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Add remaining T-Test

This commit is contained in:
Jip J. Dekker 2018-04-30 15:52:35 +10:00
parent 63a40a69a4
commit c0a3a8ea0e
2 changed files with 940 additions and 870 deletions

File diff suppressed because it is too large Load Diff

View File

@ -35,113 +35,113 @@
},
{
"cell_type": "code",
"execution_count": 2,
"execution_count": 64,
"metadata": {},
"outputs": [
{
"data": {
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" }</style> \n",
"<table id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000\" > \n",
"<table id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000\" > \n",
"<thead> <tr> \n",
" <th class=\"blank level0\" ></th> \n",
" <th class=\"col_heading level0 col0\" >ranking</th> \n",
@ -153,82 +153,82 @@
" <th class=\"col_heading level0 col6\" >height</th> \n",
" </tr></thead> \n",
"<tbody> <tr> \n",
" <th id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000level0_row0\" class=\"row_heading level0 row0\" >ranking</th> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row0_col0\" class=\"data row0 col0\" >1</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row0_col1\" class=\"data row0 col1\" >-0.165935</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row0_col2\" class=\"data row0 col2\" >-0.586707</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row0_col3\" class=\"data row0 col3\" >-0.244073</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row0_col4\" class=\"data row0 col4\" >0.17403</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row0_col5\" class=\"data row0 col5\" >-0.0826093</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row0_col6\" class=\"data row0 col6\" >0.0196139</td> \n",
" <th id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000level0_row0\" class=\"row_heading level0 row0\" >ranking</th> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row0_col0\" class=\"data row0 col0\" >1</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row0_col1\" class=\"data row0 col1\" >-0.165935</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row0_col2\" class=\"data row0 col2\" >-0.586707</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row0_col3\" class=\"data row0 col3\" >-0.244073</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row0_col4\" class=\"data row0 col4\" >0.17403</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row0_col5\" class=\"data row0 col5\" >-0.0826093</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row0_col6\" class=\"data row0 col6\" >0.0196139</td> \n",
" </tr> <tr> \n",
" <th id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000level0_row1\" class=\"row_heading level0 row1\" >age</th> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row1_col0\" class=\"data row1 col0\" >-0.165935</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row1_col1\" class=\"data row1 col1\" >1</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row1_col2\" class=\"data row1 col2\" >0.121731</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row1_col3\" class=\"data row1 col3\" >-0.140033</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row1_col4\" class=\"data row1 col4\" >-0.994296</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row1_col5\" class=\"data row1 col5\" >0.157223</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row1_col6\" class=\"data row1 col6\" >-0.0282972</td> \n",
" <th id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000level0_row1\" class=\"row_heading level0 row1\" >age</th> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row1_col0\" class=\"data row1 col0\" >-0.165935</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row1_col1\" class=\"data row1 col1\" >1</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row1_col2\" class=\"data row1 col2\" >0.121731</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row1_col3\" class=\"data row1 col3\" >-0.140033</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row1_col4\" class=\"data row1 col4\" >-0.994296</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row1_col5\" class=\"data row1 col5\" >0.157223</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row1_col6\" class=\"data row1 col6\" >-0.0282972</td> \n",
" </tr> <tr> \n",
" <th id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000level0_row2\" class=\"row_heading level0 row2\" >points</th> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row2_col0\" class=\"data row2 col0\" >-0.586707</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row2_col1\" class=\"data row2 col1\" >0.121731</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row2_col2\" class=\"data row2 col2\" >1</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row2_col3\" class=\"data row2 col3\" >-0.004905</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row2_col4\" class=\"data row2 col4\" >-0.129971</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row2_col5\" class=\"data row2 col5\" >0.159385</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row2_col6\" class=\"data row2 col6\" >-0.0153843</td> \n",
" <th id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000level0_row2\" class=\"row_heading level0 row2\" >points</th> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row2_col0\" class=\"data row2 col0\" >-0.586707</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row2_col1\" class=\"data row2 col1\" >0.121731</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row2_col2\" class=\"data row2 col2\" >1</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row2_col3\" class=\"data row2 col3\" >-0.004905</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row2_col4\" class=\"data row2 col4\" >-0.129971</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row2_col5\" class=\"data row2 col5\" >0.159385</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row2_col6\" class=\"data row2 col6\" >-0.0153843</td> \n",
" </tr> <tr> \n",
" <th id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000level0_row3\" class=\"row_heading level0 row3\" >tournplayed</th> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row3_col0\" class=\"data row3 col0\" >-0.244073</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row3_col1\" class=\"data row3 col1\" >-0.140033</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row3_col2\" class=\"data row3 col2\" >-0.004905</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row3_col3\" class=\"data row3 col3\" >1</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row3_col4\" class=\"data row3 col4\" >0.13293</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row3_col5\" class=\"data row3 col5\" >-0.139194</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row3_col6\" class=\"data row3 col6\" >-0.0712482</td> \n",
