{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Comparing means, Student's t-test, ANOVA\n", "### Dr. Tirthajyoti Sarkar, Fremont, CA 94536\n", "\n", "In this Notebook, we will examine the concept of comparing means between groups of data using Student's t-test and ANOVA.\n", "\n", "---" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy.stats as st\n", "import seaborn as sns" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## High-school class I.Q. test\n", "\n", "A principal at a certain school claims that the students in his school are above average intelligence. A random sample of 30 students have a mean score of 112.5. **Is there sufficient evidence to support the principal’s claim**? The mean population IQ is 100 with a standard deviation of 15.\n", "\n", "Note, although this problem does not sound like an example of comparing group means, it is indeed the same. Instead of comparing two sample datasets, we are comparing one sample dataset to the population mean.\n", "\n", "Some additional questions can also be asked to understand the impact of various quantities involved,\n", "\n", "- What happens to our conclusion if the population mean is higher, say 107?\n", "- What happens to our conclusion if the population standard deviation is lower, say 10? What happens if it is higher instead?\n", "- What happens if there were only 4 high-school students who could be tested for the I.Q.? What if we could test 100 students instead?\n", "- What is the impact of changing the significance level to 0.01 from 0.05?\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Given data" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "population_mean = 100\n", "population_std = 15\n", "n_sample = 30" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Generate typical distribution of a high-school class\n", "This will be considered an 'average' class i.e. not having above-average intelligence as the principal claims." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "avg_class = np.vectorize(int)(np.random.normal(loc=population_mean,scale=population_std,size=n_sample))" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A typical class I.Q.: [106 96 110 97 89 109 116 100 98 89 120 91 92 105 85 107 78 95\n", " 111 87 106 81 108 119 97 139 83 94 94 91]\n" ] } ], "source": [ "print(\"A typical class I.Q.:\",avg_class)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The given class data (generated with the given mean and assumed same variance as population)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "given_class = np.vectorize(int)(np.random.normal(loc=112.5,scale=population_std,size=n_sample))" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Given class I.Q.: [125 118 129 70 112 112 141 116 102 88 106 147 121 111 94 124 93 125\n", " 104 129 122 114 119 108 90 126 118 117 75 142]\n" ] } ], "source": [ "print(\"Given class I.Q.:\",given_class)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(7,5))\n", "sns.kdeplot(avg_class,shade=True)\n", "sns.kdeplot(given_class,shade=True)\n", "plt.legend(['Average class','Given class'],fontsize=14)\n", "plt.vlines(x=avg_class.mean(),ymin=0,ymax=0.025,color='blue',linestyle='--')\n", "plt.vlines(x=given_class.mean(),ymin=0,ymax=0.025,color='brown',linestyle='--')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Standard error of the mean: 2.7386127875258306\n", "Z-statistic: 4.844301730823469\n" ] } ], "source": [ "std_err = population_std/np.sqrt(n_sample)\n", "z_stat = (given_class.mean()-population_mean)/std_err\n", "\n", "print(\"Standard error of the mean:\",std_err)\n", "print(\"Z-statistic:\",z_stat)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "alpha = 0.05\n", "rejection_threshold = st.norm.ppf(1-alpha)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "We reject the NULL hypothesis. The class I.Q. is indeed above average\n" ] } ], "source": [ "if z_stat>rejection_threshold:\n", " print(\"We reject the NULL hypothesis. The class I.Q. is indeed above average\")\n", "else:\n", " print(\"We cannot reject the NULL hypothesis that class average is same as population average.\")" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "def hypothesis_testing(n_sample=30,population_mean=100,population_std=15,alpha=0.05):\n", " \"\"\"\n", " Tests the hypothesis of above average I.Q. and reports the conclusion\n", " \"\"\"\n", " given_class=np.vectorize(int)(np.random.normal(loc=112.5,scale=population_std,size=n_sample))\n", " \n", " std_err = population_std/np.sqrt(n_sample)\n", " z_stat = (given_class.mean()-population_mean)/std_err\n", "\n", " alpha = 0.05\n", " rejection_threshold = st.norm.ppf(1-alpha)\n", " \n", " if z_stat>rejection_threshold:\n", " print(\"We reject the NULL hypothesis. The class I.Q. is indeed above average\")\n", " else:\n", " print(\"We cannot reject the NULL hypothesis that class average is same as population average.