{ "cells": [ { "attachments": {}, "cell_type": "markdown", "id": "b1b93787", "metadata": {}, "source": [ "# 03 - Stats Review: The Most Dangerous Equation\n", "\n", "2007년 Howard Wainer는 매우 위험한 공식에 관하여 적었습니다.\n", "\"어떤 공식들은 알고 있으면 위험하고, 어떤 공식들은 모르고 있으면 위험합니다. 첫째는 경계 내의 비밀에 끔찍한 위험이 내재되어 있기 때문입니다. 이와 같은 공식은 아인슈타인의 상징적인 $E = MC^2$인데, 평범한 물질 안에 숨겨진 거대한 에너지의 척도를 제공하기 때문입니다. 대신 저는 우리가 모를 때 위험을 방출하는 공식들에 관심을 갖고 있습니다. 이 공식들은 가까이서 보면 사물들에 대해 명확하게 이해시켜주지만, 이 공식들의 부재는 우리를 위험하게 할 정도로 무지하게 만듭니다.\" \n", "\n", "그가 말한 공식은 Moivre's equation으로 아래와 같습니다: \n", "$\n", "SE = \\frac{\\sigma}{\\sqrt{n}}\n", "$\n", "위 식에서 SE는 평균의 표준오차, $\\sigma$는 표준편차, 그리고 n은 표본 크기를 의미합니다. 용감하고 진실된 사람이 정복해야 할 수학처럼 들리지만, 한번 시작해봅시다!\n", "\n", "이 공식을 모르는 것이 왜 매우 위험한지 알아보기 위해, 교육 데이터를 살펴봅시다. 저는 ENEM 점수(SAT와 유사한 브라질 표준 고등학교 점수)를 3년 동안 다른 학교들에서 수집했습니다. 또한 저는, 우리와 관련된 정보를 유지하기 위해 데이터를 전처리했습니다. 원본 데이터는 [Inep website](http://portal.inep.gov.br/web/guest/microdados#)에서 다운로드 할 수 있습니다.\n", "\n", "가장 성적이 좋은 학교를 보면, 눈을 끄는 것이 있는데, 학생들의 수가 상당히 적습니다." ] }, { "cell_type": "code", "execution_count": 1, "id": "a9b1628f", "metadata": { "tags": [ "hide-input" ] }, "outputs": [], "source": [ "import warnings\n", "warnings.filterwarnings('ignore')\n", "\n", "import pandas as pd\n", "import numpy as np\n", "from scipy import stats\n", "import seaborn as sns\n", "from matplotlib import pyplot as plt\n", "from matplotlib import style\n", "style.use(\"fivethirtyeight\")" ] }, { "cell_type": "code", "execution_count": 2, "id": "8ed84c09", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/html": [ "
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yearschool_idnumber_of_studentsavg_score
166702007330626336882.97
1679620073306540317282.04
166682005330626335981.89
1679420053306540317781.66
100432007293428804380.32
181212007331523141479.82
167812007330652508079.67
302620072202574014479.52
1463620073131172322279.41
1731820073308767921079.38
\n", "
" ], "text/plain": [ " year school_id number_of_students avg_score\n", "16670 2007 33062633 68 82.97\n", "16796 2007 33065403 172 82.04\n", "16668 2005 33062633 59 81.89\n", "16794 2005 33065403 177 81.66\n", "10043 2007 29342880 43 80.32\n", "18121 2007 33152314 14 79.82\n", "16781 2007 33065250 80 79.67\n", "3026 2007 22025740 144 79.52\n", "14636 2007 31311723 222 79.41\n", "17318 2007 33087679 210 79.38" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = pd.read_csv(\"enem_scores.csv\")\n", "df.sort_values(by=\"avg_score\", ascending=False).head(10)" ] }, { "cell_type": "markdown", "id": "25ce44db", "metadata": {}, "source": [ "다른 각도에서 보면 상위 1% 학교만 분리하고 연구할 수 있습니다. 어떻게 생겼나요? 아마도 우리는 최고로부터 배울 수 있고 다른 곳에서 복제할 수 있습니다. 그리고 당연히, 상위 1% 학교를 보면, 평균적으로 학생이 적음을 알 수 있습니다." ] }, { "cell_type": "code", "execution_count": 3, "id": "50e0f6a6", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_data = (df\n", " .assign(top_school = df[\"avg_score\"] >= np.quantile(df[\"avg_score\"], .99))\n", " [[\"top_school\", \"number_of_students\"]]\n", " .query(f\"number_of_students<{np.quantile(df['number_of_students'], .98)}\")) # remove outliers\n", "\n", "plt.figure(figsize=(6,6))\n", "sns.boxplot(x=\"top_school\", y=\"number_of_students\", data=plot_data)\n", "plt.title(\"Number of Students of 1% Top Schools (Right)\");" ] }, { "attachments": {}, "cell_type": "markdown", "id": "0469cb33", "metadata": {}, "source": [ "한 가자 당연한 결론은, 작은 학교들이 더 높은 학업 성취를 이끌어낸다는 것입니다. 