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Commit baca951

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import numpy as np
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import pandas as pd
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import scipy.stats as stats
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national = pd.DataFrame(["white"] * 100000 + ["hispanic"] * 60000 + \
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["black"] * 50000 + ["asian"] * 15000 + ["other"] * 35000)
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minnesota = pd.DataFrame(["white"] * 600 + ["hispanic"] * 300 + \
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["black"] * 250 + ["asian"] * 75 + ["other"] * 150)
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national_table = pd.crosstab(index=national[0], columns="count")
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minnesota_table = pd.crosstab(index=minnesota[0], columns="count")
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print("National")
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print(national_table)
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print(" ")
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print("Minnesota")
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print(minnesota_table)
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observed = minnesota_table
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national_ratios = national_table/len(national) # Get population ratios
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expected = national_ratios * len(minnesota) # Get expected counts
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chi_squared_stat = (((observed-expected)**2)/expected).sum()
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print(chi_squared_stat)
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crit = stats.chi2.ppf(q = 0.95, # Find the critical value for 95% confidence*
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df = 4) # Df = number of variable categories - 1
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print("Critical value")
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print(crit)
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p_value = 1 - stats.chi2.cdf(x=chi_squared_stat, # Find the p-value
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df=4)
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print("P value")
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print(p_value)
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stats.chisquare(f_obs= observed, # Array of observed counts
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f_exp= expected) # Array of expected counts
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{
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"nbformat": 4,
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"nbformat_minor": 0,
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"metadata": {
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"colab": {
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"name": "Z-Test.ipynb",
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"version": "0.3.2",
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"provenance": []
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},
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"kernelspec": {
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"name": "python3",
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"display_name": "Python 3"
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}
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},
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"cells": [
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{
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"cell_type": "code",
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"metadata": {
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"id": "AfRng3KPuSBQ",
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"colab_type": "code",
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"colab": {
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"base_uri": "https://localhost:8080/",
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"height": 51
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},
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"outputId": "01b490f3-42b4-410f-ff53-bd9bf782e0d6"
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},
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"source": [
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"def twoSampZ(X1, X2, mudiff, sd1, sd2, n1, n2):\n",
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" from numpy import sqrt, abs, round\n",
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" from scipy.stats import norm\n",
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" pooledSE = sqrt(sd1**2/n1 + sd2**2/n2)\n",
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" z = ((X1 - X2) - mudiff)/pooledSE\n",
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" pval = 2*(1 - norm.cdf(abs(z)))\n",
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" return round(z, 3), round(pval, 4)\n",
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"\n",
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"\n",
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"\n",
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"z, p = twoSampZ(28, 33, 0, 14.1, 9.5, 75, 50)\n",
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"print(\"Z Score:\",z)\n",
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"print(\"P-Value:\",p)"
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],
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"execution_count": 2,
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"outputs": [
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{
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"output_type": "stream",
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"text": [
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"Z Score: -2.369\n",
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"P-Value: 0.0179\n"
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],
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"name": "stdout"
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}
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]
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}
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]
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}
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{
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"nbformat": 4,
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"nbformat_minor": 0,
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"metadata": {
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"colab": {
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"name": "t-Test.ipynb",
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"version": "0.3.2",
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"provenance": []
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},
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"kernelspec": {
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"name": "python3",
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"display_name": "Python 3"
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}
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},
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"cells": [
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{
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"cell_type": "code",
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"metadata": {
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"id": "Y21N_2yv3Grl",
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"colab_type": "code",
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"colab": {}
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},
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"source": [
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"## Import the packages\n",
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"import numpy as np\n",
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"from scipy import stats"
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],
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"execution_count": 0,
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"outputs": []
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "Aga_0SM43OdO",
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"colab_type": "code",
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"colab": {
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"base_uri": "https://localhost:8080/",
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"height": 85
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},
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"outputId": "8d4b8f3d-a6df-4129-b3b6-867144288009"
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},
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"source": [
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"## Define 2 random distributions\n",
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"\n",
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"#Sample Size\n",
