{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Inference for numerical data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### In 2004, the state of North Carolina released a large data set containing information on births recorded in this state. This data set is useful to researchers studying the relation between habits and practices of expectant mothers and the birth of their children. We will work with a random sample of observations from this data set." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import warnings\n", "warnings.filterwarnings(\"ignore\")\n", "\n", "import numpy as np\n", "import pandas as pd\n", "import io\n", "import requests\n", "\n", "df_url = 'https://raw.githubusercontent.com/akmand/datasets/master/openintro/nc.csv'\n", "url_content = requests.get(df_url, verify=False).content\n", "nc = pd.read_csv(io.StringIO(url_content.decode('utf-8')))" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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fagemagematureweekspremievisitsmaritalgainedweightlowbirthweightgenderhabitwhitemom
0NaN13younger mom39.0full term10.0married38.07.63not lowmalenonsmokernot white
1NaN14younger mom42.0full term15.0married20.07.88not lowmalenonsmokernot white
219.015younger mom37.0full term11.0married38.06.63not lowfemalenonsmokerwhite
321.015younger mom41.0full term6.0married34.08.00not lowmalenonsmokerwhite
4NaN15younger mom39.0full term9.0married27.06.38not lowfemalenonsmokernot white
..........................................
99547.042mature mom40.0full term10.0not married26.08.44not lowmalenonsmokernot white
99634.042mature mom38.0full term18.0not married20.06.19not lowfemalenonsmokerwhite
99739.045mature mom40.0full term15.0not married32.06.94not lowfemalenonsmokerwhite
99855.046mature mom31.0premie8.0not married25.04.56lowfemalenonsmokernot white
99945.050mature mom39.0full term14.0not married23.07.13not lowfemalenonsmokerwhite
\n", "

1000 rows × 13 columns

\n", "
" ], "text/plain": [ " fage mage mature weeks premie visits marital gained \\\n", "0 NaN 13 younger mom 39.0 full term 10.0 married 38.0 \n", "1 NaN 14 younger mom 42.0 full term 15.0 married 20.0 \n", "2 19.0 15 younger mom 37.0 full term 11.0 married 38.0 \n", "3 21.0 15 younger mom 41.0 full term 6.0 married 34.0 \n", "4 NaN 15 younger mom 39.0 full term 9.0 married 27.0 \n", ".. ... ... ... ... ... ... ... ... \n", "995 47.0 42 mature mom 40.0 full term 10.0 not married 26.0 \n", "996 34.0 42 mature mom 38.0 full term 18.0 not married 20.0 \n", "997 39.0 45 mature mom 40.0 full term 15.0 not married 32.0 \n", "998 55.0 46 mature mom 31.0 premie 8.0 not married 25.0 \n", "999 45.0 50 mature mom 39.0 full term 14.0 not married 23.0 \n", "\n", " weight lowbirthweight gender habit whitemom \n", "0 7.63 not low male nonsmoker not white \n", "1 7.88 not low male nonsmoker not white \n", "2 6.63 not low female nonsmoker white \n", "3 8.00 not low male nonsmoker white \n", "4 6.38 not low female nonsmoker not white \n", ".. ... ... ... ... ... \n", "995 8.44 not low male nonsmoker not white \n", "996 6.19 not low female nonsmoker white \n", "997 6.94 not low female nonsmoker white \n", "998 4.56 low female nonsmoker not white \n", "999 7.13 not low female nonsmoker white \n", "\n", "[1000 rows x 13 columns]" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nc" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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fagemageweeksvisitsgainedweight
count829.0000001000.000000998.000000991.000000973.0000001000.00000
mean30.25573027.00000038.33466912.10494530.3257977.10100
std6.7637666.2135832.9315533.95493414.2412971.50886
min14.00000013.00000020.0000000.0000000.0000001.00000
25%25.00000022.00000037.00000010.00000020.0000006.38000
50%30.00000027.00000039.00000012.00000030.0000007.31000
75%35.00000032.00000040.00000015.00000038.0000008.06000
max55.00000050.00000045.00000030.00000085.00000011.75000
\n", "
