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Data-Science-For-Beginners/1-Introduction/04-stats-and-probability/solution/assignment.ipynb

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Add main content and assignment for prob and stats
3 years ago
{
"cells": [
{
"cell_type": "markdown",
"source": [
"## Introduction to Probability and Statistics\r\n",
"## Assignment\r\n",
"\r\n",
"In this assignment, we will use the dataset of diabetes patients taken [from here](https://www4.stat.ncsu.edu/~boos/var.select/diabetes.html)."
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 13,
"source": [
"import pandas as pd\r\n",
"import numpy as np\r\n",
"import matplotlib.pyplot as plt\r\n",
"\r\n",
"df = pd.read_csv(\"../../../data/diabetes.tsv\",sep='\\t')\r\n",
"df.head()"
],
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
" AGE SEX BMI BP S1 S2 S3 S4 S5 S6 Y\n",
"0 59 2 32.1 101.0 157 93.2 38.0 4.0 4.8598 87 151\n",
"1 48 1 21.6 87.0 183 103.2 70.0 3.0 3.8918 69 75\n",
"2 72 2 30.5 93.0 156 93.6 41.0 4.0 4.6728 85 141\n",
"3 24 1 25.3 84.0 198 131.4 40.0 5.0 4.8903 89 206\n",
"4 50 1 23.0 101.0 192 125.4 52.0 4.0 4.2905 80 135"
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" <th>BMI</th>\n",
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"\r\n",
"In this dataset, columns as the following:\r\n",
"* Age and sex are self-explanatory\r\n",
"* BMI is body mass index\r\n",
"* BP is average blood pressure\r\n",
"* S1 through S6 are different blood measurements\r\n",
"* Y is the qualitative measure of disease progression over one year\r\n",
"\r\n",
"Let's study this dataset using methods of probability and statistics.\r\n",
"\r\n",
"### Task 1: Compute mean values and variance for all values"
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 5,
"source": [
"df.describe()"
],
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
" AGE SEX BMI BP S1 S2 \\\n",
"count 442.000000 442.000000 442.000000 442.000000 442.000000 442.000000 \n",
"mean 48.518100 1.468326 26.375792 94.647014 189.140271 115.439140 \n",
"std 13.109028 0.499561 4.418122 13.831283 34.608052 30.413081 \n",
"min 19.000000 1.000000 18.000000 62.000000 97.000000 41.600000 \n",
"25% 38.250000 1.000000 23.200000 84.000000 164.250000 96.050000 \n",
"50% 50.000000 1.000000 25.700000 93.000000 186.000000 113.000000 \n",
"75% 59.000000 2.000000 29.275000 105.000000 209.750000 134.500000 \n",
"max 79.000000 2.000000 42.200000 133.000000 301.000000 242.400000 \n",
"\n",
" S3 S4 S5 S6 Y \n",
"count 442.000000 442.000000 442.000000 442.000000 442.000000 \n",
"mean 49.788462 4.070249 4.641411 91.260181 152.133484 \n",
"std 12.934202 1.290450 0.522391 11.496335 77.093005 \n",
"min 22.000000 2.000000 3.258100 58.000000 25.000000 \n",
"25% 40.250000 3.000000 4.276700 83.250000 87.000000 \n",
"50% 48.000000 4.000000 4.620050 91.000000 140.500000 \n",
"75% 57.750000 5.000000 4.997200 98.000000 211.500000 \n",
"max 99.000000 9.090000 6.107000 124.000000 346.000000 "
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" <th>BMI</th>\n",
" <th>BP</th>\n",
" <th>S1</th>\n",
" <th>S2</th>\n",
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},
"metadata": {},
"execution_count": 5
}
],
"metadata": {}
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{
"cell_type": "code",
"execution_count": 8,
"source": [
"# Another way\r\n",
"pd.DataFrame([df.mean(),df.var()],index=['Mean','Variance']).head()"
],
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
" AGE SEX BMI BP S1 S2 \\\n",
"Mean 48.51810 1.468326 26.375792 94.647014 189.140271 115.439140 \n",
"Variance 171.84661 0.249561 19.519798 191.304401 1197.717241 924.955494 \n",
"\n",
" S3 S4 S5 S6 Y \n",
"Mean 49.788462 4.070249 4.641411 91.260181 152.133484 \n",
"Variance 167.293585 1.665261 0.272892 132.165712 5943.331348 "
],
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" <th>BMI</th>\n",
" <th>BP</th>\n",
" <th>S1</th>\n",
" <th>S2</th>\n",
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},
"metadata": {},
"execution_count": 8
}
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 9,
"source": [
"# Or, more simply, for the mean (variance can be done similarly)\r\n",
"df.mean()"
],
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"AGE 48.518100\n",
"SEX 1.468326\n",
"BMI 26.375792\n",
"BP 94.647014\n",
"S1 189.140271\n",
"S2 115.439140\n",
"S3 49.788462\n",
"S4 4.070249\n",
"S5 4.641411\n",
"S6 91.260181\n",
"Y 152.133484\n",
"dtype: float64"
]
},
"metadata": {},
"execution_count": 9
}
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"### Task 2: Plot boxplots for BMI, BP and Y depending on gender"
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 17,
"source": [
"for col in ['BMI','BP','Y']:\r\n",
" df.boxplot(column=col,by='SEX')\r\n",
"plt.show()"
],
"outputs": [
{
"output_type": "display_data",
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},
{
"cell_type": "markdown",
"source": [
"### Task 3: What is the the distribution of Age, Sex, BMI and Y variables?"