이는 직관적으로 교사 한 명당 맡은 학생 수가 적을 때, 교사가 각 학생에게 주의를 기울일 수 있기 때문입니다. 그러나 이것이 Moivre's equation과 무슨 연관이 있을까요? 그리고 왜 위험할까요?\n", "\n", "이 정보를 기반으로 사람들이 중요하고 비싼 결정들을 한다면 위험해질 것입니다. 그의 기사에서 Howard는 계속 진행합니다.\n", "\n", "\"1990년대에, 학교 규모를 줄이는 것이 인기가 많았습니다. 수 많은 자선 단체들과 정부 기관들이 더 큰 학교들에게 펀딩을 하였는데, 이는 작은 학교들의 학생들이 높은 시험 점수를 위해 과도하게 대표되긴 했습니다.\"\n", "\n", "사람들은 하위 1%의 학교도 살펴보는 것을 잊었습니다. 만일 우리가 그것을 했더라면, 그들 역시 매우 적은 학생 수를 보여줍니다." ] }, { "cell_type": "code", "execution_count": 4, "id": "6959c3f3", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "q_99 = np.quantile(df[\"avg_score\"], .99)\n", "q_01 = np.quantile(df[\"avg_score\"], .01)\n", "\n", "plot_data = (df\n", " .sample(10000)\n", " .assign(Group = lambda d: np.select([d[\"avg_score\"] > q_99, d[\"avg_score\"] < q_01],\n", " [\"Top\", \"Bottom\"], \"Middle\")))\n", "plt.figure(figsize=(10,5))\n", "sns.scatterplot(y=\"avg_score\", x=\"number_of_students\", hue=\"Group\", data=plot_data)\n", "plt.title(\"ENEM Score by Number of Students in the School\");" ] }, { "attachments": {}, "cell_type": "markdown", "id": "21e01b3c", "metadata": {}, "source": [ "우리는 위의 그래프를 통해 Moivre 공식에서 무엇을 기대하는지 명확하게 볼 수 있습니다. 학생 수가 증가할 수록, 평균 점수는 더 정확해집니다. 학생 수가 적은 학교들은 운에 의해 매우 높거나 매우 낮은 점수 분포를 보여줍니다. 이 점은 큰 학교들에서는 잘 나타나지 않습니다. Moivre 공식은 정보의 실재화와 데이터 기록 형태는 항상 정확하지 않다는 기본적인 사실에 대해서 이야기 합니다. 그렇다면 질문은 얼마나 정확하지 않을까요?\n", "\n", "통계학은 이러한 부정확한 것에 대해 다루는 과학이라 우리의 허를 찌르지 않습니다. Taleb은 자신의 책에 무작위에 속았다고 적었습니다.\n", "\n", "> 확률은 단순히 주사위 던지기나 더 복잡한 것들에 대해 계산하는 것이 아닙니다. 확률은 우리의 지식에 대한 확신의 부족함을 인정하고 우리의 무지를 대하는 방법들을 발전하는 방법입니다.\n", "\n", "불확실성을 계산하는 방법 중 하나는 **분산의 추정량**을 구하는 것입니다. 분산은 중심과 가장 있을 것 같은 값으로부터 얼마나 떨어져있는지 알려줍니다. Moivre 공식이 말해주듯이, 불확실성은 관측된 데이터가 클 수록 줄어듭니다. 말이 되죠? 만일 우리가 많은 학생들이 학교에서 잘한다면, 우리는 좋은 학교라고 확신할 수 있습니다. 그렇나 만일 우리가 10명의 학생 중 8명만 잘한다고 하면, 더 의구심이 들어야 합니다. 우연으로 인해 그 학교는 평균 이상의 학생들이 다닐 가능성이 있으니까요. \n", "\n", "위의 아름다운 삼각형 그래프는 이 이야기를 보여줍니다. 표본의 수가 작을 때 우리의 추정치는 큰 분산을 갖습니다. 또한 표본이 커질 수록 분산이 줄어듬을 보여줍니다. 학교에서의 평균 점수는 이에 대해 사실이고, 우리가 추정하고 싶은 ATE를 포함한 그 어떤 요약 통계에 대해서도 마찬가지입니다.\n", "\n", "## The Standard Error of Our Estimates\n", "\n", "지금까지는 통계학의 리뷰였기 때문에 더 빨리 진행하도록 하겠습니다. 만일 분포, 분산, 표준오차에 대해 잘 모르신다면 계속 읽어주시되 추가적인 요소들이 필요함을 명심하시기 바랍니다. MIT의 기초 통계학 수업이 보편적으로 꽤 좋기 때문에 수강할 것을 권장합니다.\n", "\n", "이 전 섹션에서 우리는 평균 처리 효과 $E[Y_{1}-Y_{0}]$를 처리 군과 대조 군 평균 간 차이 $E[Y|T=1] - E[Y|T=0]$으로 다뤘습니다. 우리는 온라인 수업의 ATE를 동기부여 사례로 알아냈습니다. 또한 우리는 온라인 수업은 학생들의 수행 점수가 대면 수업일 때 보다 5점 낮은 부정적인 효과도 보았습니다. 이제 우리는 통계적으로 유의한지 확인하고자 합니다.\n", "이를 위해 우리는 표준오차를 추정해야합니다. 우리는 이미 표본크기 n에 대해 알고 있습니다. 표준오차의 추정치는 \n", "$\\hat{\\sigma} = \\sqrt{\\frac{1}{N-1}\\sum_{i=1}^N (x_{i}-\\bar{x})^2}$ \n", "\n", "$\\bar{x}$는 x의 평균을 의미합니다. 다행히도 대부분 프로그래밍 소프트웨어를 통해 이를 구현할 수 있습니다. 판다스에서는 [std](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.std.html)를 사용합니다." ] }, { "cell_type": "code", "execution_count": 5, "id": "d1cd8be1", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SE for Online: 1.5371593973041635\n", "SE for Face to Face: 0.8723511456319104\n" ] } ], "source": [ "data = pd.read_csv(\"online_classroom.csv\")\n", "online = data.query(\"format_ol==1\")[\"falsexam\"]\n", "face_to_face = data.query(\"format_ol==0 & format_blended==0\")[\"falsexam\"]\n", "\n", "def se(y: pd.Series):\n", " return y.std() / np.sqrt(len(y))\n", "\n", "print(\"SE for Online:\", se(online))\n", "print(\"SE for Face to Face:\", se(face_to_face))" ] }, { "attachments": {}, "cell_type": "markdown", "id": "4b08d199", "metadata": {}, "source": [ "## Confidence Intervals\n", "\n", "추정치에 대한 표준오차는 확신에 대한 치수입니다. 무슨 의미인지 정확하게 이해하기 위해 우리는 혼란스럽고 격렬한 통계의 물줄기에 빠져야합니다. 빈도주의자 관점에서 데이터는 정확한 데이터 생성 과정에 대한 표현일 뿐입니다. 이 과정은 추상적이고 이상적입니다. 바뀌지 않지만 우리에게 알려지지 않는 모수에 의해 지배됩니다. 학생들 시험의 문맥으로 보면, 만일 우리가 여러번 실험을 하여 많은 데이터를 얻었을 때, 모든 것은 실제 기본 데이터 생성 과정과 유사하지만 정확히 같지는 않습니다. 플라톤의 이데아와 유사합니다. \n", "\n", "> 본질의 하나 하나는 그 자신을 굉장히 다양한 조합들; 운동, 물질 등 다양한 형태로 표현합니다.\n", "\n", "우리가 학생 시험 점수가 참 평균 74, 참 표준편차 2의 정규분포를 따른 다는 것을 알고 있다고 가정합시다. 이 분포로부터 우리는 10000번의 실험을 합니다. 한 번의 실험에서 우리는 500의 표본을 얻습니다. 이것을 히스토그램으로 그리면, 실험에 대한 평균이 참 평균 근처로 분포됨을 알 수 있습니다. 어떤 실험 표본은 참 값에 비해 작을 수도 있고 클 수도 있습니다." ] }, { "cell_type": "code", "execution_count": 6, "id": "f746ff12", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "true_std = 2\n", "true_mean = 74\n", "\n", "n = 500\n", "def run_experiment(): \n", " return np.random.normal(true_mean,true_std, 500)\n", "\n", "np.random.seed(42)\n", "\n", "plt.figure(figsize=(8,5))\n", "freq, bins, img = plt.hist([run_experiment().mean() for _ in range(10000)], bins=40, label=\"Experiment Means\")\n", "plt.vlines(true_mean, ymin=0, ymax=freq.max(), linestyles=\"dashed\", label=\"True Mean\", color=\"orange\")\n", "plt.legend();" ] }, { "attachments": {}, "cell_type": "markdown", "id": "cc41ba60", "metadata": {}, "source": [ "우리는 평균들의 평균에 대해 얘기하고 있는 것을 기억하십시오. 우연하게 우리는 실험의 평균이 참 평균보다 작거나 클 수 있습니다. 이는 우리는 실험의 평균이 참 평균과 맞다고 확신할 수 없습니다. 그렇지만 **표준오차를 통해 우리는 참 평균이 95%안에 포함되도록 구간을 만들 수 있습니다.**\n", "\n", "현실 세계에서 우리는 다양한 데이터 셋을 통해 같은 실험에 대해 여러번 실험할 수 없습니다. 그렇지만 우리는 **신뢰구간**을 만들 수 있습니다. 신뢰구간은 확률이 더해져서 구해지고 가장 일반적인 구간은 95%입니다. 이 확률은 서로 다른 연구에서 얼마나 많은 가상 신뢰구간을 만들 수 있는지 알려줍니다. 예를 들어 비슷한 연구에서 95% 신뢰구간을 계산하면 실제 평균 95%가 포함됩니다.\n", "\n", "신뢰구간을 계산하기 위해서 우리는 **중심극한정리**(central limit theorem)를 이용합니다. 중심극한정리는 실험들의 **평균들이 정규분포를 따른다는 것**을 말하고 있어요. 우리는 통계학적 이론에서 정규분포 질량의 95%는 평균 위와 아래의 2 표준편차 사이에 있다는 것을 알고 있습니다. (정확하게는 1.96이지만, 2는 충분히 가깝습니다)\n", "\n", "![normal_density](./data/img/stats-review/normal_dist.jpeg)\n", "\n", "평균의 표준오차는 실험 평균의 분포에 대한 추정치 역할을 합니다. 