" ], "text/plain": [ " fage mage weeks visits gained weight\n", "count 829.000000 1000.000000 998.000000 991.000000 973.000000 1000.00000\n", "mean 30.255730 27.000000 38.334669 12.104945 30.325797 7.10100\n", "std 6.763766 6.213583 2.931553 3.954934 14.241297 1.50886\n", "min 14.000000 13.000000 20.000000 0.000000 0.000000 1.00000\n", "25% 25.000000 22.000000 37.000000 10.000000 20.000000 6.38000\n", "50% 30.000000 27.000000 39.000000 12.000000 30.000000 7.31000\n", "75% 35.000000 32.000000 40.000000 15.000000 38.000000 8.06000\n", "max 55.000000 50.000000 45.000000 30.000000 85.000000 11.75000" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nc.describe()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "RangeIndex: 1000 entries, 0 to 999\n", "Data columns (total 13 columns):\n", " # Column Non-Null Count Dtype \n", "--- ------ -------------- ----- \n", " 0 fage 829 non-null float64\n", " 1 mage 1000 non-null int64 \n", " 2 mature 1000 non-null object \n", " 3 weeks 998 non-null float64\n", " 4 premie 998 non-null object \n", " 5 visits 991 non-null float64\n", " 6 marital 999 non-null object \n", " 7 gained 973 non-null float64\n", " 8 weight 1000 non-null float64\n", " 9 lowbirthweight 1000 non-null object \n", " 10 gender 1000 non-null object \n", " 11 habit 999 non-null object \n", " 12 whitemom 998 non-null object \n", "dtypes: float64(5), int64(1), object(7)\n", "memory usage: 101.7+ KB\n" ] } ], "source": [ "nc.info()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 1: Make 2 box-plots of weight by habit." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "%matplotlib inline \n", "\n", "nc.boxplot(column = 'weight', by = 'habit')\n", "plt.title('Boxplot of weight by habit')\n", "plt.suptitle('')\n", "plt.show();" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "habit\n", "nonsmoker 7.144273\n", "smoker 6.828730\n", "Name: weight, dtype: float64" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nc.groupby(['habit'])['weight'].mean()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "n_smoker = 126.0\n", "mean_smoker = 6.828730158730159\n", "sd_smoker = 1.380668106117173\n", "\n", "n_nonsmoker = 873.0\n", "mean_nonsmoker = 7.144272623138601\n", "sd_nonsmoker = 1.5178105512705897\n", "\n", "Standard error = 0.13376049190705977\n", "Test statistic: Z = -2.3590109449334946\n", "p-value = 0.018323715325166526\n", "reject null hypothesis\n" ] } ], "source": [ "import statsmodels.stats.weightstats as st\n", "\n", "nc_weightANDsmoker = nc[nc['habit'] == 'smoker']['weight']\n", "nc_weightANDnonsmoker = nc[nc['habit'] == 'nonsmoker']['weight']\n", "\n", "dsw1 = st.DescrStatsW(nc_weightANDsmoker)\n", "dsw2 = st.DescrStatsW(nc_weightANDnonsmoker)\n", "cm = st.CompareMeans(dsw1, dsw2)\n", "\n", "# calculate number of observations, mean and standard deviation for each group\n", "n_smoker = dsw1.nobs\n", "n_nonsmoker = dsw2.nobs\n", "mean_smoker = dsw1.mean\n", "mean_nonsmoker = dsw2.mean\n", "sd_smoker = dsw1.std\n", "sd_nonsmoker = dsw2.std\n", "print(f'n_smoker = {n_smoker}')\n", "print(f'mean_smoker = {mean_smoker}')\n", "print(f'sd_smoker = {sd_smoker}')\n", "print()\n", "print(f'n_nonsmoker = {n_nonsmoker}')\n", "print(f'mean_nonsmoker = {mean_nonsmoker}')\n", "print(f'sd_nonsmoker = {sd_nonsmoker}')\n", "print()\n", "\n", "# conduct hypothesis test\n", "ht = cm.ztest_ind(alternative = 'two-sided', usevar = 'unequal', value = 0)\n", "\n", "# calculate and print the standard error, the Z-score, and p-value for the hypothesis test\n", "se = cm.std_meandiff_separatevar\n", "testZ = ht[0]\n", "p_value = ht[1]\n", "print(f'Standard error = {se}')\n", "print(f'Test statistic: Z = {testZ}')\n", "print(f'p-value = {p_value}')\n", "\n", "# reject or accept null hypothesis\n", "if(p_value) < 0.05:\n", " print('reject null hypothesis')\n", "else:\n", " print('accept null hypothesis')" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "nc_weightANDsmoker = nc[nc['habit'] == 'smoker']['weight']\n", "nc_weightANDnonsmoker = nc[nc['habit'] == 'nonsmoker']['weight']\n", "\n", "x_bar = np.mean(nc_weightANDsmoker)\n", "x_std = np.std(nc_weightANDsmoker)\n", "\n", "y_bar = np.mean(nc_weightANDnonsmoker)\n", "y_std = np.std(nc_weightANDnonsmoker)\n", "\n", "S_xy = np.sqrt((x_std**2)/len(nc_weightANDsmoker) + (y_std**2)/len(nc_weightANDnonsmoker))\n", "\n", "tobs = (x_bar - y_bar)/S_xy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 2: Conduct a hypothesis test evaluating whether the average weight gained by younger mothers is different than the average weight gained by mature mothers.\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }