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@jasonmhite
Last active August 29, 2015 14:23
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{
"cells": [
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"source": [
"%pylab inline"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import seaborn as sb\n",
"import pandas as pd\n",
"import scipy.stats as st"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"NS = 1000"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"data = random.randn(NS)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7f8f06a79350>"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
},
{
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"RU5ErkJggg==\n"
],
"text/plain": [
"<matplotlib.figure.Figure at 0x7f8f06a69e90>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sb.distplot(data)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Test statistic: 0.995384395123\n",
"P-value: 0.00407176883891\n"
]
}
],
"source": [
"w, p = st.shapiro(data)\n",
"print(\"Test statistic: {w}\\nP-value: {p}\".format(w=w, p=p))"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"tests = pd.DataFrame( \n",
" array([st.shapiro(data[:i]) for i in xrange(3, NS + 1)]),\n",
" columns=[\"Test statistic\", \"P-value\"],\n",
" index=arange(3, NS + 1),\n",
")\n",
"tests.index.name = \"Number of samples\""
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Test statistic</th>\n",
" <th>P-value</th>\n",
" </tr>\n",
" <tr>\n",
" <th>Number of samples</th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>0.874009</td>\n",
" <td>0.306983</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>0.906745</td>\n",
" <td>0.465330</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>0.953175</td>\n",
" <td>0.759839</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>0.990965</td>\n",
" <td>0.991395</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>0.982496</td>\n",
" <td>0.970762</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>0.988839</td>\n",
" <td>0.993080</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>0.979334</td>\n",
" <td>0.960762</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>0.978723</td>\n",
" <td>0.957969</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td>0.990245</td>\n",
" <td>0.997718</td>\n",
" </tr>\n",
" <tr>\n",
" <th>12</th>\n",
" <td>0.988010</td>\n",
" <td>0.999134</td>\n",
" </tr>\n",
" <tr>\n",
" <th>13</th>\n",
" <td>0.981177</td>\n",
" <td>0.984720</td>\n",
" </tr>\n",
" <tr>\n",
" <th>14</th>\n",
" <td>0.980176</td>\n",
" <td>0.975812</td>\n",
" </tr>\n",
" <tr>\n",
" <th>15</th>\n",
" <td>0.980610</td>\n",
" <td>0.973495</td>\n",
" </tr>\n",
" <tr>\n",
" <th>16</th>\n",
" <td>0.973354</td>\n",
" <td>0.889562</td>\n",
" </tr>\n",
" <tr>\n",
" <th>17</th>\n",
" <td>0.969429</td>\n",
" <td>0.808359</td>\n",
" </tr>\n",
" <tr>\n",
" <th>18</th>\n",
" <td>0.979298</td>\n",
" <td>0.942484</td>\n",
" </tr>\n",
" <tr>\n",
" <th>19</th>\n",
" <td>0.985756</td>\n",
" <td>0.987979</td>\n",
" </tr>\n",
" <tr>\n",
" <th>20</th>\n",
" <td>0.989322</td>\n",
" <td>0.997212</td>\n",
" </tr>\n",
" <tr>\n",
" <th>21</th>\n",
" <td>0.990342</td>\n",
" <td>0.998213</td>\n",
" </tr>\n",
" <tr>\n",
" <th>22</th>\n",