따라서 만일 우리가 표준오차에서 2를 곱한 실험 평균들 중 하나를 에서 더하고 빼면 참 평균에 대한 95% 신뢰구간을 만들 수 있습니다. " ] }, { "cell_type": "code", "execution_count": 7, "id": "5b976045", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(73.82718114045632, 74.17341543460314)\n" ] } ], "source": [ "np.random.seed(321)\n", "exp_data = run_experiment()\n", "exp_se = exp_data.std() / np.sqrt(len(exp_data))\n", "exp_mu = exp_data.mean()\n", "ci = (exp_mu - 2 * exp_se, exp_mu + 2 * exp_se)\n", "print(ci)" ] }, { "cell_type": "code", "execution_count": 8, "id": "e9416e67", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(exp_mu - 4*exp_se, exp_mu + 4*exp_se, 100)\n", "y = stats.norm.pdf(x, exp_mu, exp_se)\n", "plt.plot(x, y)\n", "plt.vlines(ci[1], ymin=0, ymax=1)\n", "plt.vlines(ci[0], ymin=0, ymax=1, label=\"95% CI\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "0ac3449a", "metadata": {}, "source": [ "당연히 우리는 95% 신뢰구간으로 제한할 필요는 없습니다. 우리는 표준편차를 곱하는데 필요한 것을 찾아 정규 분포의 질량의 99% 포함하는 신뢰구간도 만들 수 있습니다.\n", "\n", "파이썬의 ppf 함수는 누적 분포 함수의 역함수를 알려줍니다. 85% 신뢰구간을 찾기 위해 표준오차 2를 곱하는 대신에, 99% 신뢰구간을 만들 z를 곱할 것입니다. 따라서 ppf(0.5)는 정규분포 질량의 50%가 0 아래 있음을 나타내는 0을 나타낼 것입니다. 같은 방법으로 우리가 99.5%를 넣으면 분포 질량의 99.5%가 z값 아래 형성되도록 만드는 z를 구할 것입니다. 다시 말해 분포 질량의 0.5%는 z값보다 큽니다." ] }, { "cell_type": "code", "execution_count": 9, "id": "887a493b", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2.5758293035489004\n" ] }, { "data": { "text/plain": [ "(73.7773381773405, 74.22325839771896)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from scipy import stats\n", "z = stats.norm.ppf(.995)\n", "print(z)\n", "ci = (exp_mu - z * exp_se, exp_mu + z * exp_se)\n", "ci" ] }, { "cell_type": "code", "execution_count": 10, "id": "abd3ef44", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(exp_mu - 4*exp_se, exp_mu + 4*exp_se, 100)\n", "y = stats.norm.pdf(x, exp_mu, exp_se)\n", "plt.plot(x, y)\n", "plt.vlines(ci[1], ymin=0, ymax=1)\n", "plt.vlines(ci[0], ymin=0, ymax=1, label=\"99% CI\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "fb43dc22", "metadata": {}, "source": [ "우리의 교실 실험으로 돌아오겠습니다. 우리는 온라인 수업과 대면 수업의 학생들의 평균 시험 점수에 대한 신뢰구간을 만들 수 있습니다." ] }, { "cell_type": "code", "execution_count": 11, "id": "0f03478f", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "95% CI for Online: (70.56094429049804, 76.7095818797147)\n", "95% for Face to Face: (76.80278229206948, 80.29218687459712)\n" ] } ], "source": [ "def ci(y: pd.Series):\n", " return (y.mean() - 2 * se(y), y.mean() + 2 * se(y))\n", "\n", "print(\"95% CI for Online:\", ci(online))\n", "print(\"95% for Face to Face:\", ci(face_to_face))" ] }, { "attachments": {}, "cell_type": "markdown", "id": "753d4c37", "metadata": {}, "source": [ "집단 간 95% 신뢰구간이 겹치지 않습니다. 대면 수업 신뢰구간의 하한은 온라인 수업 신뢰구간의 상한보다 높습니다. 이는 대면 수업 학생들의 실제 평균 값이 온라인 수업 학생들의 실제 평균 값보다 높다는 결과가 우연적이지 않음을 나타냅니다. 다시 말해 대면 수업에서 온라인 수업으로 전환할 경우 학업 성취에 대해 유의한 인과적 감소를 주장할 수 있습니다. \n", "\n", "요약하자면, 신뢰구간은 추정치들에 대한 불확실성을 배치하는 방법입니다. 표본이 작을 수록, 표준오차는 커지고 신뢰구간은 넓어집니다. 표준오차와 신뢰구간은 계산하기 쉽기 때문에, 신뢰구간의 신호 부족은 나쁜 의도나 지식의 부족을 의미하는데, 동등하게 우려됩니다. 마지막으로 불확실성에 대한 척도가 없다면 항상 의심하셔야합니다.\n", "\n", "![img](data/img/stats-review/ci_xkcd.png)\n", "\n", "마지막으로 주의 한마디를 하겠습니다. 신뢰구간은 한 눈에 보는 것보다 해석하기 까다롭습니다. 예를 들면, 이 특정 95% 신뢰구간에 95% 확률로 실제 모집단 평균이 포함되어 있다고 말하면 안됩니다. 빈도주의자 입장에서 모집단 평균은 실제 모수로 간주합니다. 그렇기 때문에 우리의 특정 신뢰구간에 존재한다고 할 수 없습니다. 