n },\n{\n 'v': 190.54977979954162,\n 'f': \"190.54977979954162\",\n },\ntrue],\n [{\n 'v': 1985,\n 'f': \"1985\",\n },\n{\n 'v': 163.23743951455808,\n 'f': \"163.23743951455808\",\n },\n{\n 'v': 7.493032435499339,\n 'f': \"7.493032435499339\",\n },\n{\n 'v': 151.31435281969306,\n 'f': \"151.31435281969306\",\n },\n{\n 'v': 175.1605262094231,\n 'f': \"175.1605262094231\",\n },\ntrue],\n [{\n 'v': 1986,\n 'f': \"1986\",\n },\n{\n 'v': 170.4791500909345,\n 'f': \"170.4791500909345\",\n },\n{\n 'v': 5.583156034055165,\n 'f': \"5.583156034055165\",\n },\n{\n 'v': 161.5951029447323,\n 'f': \"161.5951029447323\",\n },\n{\n 'v': 179.3631972371367,\n 'f': \"179.3631972371367\",\n },\ntrue],\n [{\n 'v': 1987,\n 'f': \"1987\",\n },\n{\n 'v': 168.97097691210243,\n 'f': \"168.97097691210243\",\n },\n{\n 'v': 6.9542334087696265,\n 'f': \"6.9542334087696265\",\n },\n{\n 'v': 157.90523970319077,\n 'f': \"157.90523970319077\",\n },\n{\n 'v': 180.03671412101409,\n 'f': \"180.03671412101409\",\n },\ntrue],\n [{\n 'v': 1988,\n 'f': \"1988\",\n },\n{\n 'v': 171.17954923586336,\n 'f': \"171.17954923586336\",\n },\n{\n 'v': 9.681760024968272,\n 'f': \"9.681760024968272\",\n },\n{\n 'v': 155.7737085258088,\n 'f': \"155.7737085258088\",\n },\n{\n 'v': 186.58538994591794,\n 'f': \"186.58538994591794\",\n },\ntrue],\n [{\n 'v': 1989,\n 'f': \"1989\",\n },\n{\n 'v': 171.24599903387264,\n 'f': \"171.24599903387264\",\n },\n{\n 'v': 7.0826953803947355,\n 'f': \"7.0826953803947355\",\n },\n{\n 'v': 159.97585016147707,\n 'f': \"159.97585016147707\",\n },\n{\n 'v': 182.5161479062682,\n 'f': \"182.5161479062682\",\n },\ntrue],\n [{\n 'v': 1990,\n 'f': \"1990\",\n },\n{\n 'v': 169.7071051537502,\n 'f': \"169.7071051537502\",\n },\n{\n 'v': 7.096024340846283,\n 'f': \"7.096024340846283\",\n },\n{\n 'v': 158.41574693088347,\n 'f': \"158.41574693088347\",\n },\n{\n 'v': 180.99846337661694,\n 'f': \"180.99846337661694\",\n },\ntrue],\n [{\n 'v': 1991,\n 'f': \"1991\",\n },\n{\n 'v': 167.34456749383278,\n 'f': \"167.34456749383278\",\n },\n{\n 'v': 4.623595454733244,\n 'f': \"4.623595454733244\",\n },\n{\n 'v': 159.98739535781033,\n 'f': \"159.98739535781033\",\n },\n{\n 'v': 174.70173962985524,\n 'f': \"174.70173962985524\",\n },\ntrue],\n [{\n 'v': 1992,\n 'f': \"1992\",\n },\n{\n 'v': 173.27192113531214,\n 'f': \"173.27192113531214\",\n },\n{\n 'v': 5.276308832757528,\n 'f': \"5.276308832757528\",\n },\n{\n 'v': 164.8761363601382,\n 'f': \"164.8761363601382\",\n },\n{\n 'v': 181.6677059104861,\n 'f': \"181.6677059104861\",\n },\ntrue],\n [{\n 'v': 1993,\n 'f': \"1993\",\n },\n{\n 'v': 166.64295401507087,\n 'f': \"166.64295401507087\",\n },\n{\n 'v': 2.8680383759343657,\n 'f': \"2.8680383759343657\",\n },\n{\n 'v': 162.07926494861798,\n 'f': \"162.07926494861798\",\n },\n{\n 'v': 171.20664308152377,\n 'f': \"171.20664308152377\",\n },\ntrue],\n [{\n 'v': 1994,\n 'f': \"1994\",\n },\n{\n 'v': 164.63633424678378,\n 'f': \"164.63633424678378\",\n },\n{\n 'v': 6.690457447633436,\n 'f': \"6.690457447633436\",\n },\n{\n 'v': 153.99032345434247,\n 'f': \"153.99032345434247\",\n },\n{\n 'v': 175.28234503922508,\n 'f': \"175.28234503922508\",\n },\ntrue],\n [{\n 'v': 1995,\n 'f': \"1995\",\n },\n{\n 'v': 168.68047456222723,\n 'f': \"168.68047456222723\",\n },\n{\n 'v': 7.659276481377647,\n 'f': \"7.659276481377647\",\n },\n{\n 'v': 156.49285649257178,\n 'f': \"156.49285649257178\",\n },\n{\n 'v': 180.8680926318827,\n 'f': \"180.8680926318827\",\n },\ntrue],\n [{\n 'v': 1996,\n 'f': \"1996\",\n },\n{\n 'v': 166.69704788974235,\n 'f': \"166.69704788974235\",\n },\n{\n 'v': 3.178304041148559,\n 'f': \"3.178304041148559\",\n },\n{\n 'v': 161.63965691333073,\n 'f': \"161.63965691333073\",\n },\n{\n 'v': 171.75443886615398,\n 'f': \"171.75443886615398\",\n },\ntrue],\n [{\n 'v': 1997,\n 'f': \"1997\",\n },\n{\n 'v': 171.71022938866844,\n 'f': \"171.71022938866844\",\n },\n{\n 'v': 3.2010058769506107,\n 'f': \"3.2010058769506107\",\n },\n{\n 'v': 166.6167147255211,\n 'f': \"166.6167147255211\",\n },\n{\n 'v': 176.80374405181578,\n 'f': \"176.80374405181578\",\n },\ntrue],\n [{\n 'v': 1998,\n 'f': \"1998\",\n },\n{\n 'v': 175.18768377715335,\n
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