{ "cells": [ { "cell_type": "markdown", "id": "6e0e2de7-dfaf-4db4-ac60-537a079eab3b", "metadata": {}, "source": [ "## Mendel's model" ] }, { "cell_type": "code", "execution_count": 42, "id": "990f729a-8bff-4f7e-b9db-ed50034e64cc", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from matplotlib.pyplot import subplots\n", "\n", "# simulating the test statistic\n", "num_repetitions = 10000\n", "L = []\n", "for i in range(num_repetitions):\n", " n = np.random.choice([1, 0], size = 929, replace=True, p = [0.75, 0.25])\n", " L.append(n.sum())\n", "\n", "L = np.array(L)\n", "L = np.abs(L/929 - 0.75)\n", "\n", "fig, ax = subplots(figsize = (4, 4))\n", "ax.hist(L, density = True);\n", "ax.scatter(0.0088, 0, color='red');" ] }, { "cell_type": "code", "execution_count": 43, "id": "81b12d1e-3ab6-4f8f-b4d8-04c9374d0cd5", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.float64(0.5439)" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Calculating the empirical p-value for Mendel's model\n", "empirical_pvalue = np.sum(L >= 0.0088)/num_repetitions\n", "empirical_pvalue" ] }, { "cell_type": "markdown", "id": "06bf1e7c-bc55-413a-bcc8-58a420310c31", "metadata": {}, "source": [ "## Smoking and birth weight" ] }, { "cell_type": "code", "execution_count": 44, "id": "a70d9bfa-cf07-4c6b-80e0-eccefd31fee8", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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Maternal SmokerBirth Weight
0False120
1False113
2True128
3True108
4False136
.........
1169False113
1170False128
1171True130
1172False125
1173False117
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1174 rows × 2 columns

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" ], "text/plain": [ " Maternal Smoker Birth Weight\n", "0 False 120\n", "1 False 113\n", "2 True 128\n", "3 True 108\n", "4 False 136\n", "... ... ...\n", "1169 False 113\n", "1170 False 128\n", "1171 True 130\n", "1172 False 125\n", "1173 False 117\n", "\n", "[1174 rows x 2 columns]" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "\n", "baby = pd.read_csv('baby.csv')\n", "births = baby[['Maternal Smoker', 'Birth Weight']]\n", "births" ] }, { "cell_type": "code", "execution_count": 45, "id": "5f5f22a7-dc60-453d-a593-e64c00616343", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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Maternal SmokerBirth Weight
0False715
1True459
\n", "
" ], "text/plain": [ " Maternal Smoker Birth Weight\n", "0 False 715\n", "1 True 459" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "births.groupby('Maternal Smoker')['Birth Weight'].count().reset_index()" ] }, { "cell_type": "code", "execution_count": 46, "id": "bbbcc063-ff4a-44d5-8d42-c0ddc2386c44", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0 120\n", "1 113\n", "4 136\n", "5 138\n", "6 132\n", " ... \n", "1168 132\n", "1169 113\n", "1170 128\n", "1172 125\n", "1173 117\n", "Name: Birth Weight, Length: 715, dtype: int64" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Checking the birth weights of non smokers\n", "births[births['Maternal Smoker'] == False]['Birth Weight']" ] }, { "cell_type": "code", "execution_count": 27, "id": "e081a9dc-069e-4a61-a637-16cb3f6d9669", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = subplots(figsize = (4, 4))\n", "ax.hist(births[births['Maternal Smoker'] == False]['Birth Weight'], alpha=0.5, label = 'Non Smoker')\n", "ax.hist(births[births['Maternal Smoker'] == True]['Birth Weight'], alpha=0.5, label = 'Smoker')\n", "ax.legend();" ] }, { "cell_type": "code", "execution_count": 47, "id": "c49f2581-cd21-48aa-9814-2f78c79d1bb3", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Maternal SmokerBirth Weight
0False123.085315
1True113.819172
\n", "
" ], "text/plain": [ " Maternal Smoker Birth Weight\n", "0 False 123.085315\n", "1 True 113.819172" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Finding the average weight of the groups\n", "means = births.groupby('Maternal Smoker')['Birth Weight'].mean().reset_index()\n", "means" ] }, { "cell_type": "code", "execution_count": 49, "id": "a5a86aaa-11e1-43af-8b06-fb22c533b20f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.float64(-9.266142572024918)" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Finding the observed value\n", "observed_value = means.iloc[1, 1] - means.iloc[0, 1]\n", "observed_value" ] }, { "cell_type": "code", "execution_count": 50, "id": "6e1a64fe-4e58-48e6-9547-9f4b65265ca4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "121 True\n", "320 False\n", "420 False\n", "196 False\n", "70 False\n", " ... \n", "865 True\n", "35 False\n", "185 False\n", "132 False\n", "969 False\n", "Name: Maternal Smoker, Length: 1174, dtype: bool" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Finding a random permutation of labels\n", "shuffle = births.sample(frac=1.0, replace = False)['Maternal Smoker']\n", "shuffle" ] }, { "cell_type": "code", "execution_count": 39, "id": "08b89b78-b3ad-4dff-9134-64e95ef99947", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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Maternal SmokerBirth WeightShuffled_label
0False120True
1False113False
2True128True
3True108True
4False136False
............
1169False113True
1170False128True
1171True130False
1172False125True
1173False117False
\n", "