다시 말해, 만일 존재 한다면, 95%가 아니라 100%입니다. 만일 존재하지 않는다면 0%입니다. 대신 신뢰구간에서 95%는 많은 연구에서 계산된 신뢰구간이 실제 평균을 포함하는 빈도를 나타냅니다. 95%는 특정 간격 자체가 아니라 95%를 신뢰구간을 계산하는데 사용되는 알고리즘에 대한 우리의 신뢰도 입니다.\n", "\n", "경제학자로서(통계학자들은 한 눈 팔아주세요 ^^) 저는 이 순수주의가 그다지 유용하다고 생각하지 않습니다. 실제로 특정 신뢰구간에 실제 평균 95%가 포함되어 있다고 말하는 사람들을 볼 수 있습니다. 틀리긴 했지만, 우리의 추정치에 대한 불확실성의 정도를 정확하게 표현한다는 점에서 유해하지는 않습니다. 게다가, 베이지안 통계학으로 바꿔서 신뢰구간 대신 신용구간을 사용한다면, 우리는 구간 안에 분포의 평균이 95% 포함되어 있다고 할 수 있습니다. 또한, 실제로 제가 본 바에 따르면, 어느 정도 큰 표본에서 빈도주의자도 인정 하시겠지만, 베이지안 확률 구간은 베이지안보다 신뢰구간에 더 유사합니다. \n", "\n", "그러니, 만일 제 말에 중요한 것이 있다면, 신뢰구간에 대해 여러분이 원하는 어떤 것이든 자유롭게 말해주시기 바랍니다. 저는 여러분들이 실제 평균의 95% 포함하고 있다고 말해도 상관 없습니다. 여러분들의 추정치에 신뢰구간을 배치하는 것을 잊지 마세요. 그렇지 않으면 바보처럼 보일 것입니다.\n", "\n", "## Hypothesis Testing\n", "\n", "불확실성을 표현하는 또 다른 방법은 가설검정입니다. 평균 간 차이가 통계학적으로 0(혹은 다른 값)과 다릅니까? 독립 정규분포 2개의 합과 차는 정규분포임을 기억하십시오. 평균의 결과는 두 분포 간 합 또는 차인 반면, 분산의 결과는 항상 분산의 합이 됩니다. \n", "\n", "$N(\\mu_{1}, \\sigma_{1}^2) - N(\\mu_{2}, \\sigma_{2}^2) = N(\\mu_{1} - \\mu_{2}, \\sigma_{1}^2 + \\sigma_{2}^2)$ \n", "\n", "$N(\\mu_{1}, \\sigma_{1}^2) + N(\\mu_{2}, \\sigma_{2}^2) = N(\\mu_{1} + \\mu_{2}, \\sigma_{1}^2 + \\sigma_{2}^2)$ \n", "\n", "기억 못하셔도 괜찮습니다. 우리는 항상 코드를 통해 체크할 수 있습니다." ] }, { "cell_type": "code", "execution_count": 12, "id": "01836e1f", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "np.random.seed(123)\n", "n1 = np.random.normal(4, 3, 30000)\n", "n2 = np.random.normal(1, 4, 30000)\n", "n_diff = n2 - n1\n", "sns.distplot(n1, hist=False, label=\"$N(4,3^2)$\")\n", "sns.distplot(n2, hist=False, label=\"$N(1,4^2)$\")\n", "sns.distplot(n_diff, hist=False, label=f\"$N(1,4^2) - (4,3^2) = N(-3, 5^2)$\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "235651df", "metadata": {}, "source": [ "만일 우리가 두 집단들의 분포에서 평균을 뺀다면, 우리는 3번째 분포를 얻게 될 것입니다. 이 최종 분포의 평균은 평균들 간 차이이고, 표준편차는 표준편차들의 합의 제곱근입니다. \n", "\n", "$\\mu_{diff} = \\mu_{1} - \\mu_{2}$ \n", "$SE_{diff} = \\sqrt{SE_{1} + SE_{2}} = \\sqrt{\\frac{\\sigma_{1}^2}{n_{1}} + \\frac{\\sigma_{2}^2}{n_{2}}}$ \n", "\n", "교실 예제로 돌아갑시다. 우리는 차이에 대한 분포를 만들 것입니다. 당연히 95% 신뢰구간도 만들 것입니다." ] }, { "cell_type": "code", "execution_count": 13, "id": "57bc55e7", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(-8.376410208363357, -1.4480327880904964)\n" ] } ], "source": [ "diff_mu = online.mean() - face_to_face.mean()\n", "diff_se = np.sqrt(face_to_face.var()/len(face_to_face) + online.var()/len(online))\n", "ci = (diff_mu - 1.96*diff_se, diff_mu + 1.96*diff_se)\n", "print(ci)" ] }, { "cell_type": "code", "execution_count": 14, "id": "3ebf4581", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(diff_mu - 4*diff_se, diff_mu + 4*diff_se, 100)\n", "y = stats.norm.pdf(x, diff_mu, diff_se)\n", "plt.plot(x, y)\n", "plt.vlines(ci[1], ymin=0, ymax=.05)\n", "plt.vlines(ci[0], ymin=0, ymax=.05, label=\"95% CI\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "5e5dae73", "metadata": {}, "source": [ "이를 통해 온라인 집단과 대면 집단 간 실제 차이가 -8.37에서 -1.44 사이에 있다고 95% 신뢰할 수 있다고 할 수 있습니다. 우리는 또한 평균 간 차이에 차이에 대한 표준오차를 나누어서 z통계량을 만들 수 있습니다. \n", "\n", "$z = \\frac{\\mu_{diff}-H_{0}}{SE_{diff}} = \\frac{(\\mu_{1}-\\mu_{2})}{\\sqrt{\\frac{\\sigma_{1}^2}{n_{1}} + \\frac{\\sigma_{2}^2}{n_{2}}}}$ \n", "\n", "$H_{0}$는 우리가 차이를 검정하고 싶은 값입니다. \n", "z통계량은 관측된 차이가 얼마나 극단적인지 측정해줍니다. 우리는 평균의 차이가 0과 통계적으로 다르다는 가설을 검정하기 위해 모순을 이용할 것입니다. 우리는 반대(차이가 0이다)를 참으로 가정할 것입니다. 이를 귀무가설 혹은 $H_{0}$으로 표현합니다. 그리고 우리 자신에게 \"만일 진정한 차이가 0이라면 우리는 이런 차이를 관찰할 가능성이 있을까?\" 물어봅니다. 우리는 이 질문을 통계학적 수학 용어로 z통계량이 0에서 얼마나 멀리 있는지 확인하는 것으로 변환할 수 있습니다. \n", "\n", "귀무가설 하에, z통계량은 표준 정규 분포를 따릅니다. 따라서 만일 차이가 정말 0이라면, 우리는 z통계량이 평균적으로 95%의 확률로 2 표준편차 내에 확인할 수 있습니다. z가 2 표준편차보다 높거나 낮으면, 95% 신뢰도로 귀무가설을 기각할 수 있습니다. \n", "\n", "교실예제에서 한번 살펴봅시다." ] }, { "cell_type": "code", "execution_count": 15, "id": "27db611d", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-2.7792810791031064\n" ] } ], "source": [ "z = diff_mu / diff_se\n", "print(z)" ] }, { "cell_type": "code", "execution_count": 16, "id": "b3e952fb", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-4,4,100)\n", "y = stats.norm.pdf(x, 0, 1)\n", "plt.plot(x, y, label=\"Standard Normal\")\n", "plt.vlines(z, ymin=0, ymax=.05, label=\"Z statistic\", color=\"C1\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "1f8ede25", "metadata": {}, "source": [ "꽤 극단적인 값으로 보입니다. 실제로 2보다 큰데, 이는 집단 간 차이가 없다면 우리가 이런 극단적인 값을 볼 확률이 5% 미만을 의미합니다. 이는 또한 대면 수업에서 온라인 수업으로 전환하는 것이 통계적으로 유의미한 학업 성취도를 떨어뜨린다는 결론을 내리게 합니다.\n", "\n", "가설검정의 마지막 흥미로운 점은 처리된 집단과 처리되지 않은 집단의 95% 신뢰구간이 겹치는지 확인하는 것보다 덜 보수적이라는 점입니다. 다시 말해 만일 두 집단 간 신뢰구간이 겹친다 하더라도 통계적으로 유의할 수 있습니다. 예를 들어 대면 집단이 평균 80점에, 표준오차 4, 온라인 집단이 평균 71점에 표준오차 2를 받았다고 가정합시다." ] }, { "cell_type": "code", "execution_count": 17, "id": "65b1198c", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Control 95% CI: (67.08, 74.92)\n", "Test 95% CI: (72.16, 87.84)\n", "Diff 95% CI: (0.23461352820082482, 17.765386471799175)\n" ] } ], "source": [ "cont_mu, cont_se = (71, 2)\n", "test_mu, test_se = (80, 4)\n", "\n", "diff_mu = test_mu - cont_mu\n", "diff_se = np.sqrt(cont_se**2 + test_se**2)\n", "\n", "print(\"Control 95% CI:\", (cont_mu-1.96*cont_se, cont_mu+1.96*cont_se))\n", "print(\"Test 95% CI:\", (test_mu-1.96*test_se, test_mu+1.96*test_se))\n", "print(\"Diff 95% CI:\", (diff_mu-1.96*diff_se, diff_mu+1.96*diff_se))" ] }, { "attachments": {}, "cell_type": "markdown", "id": "b5de9230", "metadata": {}, "source": [ "만일 우리가 두 집단에 대해 신뢰구간을 만들면 겹칩니다. 온라인 집단의 상한은 74.92이고 대면 집단의 하한은 72.16입니다. 그러나 집단 간 차이에 대한 95% 신뢰구간을 계산하면 0이 포함되지 않습니다. 개별 신뢰구간이 겹치더라도 여전히 통계학적으로 0과 다를 수 있습니다.\n", "\n", "## P-values\n", "\n", "이전에 저는 온라인 집단과 대면 집단의 차이가 실제로 0이라면 우리가 이러한 극단적인 값을 관찰할 확률은 5% 미만이라고 말했습니다. 하지만 우리가 그 가능성을 정확히 예측할 수 있을까요? 우리가 이러한 극단적인 값을 관찰할 가능성이 얼마나 될까요? p값을 입력하세요!\n", "\n", "신뢰구간(사실 가장 빈도주의 통계학)과 마찬가지로 p값으 진정한 정의는 매우 헷갈릴 수 있습니다. 따라서 어떠한 위험도 감수하지 않기 위해 위키피디아에서 정의를 복사해왔습니다. \"p값은 귀무가설이 올바르다고 가정할 때, 검정 중에 실제 관찰될 수 있는 가장 극단적인 검정결과를 얻을 확률입니다\"\n", "\n", "좀 더 간결히 설명하면, 귀무가설이 참이라는 가정하에 p값은 그러한 데이터를 볼 확률입니다. 귀무가설이 참일 경우 측정값을 볼 가능성이 얼마나 낮은지를 측정합니다. 자연스럽게 이는 귀무가설이 참일 확률과 혼동됩니다. 여기서 차이점을 주의하십시오. p값은 $P(H_{0}|data)$가 아니라 $P(data|H_{0})$입니다.\n", "\n", "하지만 이런 복잡함이 당신을 속이게 하지 마십시오. 