\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Test with default values" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "We reject the NULL hypothesis. The class I.Q. is indeed above average\n" ] } ], "source": [ "hypothesis_testing()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### What if the population mean is higher 110?" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "We cannot reject the NULL hypothesis that class average is same as population average.\n" ] } ], "source": [ "hypothesis_testing(population_mean=107)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### What if the population standard deviation is lower, say 10? What happens if it is higher instead?" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "We reject the NULL hypothesis. The class I.Q. is indeed above average\n" ] } ], "source": [ "hypothesis_testing(population_std=10)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "We cannot reject the NULL hypothesis that class average is same as population average.\n" ] } ], "source": [ "hypothesis_testing(population_std=40)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### What if there were only 4 high-school students? What if we could test 100 students instead?" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "We cannot reject the NULL hypothesis that class average is same as population average.\n" ] } ], "source": [ "hypothesis_testing(n_sample=4)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "We reject the NULL hypothesis. The class I.Q. is indeed above average\n" ] } ], "source": [ "hypothesis_testing(n_sample=100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### What is the impact of changing the significance level to 0.01 (or even 0.001) from 0.05?" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "We reject the NULL hypothesis. The class I.Q. is indeed above average\n" ] } ], "source": [ "hypothesis_testing(alpha=0.01)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "We reject the NULL hypothesis. The class I.Q. is indeed above average\n" ] } ], "source": [ "hypothesis_testing(alpha=0.001)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Independent Student's t-test implementation\n", "\n", "The Student’s t-Test is a statistical hypothesis test for testing whether two samples are expected to have been drawn from the same population.\n", "\n", "It is named for the pseudonym “Student” used by [William Gosset](https://en.wikipedia.org/wiki/William_Sealy_Gosset), who developed the test.\n", "\n", "The test works by checking the means from two samples to see if they are significantly different from each other. It does this by calculating the standard error in the difference between means, which can be interpreted to see how likely the difference is, if the two samples have the same mean (the null hypothesis).\n", "\n", "The t-statistic calculated by the test can be interpreted by comparing it to critical values from the [t-distribution](https://en.wikipedia.org/wiki/Student%27s_t-distribution). The critical value can be calculated using the degrees of freedom and a significance level with the percent point function (PPF).\n", "\n", "We can interpret the statistic value in a two-tailed test, meaning that if we reject the null hypothesis, it could be because the first mean is smaller or greater than the second mean." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### A custom function" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "def independent_ttest(data1, data2, alpha=0.05):\n", " \"\"\"\n", " Student's t-test for independent groups\n", " \n", " Argument:\n", " data1: First group data in numpy array format\n", " data2: Second group two data in numpy array format\n", " alpha: Significance level\n", " \n", " Returns:\n", " t_stat: Computed t-statistic\n", " df: Degrees of freedom\n", " cv: Critical value\n", " p: p-value (of NULL hypothesis)\n", " \"\"\"\n", " import scipy.stats as st\n", " # calculate means\n", " mean1, mean2 = np.mean(data1), np.mean(data2)\n", " # calculate standard errors\n", " se1, se2 = st.sem(data1), st.sem(data2)\n", " # standard error on the difference between the samples\n", " sed = np.sqrt(se1**2.0 + se2**2.0)\n", " # calculate the t statistic\n", " t_stat = (mean1 - mean2) / sed\n", " # degrees of freedom\n", " df = len(data1) + len(data2) - 2\n", " # calculate the critical value\n", " cv = st.t.ppf(1.0 - alpha, df)\n", " # calculate the p-value\n", " p = (1.0 - st.t.cdf(abs(t_stat), df)) * 2.0\n", " # return everything\n", " return t_stat, df, cv, p" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Apply the function for testing hypothesis of equal mean" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "n_sample = 20" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "data1 = 5 * np.random.randn(n_sample) + 50\n", "data2 = 5 * np.random.randn(n_sample) + 51\n", "\n", "plt.figure(figsize=(7,5))\n", "sns.kdeplot(data1,shade=True)\n", "sns.kdeplot(data2,shade=True)\n", "plt.legend(['data1','data2'],fontsize=14)\n", "plt.vlines(x=data1.mean(),ymin=0,ymax=0.09,color='blue',linestyle='--')\n", "plt.vlines(x=data2.mean(),ymin=0,ymax=0.09,color='brown',linestyle='--')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "t=-0.780, df=38, cv=1.686, p=0.440\n", "\n", "Fail to reject null hypothesis that the means are equal.