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"N = 10\n",
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"\n",
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"#Gaussian distributed data with mean = 2 and var = 1\n",
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"a = np.random.randn(N) + 2\n",
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"print(a)\n",
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"\n",
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"#Gaussian distributed data with with mean = 0 and var = 1\n",
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"b = np.random.randn(N)\n",
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"print(b)"
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],
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"execution_count": 6,
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"outputs": [
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{
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"output_type": "stream",
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"text": [
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"[3.41987841 2.4642942 1.3074381 1.88900262 1.5018451 2.08785958\n",
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" 4.18763608 2.76111147 1.25673154 1.22916177]\n",
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"[ 0.09625918 -0.426427 -0.81593085 -0.27386856 -0.19758738 0.71729565\n",
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" -0.44211666 0.07106772 -0.53144206 -0.21403634]\n"
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],
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"name": "stdout"
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}
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "DGw_0SoQ2Uhj",
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"colab_type": "code",
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"colab": {
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"base_uri": "https://localhost:8080/",
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"height": 51
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},
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"outputId": "b6caa6b7-64df-44e7-b626-13fb8165baeb"
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},
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"source": [
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"## Calculate the Standard Deviation\n",
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"\n",
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"#Calculate the variance to get the standard deviation\n",
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"\n",
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"#For unbiased max likelihood estimate we have to divide the var by N-1, and therefore the parameter ddof = 1\n",
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"var_a = a.var(ddof=1)\n",
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"var_b = b.var(ddof=1)\n",
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"\n",
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"#std deviation\n",
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"s = np.sqrt((var_a + var_b)/2)\n",
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"\n",
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"print(\"Std Deviation:\", s)\n",
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"\n",
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"## Calculate the t-statistics\n",
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"t = (a.mean() - b.mean())/(s*np.sqrt(2/N))\n",
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"\n",
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"print(\"T-value:\", t)"
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],
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"execution_count": 8,
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"outputs": [
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{
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"output_type": "stream",
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"text": [
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"Std Deviation: 0.7693967525636721\n",
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"T-value: 7.0104093570005945\n"
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],
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"name": "stdout"
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}
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "9atPC3HO3Z2U",
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"colab_type": "code",
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"colab": {
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"base_uri": "https://localhost:8080/",
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"height": 51
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},
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"outputId": "683ac7bd-8bd8-4e55-d3fc-7942748b66d1"
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},
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"source": [
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"## Compare with the critical t-value\n",
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"\n",
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"#Degrees of freedom\n",
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"df = 2*N - 2\n",
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"\n",
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"#p-value after comparison with the t\n",
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"p = 1 - stats.t.cdf(t,df=df)\n",
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"\n",
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"print(\"t-Score = \" + str(t))\n",
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"print(\"p-Value = \" + str(2*p))\n",
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"\n",
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"#Note that we multiply the p value by 2 because its a twp tail t-test\n",
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"\n",
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"### You can see that after comparing the t statistic with the critical t value (computed internally)\n",
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"# we get a good p value of 0.0005 and thus we reject the null hypothesis and thus it proves that the mean\n",
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"# of the two distributions are different and statistically significant."
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],
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"execution_count": 9,
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"outputs": [
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{
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"output_type": "stream",
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"text": [
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"t-Score = 7.0104093570005945\n",
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"p-Value = 1.522899394812427e-06\n"
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],
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"name": "stdout"
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}
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "I_ve3N6a3Mlo",
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"colab_type": "code",
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"colab": {
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"base_uri": "https://localhost:8080/",
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"height": 51
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},
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"outputId": "cc8bcc64-e1a2-4c05-98b9-db0cf91a0a01"
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},
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"source": [
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"## Cross Checking with the internal scipy function\n",
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"t2, p2 = stats.ttest_ind(a,b)\n",
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"print(\"t = \" + str(t2))\n",
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"print(\"p = \" + str(2*p2))"
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],
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"execution_count": 10,
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"outputs": [
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{
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"output_type": "stream",
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"text": [
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"t = 7.010409357000594\n",
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"p = 3.045798789679482e-06\n"
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],
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"name": "stdout"
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}
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]
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}
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]
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}

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