실용적인 측면에서 사용하기 쉽습니다. \n", "\n", "p값을 구하려면, z통계량 전후에 표준 정규분포 면적을 계산해야합니다. 다행히도, 이 계산을 해 줄 컴퓨터가 있습니다. 누적 표준 정규분포에 z통계량을 넣으면 됩니다. " ] }, { "cell_type": "code", "execution_count": 18, "id": "1e7649e8", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "P-value: 0.0027239680835564706\n" ] } ], "source": [ "print(\"P-value:\", stats.norm.cdf(z))" ] }, { "cell_type": "markdown", "id": "68a66574", "metadata": {}, "source": [ "p값은 95% 혹은 99%와 같은 신뢰수준을 지정할 필요 없기에 흥미롭습니다. 하지만 p값에서 하나를 보고자 하는 경우 어떤 신뢰 수준에서 우리의 검정이 합격 혹은 불합격인지 정확히 알 수 있습니다. 예를 들어 p값이 0.0027이라면, 유의수준이 0.2%임을 알 수 있습니다. 따라서 95% 신뢰구간과 99% 신뢰구간에서는 0이 포함되지 않지만, 99.9% 신뢰구간에서는 포함됩니다. 이는 만일 차이가 0이라면 이 극단적인 z통계량을 관측할 확률이 0.2%임을 의미합니다." ] }, { "cell_type": "code", "execution_count": 19, "id": "7529adba", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "95% CI: (-8.37634655308288, -1.4480964433709733)\n", "99% CI: (-9.464853535264012, -0.3595894611898425)\n", "99.9% CI: (-10.72804065824553, 0.9035976617916743)\n" ] } ], "source": [ "diff_mu = online.mean() - face_to_face.mean()\n", "diff_se = np.sqrt(face_to_face.var()/len(face_to_face) + online.var()/len(online))\n", "print(\"95% CI:\", (diff_mu - stats.norm.ppf(.975)*diff_se, diff_mu + stats.norm.ppf(.975)*diff_se))\n", "print(\"99% CI:\", (diff_mu - stats.norm.ppf(.995)*diff_se, diff_mu + stats.norm.ppf(.995)*diff_se))\n", "print(\"99.9% CI:\", (diff_mu - stats.norm.ppf(.9995)*diff_se, diff_mu + stats.norm.ppf(.9995)*diff_se))" ] }, { "attachments": {}, "cell_type": "markdown", "id": "80d71679", "metadata": {}, "source": [ "## Key Ideas\n", "\n", "이번 챕터에서 Moivre의 공식을 아는 것이 얼마나 중요한지 보았고, 그것이 우리 추정치에 어느정도 확신이 되는지 알기 위해 사용했습니다. 우리는 온라인 수업이 대면 수업에 비해 학업성취도 저하를 유발하는 것을 알아냈습니다. 우리는 또한 통계학적으로 유의한 결과임을 확인했습니다. 우리는 두 집단의 평균 신뢰구간을 비교하고, 차이에 대한 신뢰구간을 살펴보고, 가설검정을 수행했고 p값을 확인했습니다. 이전에 했던 것 처럼 단일 A/B 테스트 비교 함수를 만드는 것으로 이번 장을 마무리하려고 해요." ] }, { "cell_type": "code", "execution_count": 20, "id": "a3ec3b7d", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Test 95.0% CI: 73.63526308510637 +- 3.0127770572134565\n", "Control 95.0% CI: 78.5474845833333 +- 1.7097768273108\n", "Test-Control 95.0% CI: -4.912221498226927 +- 3.4641250548559537\n", "Z Statistic -2.7792810791031064\n", "P-Value 0.0027239680835564706\n" ] } ], "source": [ "def AB_test(test: pd.Series, control: pd.Series, confidence=0.95, h0=0):\n", " mu1, mu2 = test.mean(), control.mean()\n", " se1, se2 = test.std() / np.sqrt(len(test)), control.std() / np.sqrt(len(control))\n", " \n", " diff = mu1 - mu2\n", " se_diff = np.sqrt(test.var()/len(test) + control.var()/len(control))\n", " \n", " z_stats = (diff-h0)/se_diff\n", " p_value = stats.norm.cdf(z_stats)\n", " \n", " def critial(se): return -se*stats.norm.ppf((1 - confidence)/2)\n", " \n", " print(f\"Test {confidence*100}% CI: {mu1} +- {critial(se1)}\")\n", " print(f\"Control {confidence*100}% CI: {mu2} +- {critial(se2)}\")\n", " print(f\"Test-Control {confidence*100}% CI: {diff} +- {critial(se_diff)}\")\n", " print(f\"Z Statistic {z_stats}\")\n", " print(f\"P-Value {p_value}\")\n", " \n", "AB_test(online, face_to_face)" ] }, { "attachments": {}, "cell_type": "markdown", "id": "940cab58", "metadata": {}, "source": [ "위 함수는 충분히 일반적이기 때문에, 다른 귀무가설 검정도 할 수 있어요. 