" <td>0.991859</td>\n",
" <td>0.999316</td>\n",
" </tr>\n",
" <tr>\n",
" <th>23</th>\n",
" <td>0.993393</td>\n",
" <td>0.999821</td>\n",
" </tr>\n",
" <tr>\n",
" <th>24</th>\n",
" <td>0.991788</td>\n",
" <td>0.998941</td>\n",
" </tr>\n",
" <tr>\n",
" <th>25</th>\n",
" <td>0.991929</td>\n",
" <td>0.998879</td>\n",
" </tr>\n",
" <tr>\n",
" <th>26</th>\n",
" <td>0.987586</td>\n",
" <td>0.983099</td>\n",
" </tr>\n",
" <tr>\n",
" <th>27</th>\n",
" <td>0.990275</td>\n",
" <td>0.994946</td>\n",
" </tr>\n",
" <tr>\n",
" <th>28</th>\n",
" <td>0.988472</td>\n",
" <td>0.985089</td>\n",
" </tr>\n",
" <tr>\n",
" <th>29</th>\n",
" <td>0.984913</td>\n",
" <td>0.941618</td>\n",
" </tr>\n",
" <tr>\n",
" <th>30</th>\n",
" <td>0.986482</td>\n",
" <td>0.959656</td>\n",
" </tr>\n",
" <tr>\n",
" <th>31</th>\n",
" <td>0.985221</td>\n",
" <td>0.935069</td>\n",
" </tr>\n",
" <tr>\n",
" <th>32</th>\n",
" <td>0.984891</td>\n",
" <td>0.922547</td>\n",
" </tr>\n",
" <tr>\n",
" <th>...</th>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" </tr>\n",
" <tr>\n",
" <th>971</th>\n",
" <td>0.998412</td>\n",
" <td>0.524920</td>\n",
" </tr>\n",
" <tr>\n",
" <th>972</th>\n",
" <td>0.998422</td>\n",
" <td>0.530492</td>\n",
" </tr>\n",
" <tr>\n",
" <th>973</th>\n",
" <td>0.998440</td>\n",
" <td>0.540700</td>\n",
" </tr>\n",
" <tr>\n",
" <th>974</th>\n",
" <td>0.998423</td>\n",
" <td>0.529199</td>\n",
" </tr>\n",
" <tr>\n",
" <th>975</th>\n",
" <td>0.998437</td>\n",
" <td>0.536995</td>\n",
" </tr>\n",
" <tr>\n",
" <th>976</th>\n",
" <td>0.998405</td>\n",
" <td>0.516238</td>\n",
" </tr>\n",
" <tr>\n",
" <th>977</th>\n",
" <td>0.998412</td>\n",
" <td>0.519264</td>\n",
" </tr>\n",
" <tr>\n",
" <th>978</th>\n",
" <td>0.998401</td>\n",
" <td>0.511663</td>\n",
" </tr>\n",
" <tr>\n",
" <th>979</th>\n",
" <td>0.998398</td>\n",
" <td>0.508920</td>\n",
" </tr>\n",
" <tr>\n",
" <th>980</th>\n",
" <td>0.998388</td>\n",
" <td>0.501643</td>\n",
" </tr>\n",
" <tr>\n",
" <th>981</th>\n",
" <td>0.998402</td>\n",
" <td>0.509417</td>\n",
" </tr>\n",
" <tr>\n",
" <th>982</th>\n",
" <td>0.998395</td>\n",
" <td>0.504170</td>\n",
" </tr>\n",
" <tr>\n",
" <th>983</th>\n",
" <td>0.998389</td>\n",
" <td>0.500010</td>\n",
" </tr>\n",
" <tr>\n",
" <th>984</th>\n",
" <td>0.998378</td>\n",
" <td>0.492246</td>\n",
" </tr>\n",
" <tr>\n",
" <th>985</th>\n",
" <td>0.998376</td>\n",
" <td>0.490070</td>\n",
" </tr>\n",
" <tr>\n",
" <th>986</th>\n",
" <td>0.998339</td>\n",
" <td>0.467053</td>\n",
" </tr>\n",
" <tr>\n",
" <th>987</th>\n",
" <td>0.998328</td>\n",
" <td>0.459690</td>\n",
" </tr>\n",
" <tr>\n",
" <th>988</th>\n",
" <td>0.998320</td>\n",
" <td>0.453759</td>\n",
" </tr>\n",
" <tr>\n",
" <th>989</th>\n",
" <td>0.998328</td>\n",
" <td>0.457874</td>\n",
" </tr>\n",
" <tr>\n",
" <th>990</th>\n",
" <td>0.998336</td>\n",
" <td>0.461257</td>\n",
" </tr>\n",
" <tr>\n",
" <th>991</th>\n",
" <td>0.998321</td>\n",
" <td>0.451501</td>\n",
" </tr>\n",
" <tr>\n",
" <th>992</th>\n",
" <td>0.998320</td>\n",
" <td>0.450019</td>\n",
" </tr>\n",
" <tr>\n",
" <th>993</th>\n",
" <td>0.998330</td>\n",
" <td>0.454996</td>\n",
" </tr>\n",
" <tr>\n",
" <th>994</th>\n",
" <td>0.998316</td>\n",
" <td>0.445879</td>\n",
" </tr>\n",
" <tr>\n",
" <th>995</th>\n",
" <td>0.998283</td>\n",