\n", "Fail to reject null hypothesis that the means are equal.\n" ] } ], "source": [ "# calculate the t test\n", "alpha = 0.05\n", "t_stat, df, cv, p = independent_ttest(data1, data2, alpha)\n", "print('t=%.3f, df=%d, cv=%.3f, p=%.3f' % (t_stat, df, cv, p))\n", "print()\n", "\n", "# interpret via critical value\n", "if abs(t_stat) <= cv:\n", " print('Fail to reject null hypothesis that the means are equal.')\n", "else:\n", " print('Reject the null hypothesis that the means are equal.')\n", "# interpret via p-value\n", "if p > alpha:\n", " print('Fail to reject null hypothesis that the means are equal.')\n", "else:\n", " print('Reject the null hypothesis that the means are equal.')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### More numner of sample, more _statistical power_!\n", "\n", "The power of a binary hypothesis test is the probability that the test rejects the null hypothesis ($H_0$) when a specific alternative hypothesis ($H_a$) is true. \n", "\n", "The statistical power ranges from 0 to 1, and **as statistical power increases, the probability of making a type II error (wrongly failing to reject the null hypothesis) decreases**. For a type II error probability of $\\beta$, the corresponding statistical power is 1 − $\\beta$. \n", "\n", "For example, if experiment 1 has a statistical power of 0.7, and experiment 2 has a statistical power of 0.95, then there is a stronger probability that experiment 1 had a type II error than experiment 2, and experiment 2 is more reliable than experiment 1 due to the reduction in probability of a type II error. \n", "\n", "It can be equivalently thought of as the probability of accepting the alternative hypothesis ($H_a$) when it is true—that is, the **ability of a test to detect a specific effect**, if that specific effect actually exists." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "n_sample = 200" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "data1 = 5 * np.random.randn(n_sample) + 50\n", "data2 = 5 * np.random.randn(n_sample) + 51\n", "\n", "plt.figure(figsize=(7,5)\n", " )\n", "sns.kdeplot(data1,shade=True)\n", "sns.kdeplot(data2,shade=True)\n", "plt.legend(['data1','data2'],fontsize=14)\n", "plt.vlines(x=data1.mean(),ymin=0,ymax=0.09,color='blue',linestyle='--')\n", "plt.vlines(x=data2.mean(),ymin=0,ymax=0.09,color='brown',linestyle='--')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "t=-2.858, df=398, cv=1.649, p=0.004\n", "\n", "Reject the null hypothesis that the means are equal.\n", "Reject the null hypothesis that the means are equal.\n" ] } ], "source": [ "# calculate the t test\n", "alpha = 0.05\n", "t_stat, df, cv, p = independent_ttest(data1, data2, alpha)\n", "print('t=%.3f, df=%d, cv=%.3f, p=%.3f' % (t_stat, df, cv, p))\n", "print()\n", "\n", "# interpret via critical value\n", "if abs(t_stat) <= cv:\n", " print('Fail to reject null hypothesis that the means are equal.')\n", "else:\n", " print('Reject the null hypothesis that the means are equal.')\n", "# interpret via p-value\n", "if p > alpha:\n", " print('Fail to reject null hypothesis that the means are equal.')\n", "else:\n", " print('Reject the null hypothesis that the means are equal.')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## ANOVA using Scipy (`f_oneway()` method)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "n_sample = 50" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "group1 = 5 * np.random.randn(n_sample) + 50\n", "group2 = 5 * np.random.randn(n_sample) + 52\n", "\n", "plt.figure(figsize=(7,5)\n", " )\n", "sns.kdeplot(group1,shade=True)\n", "sns.kdeplot(group2,shade=True)\n", "plt.legend(['group1','gropu2'],fontsize=14)\n", "plt.vlines(x=group1.mean(),ymin=0,ymax=0.09,color='blue',linestyle='--')\n", "plt.vlines(x=group2.mean(),ymin=0,ymax=0.09,color='brown',linestyle='--')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(7,5))\n", "sns.boxplot(data=[group1,group2])\n", "sns.swarmplot(data=[group1,group2],color='.2')\n", "plt.legend(['group1','gropu2'],fontsize=14)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "f,p=st.f_oneway(group1,group2)" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The