예를 들어, 온라인과 대면 수업의 효과 차이가 -1인지 기각할 수 있을까요? 우리가 얻는 결과를 통해 우리는 95% 신뢰도를 통해 차이가 -1보다 유의하다고 할 수 있습니다. 그렇지만 99% 신뢰도로는 할 수 없습니다." ] }, { "cell_type": "code", "execution_count": 21, "id": "b8cc749b", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Test 95.0% CI: 73.63526308510637 +- 3.0127770572134565\n", "Control 95.0% CI: 78.5474845833333 +- 1.7097768273108\n", "Test-Control 95.0% CI: -4.912221498226927 +- 3.4641250548559537\n", "Z Statistic -2.2134920404560723\n", "P-Value 0.013431870694630667\n" ] } ], "source": [ "AB_test(online, face_to_face, h0=-1)" ] }, { "attachments": {}, "cell_type": "markdown", "id": "a66a6972", "metadata": {}, "source": [ "## References\n", "\n", "이 책을 쓰기 위해 Joshua Angrist, Alberto Abadie, Christopher Walters의 대단한 계량 경제학 수업 자료를 많이 참고했습니다. 해당 자료에 있는 대부분의 아이디어는 전미경제학회(American Economic Association)의 수업에서 가져왔어요. 이렇게 좋은 참고자료를 보는 것이 2020년의 힘든 한 해를 지탱하게 만들어준 원동력이었다고 생각해요.\n", "\n", "* [Cross-Section Econometrics](https://www.aeaweb.org/conference/cont-ed/2017-webcasts)\n", "* [Mastering Mostly Harmless Econometrics](https://www.aeaweb.org/conference/cont-ed/2020-webcasts)\n", "\n", "또한, Angrist의 정말 좋은 책들을 참고자료에 넣고 싶어요. 해당 저자가 쓴 책들은 계량경제학(Econometrics) 또는 '메트릭스(Metrics, 계량적 분석)'가 매우 유용할 뿐만 아니라 매우 흥미롭다는 걸 알려주었어요.\n", "\n", "* [Mostly Harmless Econometrics](https://www.mostlyharmlesseconometrics.com/)\n", "* [Mastering ‘Metrics](https://www.masteringmetrics.com/)\n", "\n", "마지막으로 참고한 자료는 Miguel Hernan과 Jamie Robins의 책입니다. 이 책들은 제가 대답해야 했던 까다로운 인과적인 질문에서 신뢰할 수 있는 동반자 같은 존재였어요.\n", "\n", "* [Causal Inference Book](https://www.hsph.harvard.edu/miguel-hernan/causal-inference-book/)\n", "\n", "해당 챕터에서 사용된 데이터는 해당 논문의 자료를 참조했습니다. Alpert, William T., Kenneth A. Couch, and Oskar R. Harmon. 2016. [\"A Randomized Assessment of Online Learning\"](https://www.aeaweb.org/articles?id=10.1257/aer.p20161057)\n", "\n", "## Contribute\n", "\n", "Causal Inference for the Brave and True는 인과추론, 통계학에 대한 오픈소스 자료입니다. 이 자료는 금전적으로나 모든 분들이 쉽게 접근하실 수 있도록 하는 것이 목표입니다. 또한, 이 책은 Python 기반의 무료 소프트웨어만 사용해요.\n", "여러분들께서 이 자료가 가치 있다고 생각하시고, 금전적으로 지원을 원하신다면 [Patreon](https://www.patreon.com/causal_inference_for_the_brave_and_true)를 방문해주세요. \n", "만약 여러분이 금전적으로 기여하기가 쉽지 않으시다면, 오타 수정, 수정 제안, 이해하기 난해한 부분에 대한 피드백 제공 등을 통해 도움을 주실 수 있어요. 이 책의 Github 저장소 [이슈 페이지](https://github.com/CausalInferenceLab/Causal-Inference-with-Python/issues)를 방문해주세요. 마지막으로 이 자료가 여러분의 마음에 드셨다면 도움이 될 수 있는 다른 사람들과 공유해주시고, [한국어 번역 자료](https://github.com/CausalInferenceLab/Causal-Inference-with-Python/stargazers)와 [해당 번역본의 원서](https://github.com/matheusfacure/python-causality-handbook/stargazers)에 star 부탁드립니다!" ] } ], "metadata": { "kernelspec": { "display_name": "Workspace_JS", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.7" }, "vscode": { "interpreter": { "hash": "a812027cb36d52afc6bf34b1f842ed1960d479f5dea7272b4a52eb53764f32d8" } } }, "nbformat": 4, "nbformat_minor": 5 }