" <td>0.426284</td>\n",
" </tr>\n",
" <tr>\n",
" <th>996</th>\n",
" <td>0.998292</td>\n",
" <td>0.430655</td>\n",
" </tr>\n",
" <tr>\n",
" <th>997</th>\n",
" <td>0.998277</td>\n",
" <td>0.420858</td>\n",
" </tr>\n",
" <tr>\n",
" <th>998</th>\n",
" <td>0.998291</td>\n",
" <td>0.427900</td>\n",
" </tr>\n",
" <tr>\n",
" <th>999</th>\n",
" <td>0.998307</td>\n",
" <td>0.436221</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1000</th>\n",
" <td>0.998290</td>\n",
" <td>0.425738</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>998 rows × 2 columns</p>\n",
"</div>"
],
"text/plain": [
" Test statistic P-value\n",
"Number of samples \n",
"3 0.874009 0.306983\n",
"4 0.906745 0.465330\n",
"5 0.953175 0.759839\n",
"6 0.990965 0.991395\n",
"7 0.982496 0.970762\n",
"8 0.988839 0.993080\n",
"9 0.979334 0.960762\n",
"10 0.978723 0.957969\n",
"11 0.990245 0.997718\n",
"12 0.988010 0.999134\n",
"13 0.981177 0.984720\n",
"14 0.980176 0.975812\n",
"15 0.980610 0.973495\n",
"16 0.973354 0.889562\n",
"17 0.969429 0.808359\n",
"18 0.979298 0.942484\n",
"19 0.985756 0.987979\n",
"20 0.989322 0.997212\n",
"21 0.990342 0.998213\n",
"22 0.991859 0.999316\n",
"23 0.993393 0.999821\n",
"24 0.991788 0.998941\n",
"25 0.991929 0.998879\n",
"26 0.987586 0.983099\n",
"27 0.990275 0.994946\n",
"28 0.988472 0.985089\n",
"29 0.984913 0.941618\n",
"30 0.986482 0.959656\n",
"31 0.985221 0.935069\n",
"32 0.984891 0.922547\n",
"... ... ...\n",
"971 0.998412 0.524920\n",
"972 0.998422 0.530492\n",
"973 0.998440 0.540700\n",
"974 0.998423 0.529199\n",
"975 0.998437 0.536995\n",
"976 0.998405 0.516238\n",
"977 0.998412 0.519264\n",
"978 0.998401 0.511663\n",
"979 0.998398 0.508920\n",
"980 0.998388 0.501643\n",
"981 0.998402 0.509417\n",
"982 0.998395 0.504170\n",
"983 0.998389 0.500010\n",
"984 0.998378 0.492246\n",
"985 0.998376 0.490070\n",
"986 0.998339 0.467053\n",
"987 0.998328 0.459690\n",
"988 0.998320 0.453759\n",
"989 0.998328 0.457874\n",
"990 0.998336 0.461257\n",
"991 0.998321 0.451501\n",
"992 0.998320 0.450019\n",
"993 0.998330 0.454996\n",
"994 0.998316 0.445879\n",
"995 0.998283 0.426284\n",
"996 0.998292 0.430655\n",
"997 0.998277 0.420858\n",
"998 0.998291 0.427900\n",
"999 0.998307 0.436221\n",
"1000 0.998290 0.425738\n",
"\n",
"[998 rows x 2 columns]"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tests"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You can see that the test statistic converges $\\to$ 1 as it gets closer to a normal distribution. After ~200 samples, it's probably good enough."
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7f8f0602af10>"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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"RK5CYII=\n"
],
"text/plain": [
"<matplotlib.figure.Figure at 0x7f8f05ecbf90>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tests['Test statistic'].plot()"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7f8f05ea5b50>"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x7f8f05e16110>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tests['P-value'].plot()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
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},
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