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 19,
"source": [
"for col in ['AGE','SEX','BMI','Y']:\r\n",
" df[col].hist()\r\n",
" plt.show()"
],
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
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"metadata": {}
}
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"Conclusions:\r\n",
"* Age - normal\r\n",
"* Sex - uniform\r\n",
"* BMI, Y - hard to tell"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"### Task 4: Test the correlation between different variables and disease progression (Y)\r\n",
"\r\n",
"> **Hint** Correlation matrix would give you the most useful information on which values are dependent."
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 20,
"source": [
"df.corr()"
],
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
" AGE SEX BMI BP S1 S2 S3 \\\n",
"AGE 1.000000 0.173737 0.185085 0.335428 0.260061 0.219243 -0.075181 \n",
"SEX 0.173737 1.000000 0.088161 0.241010 0.035277 0.142637 -0.379090 \n",
"BMI 0.185085 0.088161 1.000000 0.395411 0.249777 0.261170 -0.366811 \n",
"BP 0.335428 0.241010 0.395411 1.000000 0.242464 0.185548 -0.178762 \n",
"S1 0.260061 0.035277 0.249777 0.242464 1.000000 0.896663 0.051519 \n",
"S2 0.219243 0.142637 0.261170 0.185548 0.896663 1.000000 -0.196455 \n",
"S3 -0.075181 -0.379090 -0.366811 -0.178762 0.051519 -0.196455 1.000000 \n",
"S4 0.203841 0.332115 0.413807 0.257650 0.542207 0.659817 -0.738493 \n",
"S5 0.270774 0.149916 0.446157 0.393480 0.515503 0.318357 -0.398577 \n",
"S6 0.301731 0.208133 0.388680 0.390430 0.325717 0.290600 -0.273697 \n",
"Y 0.187889 0.043062 0.586450 0.441482 0.212022 0.174054 -0.394789 \n",
"\n",
" S4 S5 S6 Y \n",
"AGE 0.203841 0.270774 0.301731 0.187889 \n",
"SEX 0.332115 0.149916 0.208133 0.043062 \n",
"BMI 0.413807 0.446157 0.388680 0.586450 \n",
"BP 0.257650 0.393480 0.390430 0.441482 \n",
"S1 0.542207 0.515503 0.325717 0.212022 \n",
"S2 0.659817 0.318357 0.290600 0.174054 \n",
"S3 -0.738493 -0.398577 -0.273697 -0.394789 \n",
"S4 1.000000 0.617859 0.417212 0.430453 \n",
"S5 0.617859 1.000000 0.464669 0.565883 \n",
"S6 0.417212 0.464669 1.000000 0.382483 \n",
"Y 0.430453 0.565883 0.382483 1.000000 "
],
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" <td>1.000000</td>\n",
" <td>0.242464</td>\n",
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" <td>-0.178762</td>\n",
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" <td>0.290600</td>\n",
" <td>-0.273697</td>\n",
" <td>0.417212</td>\n",
" <td>0.464669</td>\n",
" <td>1.000000</td>\n",
" <td>0.382483</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Y</th>\n",
" <td>0.187889</td>\n",
" <td>0.043062</td>\n",
" <td>0.586450</td>\n",
" <td>0.441482</td>\n",
" <td>0.212022</td>\n",
" <td>0.174054</td>\n",
" <td>-0.394789</td>\n",
" <td>0.430453</td>\n",
" <td>0.565883</td>\n",
" <td>0.382483</td>\n",
" <td>1.000000</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
]
},
"metadata": {},
"execution_count": 20
}
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"Conclusion:\r\n",
"* The strongest correlation of Y is BMI and S5 (blood sugar). This sounds reasonable."
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 26,
"source": [
"fig, ax = plt.subplots(1,3,figsize=(10,5))\r\n",
"for i,n in enumerate(['BMI','S5','BP']):\r\n",
" ax[i].scatter(df['Y'],df[n])\r\n",
" ax[i].set_title(n)\r\n",
"plt.show()"
],
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 1000x500 with 3 Axes>"
],
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},
"metadata": {}
}
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"### Task 5: Test the hypothesis that the degree of diabetes progression is different between men and women"
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 27,
"source": [
"from scipy.stats import ttest_ind\r\n",
"\r\n",
"tval, pval = ttest_ind(df.loc[df['SEX']==1,['Y']], df.loc[df['SEX']==2,['Y']],equal_var=False)\r\n",
"print(f\"T-value = {tval[0]:.2f}\\nP-value: {pval[0]}\")"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"T-value = -0.90\n",
"P-value: 0.3674449793083975\n"
]
}
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"Conclusion: p-value close to 0 (typically, below 0.05) would indicate high confidence in our hypothesis. In our case, there is no strong evidence that sex affects progression of diabetes."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [],
"metadata": {}
}
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