1174 rows × 3 columns

\n", "
" ], "text/plain": [ " Maternal Smoker Birth Weight Shuffled_label\n", "0 False 120 True\n", "1 False 113 False\n", "2 True 128 True\n", "3 True 108 True\n", "4 False 136 False\n", "... ... ... ...\n", "1169 False 113 True\n", "1170 False 128 True\n", "1171 True 130 False\n", "1172 False 125 True\n", "1173 False 117 False\n", "\n", "[1174 rows x 3 columns]" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ons = births.assign(Shuffled_label=shuffle.reset_index().iloc[:, 1])\n", "ons" ] }, { "cell_type": "code", "execution_count": 41, "id": "4cb420f9-405c-4696-97b7-c8929d01ca3e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.float64(0.9561893444246437)" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Checking the test statistic for one shuffle\n", "means = ons.groupby('Shuffled_label')['Birth Weight'].mean()\n", "means.reset_index().iloc[0, 1] - means.reset_index().iloc[1, 1]" ] }, { "cell_type": "code", "execution_count": 52, "id": "64d0a9e7-197b-4d75-8be2-a14e496d6da8", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 0.34090224, -0.47828816, 0.24073922, ..., 0.21569846,\n", " 1.42838643, 0.02610418])" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Repeated shuffling to find empirical p-value\n", "num_repetitions = 10000\n", "\n", "L=[]\n", "for i in range(num_repetitions):\n", " shuffle = births.sample(frac=1.0, replace=False)['Maternal Smoker']\n", " ons = births.assign(Shuffled_label = shuffle.reset_index().iloc[:, 1])\n", " means = ons.groupby('Shuffled_label')['Birth Weight'].mean()\n", " L.append(means.reset_index().iloc[0, 1] - means.reset_index().iloc[1, 1])\n", "\n", "L = np.array(L)\n", "L" ] }, { "cell_type": "code", "execution_count": 53, "id": "75d9d519-eb1d-4119-a53f-5c4ddc7f0d1a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Prediction under null hypothesis')" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = subplots(figsize = (4, 4))\n", "ax.hist(L, density=True);\n", "ax.set_xlabel('Difference between group means')\n", "ax.set_title('Prediction under null hypothesis')" ] }, { "cell_type": "code", "execution_count": 55, "id": "1a59e590-678f-4314-af70-3fbd80d3f13f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.int64(0)" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Calculating empirical p-value\n", "empirical_pvalue = np.sum(L <= observed_value)\n", "empirical_pvalue" ] }, { "cell_type": "code", "execution_count": null, "id": "54363616-ce0f-4c33-8582-40030465bd6b", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.9.6" } }, "nbformat": 4, "nbformat_minor": 5 }