F-statistic obtained running ANOVA on the data groups: 6.594206103395201\n", "The p-value of the ANOVA test: 0.011741263190136573\n", "\n", "We reject the hypothesis of equal mean as per ANOVA test result\n" ] } ], "source": [ "print(\"The F-statistic obtained running ANOVA on the data groups:\",f)\n", "print(\"The p-value of the ANOVA test:\",p)\n", "if p>0.05:\n", " print(\"\\nANOVA fails to reject the hypothesis of equal mean\")\n", "else:\n", " print(\"\\nWe reject the hypothesis of equal mean as per ANOVA test result\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### For multiple groups, two-way pair comparisons are done" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "def multi_anova(groups,alpha=0.05):\n", " \"\"\"\n", " Two-way ANOVA between multiple groups\n", " groups: A dictionary object of trial groups\n", " \"\"\"\n", " from itertools import combinations\n", " list_anova = list(combinations(list(groups.keys()),2))\n", " \n", " for comb in list_anova:\n", " _,p=st.f_oneway(groups[comb[0]],groups[comb[1]])\n", " if p>0.05:\n", " print(\"\\nANOVA fails to reject the hypothesis of equal mean for {} and {}\".format(comb[0],comb[1]))\n", " else:\n", " print(\"\\nWe reject the hypothesis of equal mean for {} and {} as per ANOVA test result\".format(comb[0],comb[1]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Imaginary drug trial\n", "\n", "Let's suppose we have three versions of a blood pressure medicine developed - 'A','B','C'.\n", "\n", "We give this medicine to four groups - three trial groups and one control group, whose participants were given placebo (being a blind experiment, they did not know). There were total 155 participants and due to some logistic reason, the divisions were slightly uneven.\n", "\n", "No problem, ANOVA can handle slight difference in the sample count among groups!\n", "\n", "As a data scientist, you have been asked to analyze the clinical trial data and recommend whether to go ahead with further development on any (or more than one) of these drugs.\n", "\n", "Since they all the variations of same fundamental molecule, their impact is not drastically different and depending on trial participants physiology, there are lot of variations among the trial groups.\n", "\n", "Let's put our `multi_anova` function to use for this imaginary study!" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [], "source": [ "trial_A = 9*np.random.randn(34) + 102\n", "trial_B = 6*np.random.randn(48) + 109\n", "trial_C = 12*np.random.randn(38) + 103\n", "trial_CONTROL = 10*np.random.randn(35) + 110" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,5))\n", "ax=sns.boxplot(data=[trial_A,trial_B,trial_C,trial_CONTROL])\n", "ax=sns.swarmplot(data=[trial_A,trial_B,trial_C,trial_CONTROL],color='.2')\n", "ax.set_xticklabels(['trial_A','trial_B','trial_C','trial_CONTROL'],fontsize=15)\n", "ax.tick_params(axis=\"y\", labelsize=15)\n", "plt.grid(True)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(9,5))\n", "sns.kdeplot(trial_A,shade=True,color='Blue')\n", "sns.kdeplot(trial_B,shade=True,color='red')\n", "sns.kdeplot(trial_C,shade=True,color='yellow')\n", "sns.kdeplot(trial_CONTROL,shade=True,color='black')\n", "plt.legend(['trial_A','trial_B','trial_C','trial_CONTROL'],fontsize=14)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [], "source": [ "groups = {'trial_A':trial_A,'trial_B':trial_B,'trial_C':trial_C,'trial_CONTROL':trial_CONTROL}" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "We reject the hypothesis of equal mean for trial_A and trial_B as per ANOVA test result\n", "\n", "ANOVA fails to reject the hypothesis of equal mean for trial_A and trial_C\n", "\n", "We reject the hypothesis of equal mean for trial_A and trial_CONTROL as per ANOVA test result\n", "\n", "We reject the hypothesis of equal mean for trial_B and trial_C as per ANOVA test result\n", "\n", "ANOVA fails to reject the hypothesis of equal mean for trial_B and trial_CONTROL\n", "\n", "We reject the hypothesis of equal mean for trial_C and trial_CONTROL as per ANOVA test result\n" ] } ], "source": [ "multi_anova(groups)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### What's the conclusion?\n", "\n", "From the results, printed out, we see that equal mean hypothesis (with CONTROL group) could not be rejected for trial_B, whereas the hypothesis was rejected for the cases - trial_A and trial_CONTROL, trial_B and trial_CONTROL.\n", "\n", "Therefore, the trials of medicine A and medicine C showed statistically significant lowering of blood pressure whereas medicine B did not." ] } ], "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": "3.7.0" } }, "nbformat": 4, "nbformat_minor": 4 }