" <th id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000level0_row3\" class=\"row_heading level0 row3\" >tournplayed</th> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row3_col0\" class=\"data row3 col0\" >-0.244073</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row3_col1\" class=\"data row3 col1\" >-0.140033</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row3_col2\" class=\"data row3 col2\" >-0.004905</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row3_col3\" class=\"data row3 col3\" >1</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row3_col4\" class=\"data row3 col4\" >0.13293</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row3_col5\" class=\"data row3 col5\" >-0.139194</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row3_col6\" class=\"data row3 col6\" >-0.0712482</td> \n",
" </tr> <tr> \n",
" <th id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000level0_row4\" class=\"row_heading level0 row4\" >born</th> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row4_col0\" class=\"data row4 col0\" >0.17403</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row4_col1\" class=\"data row4 col1\" >-0.994296</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row4_col2\" class=\"data row4 col2\" >-0.129971</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row4_col3\" class=\"data row4 col3\" >0.13293</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row4_col4\" class=\"data row4 col4\" >1</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row4_col5\" class=\"data row4 col5\" >-0.163677</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row4_col6\" class=\"data row4 col6\" >0.0333731</td> \n",
" <th id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000level0_row4\" class=\"row_heading level0 row4\" >born</th> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row4_col0\" class=\"data row4 col0\" >0.17403</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row4_col1\" class=\"data row4 col1\" >-0.994296</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row4_col2\" class=\"data row4 col2\" >-0.129971</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row4_col3\" class=\"data row4 col3\" >0.13293</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row4_col4\" class=\"data row4 col4\" >1</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row4_col5\" class=\"data row4 col5\" >-0.163677</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row4_col6\" class=\"data row4 col6\" >0.0333731</td> \n",
" </tr> <tr> \n",
" <th id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000level0_row5\" class=\"row_heading level0 row5\" >weight</th> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row5_col0\" class=\"data row5 col0\" >-0.0826093</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row5_col1\" class=\"data row5 col1\" >0.157223</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row5_col2\" class=\"data row5 col2\" >0.159385</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row5_col3\" class=\"data row5 col3\" >-0.139194</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row5_col4\" class=\"data row5 col4\" >-0.163677</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row5_col5\" class=\"data row5 col5\" >1</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row5_col6\" class=\"data row5 col6\" >0.757689</td> \n",
" <th id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000level0_row5\" class=\"row_heading level0 row5\" >weight</th> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row5_col0\" class=\"data row5 col0\" >-0.0826093</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row5_col1\" class=\"data row5 col1\" >0.157223</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row5_col2\" class=\"data row5 col2\" >0.159385</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row5_col3\" class=\"data row5 col3\" >-0.139194</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row5_col4\" class=\"data row5 col4\" >-0.163677</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row5_col5\" class=\"data row5 col5\" >1</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row5_col6\" class=\"data row5 col6\" >0.757689</td> \n",
" </tr> <tr> \n",
" <th id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000level0_row6\" class=\"row_heading level0 row6\" >height</th> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row6_col0\" class=\"data row6 col0\" >0.0196139</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row6_col1\" class=\"data row6 col1\" >-0.0282972</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row6_col2\" class=\"data row6 col2\" >-0.0153843</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row6_col3\" class=\"data row6 col3\" >-0.0712482</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row6_col4\" class=\"data row6 col4\" >0.0333731</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row6_col5\" class=\"data row6 col5\" >0.757689</td> \n",
" <td id=\"T_85bdf18c_4c33_11e8_ad01_32001d384000row6_col6\" class=\"data row6 col6\" >1</td> \n",
" <th id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000level0_row6\" class=\"row_heading level0 row6\" >height</th> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row6_col0\" class=\"data row6 col0\" >0.0196139</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row6_col1\" class=\"data row6 col1\" >-0.0282972</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row6_col2\" class=\"data row6 col2\" >-0.0153843</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row6_col3\" class=\"data row6 col3\" >-0.0712482</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row6_col4\" class=\"data row6 col4\" >0.0333731</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row6_col5\" class=\"data row6 col5\" >0.757689</td> \n",
" <td id=\"T_75b4b348_4c3a_11e8_bc4a_32001d384000row6_col6\" class=\"data row6 col6\" >1</td> \n",
" </tr></tbody> \n",
"</table> "
],
"text/plain": [
"<pandas.io.formats.style.Styler at 0x10a484710>"
"<pandas.io.formats.style.Styler at 0x1127ee438>"
]
},
"execution_count": 2,
"execution_count": 64,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data.corr().style.background_gradient(cmap='viridis')"
"data.corr().style.background_gradient(cmap='Wistia')"
]
},
{
@ -420,21 +420,91 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"# Handedness t-test\n",
"\n",
"Initial investigation using simple data aggragation showed that left handed players hold higher ranks within the tennis board and on average they have more points than right handed players:"
"# Height is an advantage"
]
},
{
"cell_type": "code",
"execution_count": 41,
"execution_count": 50,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Average rank of right-handed players: 198.5\n",
"Average height of men: 185.64912280701753\n",
"Average height of women: 180.37142857142857\n"
]
}
],
"source": [
"male_mean = data.loc[data[\"gender\"] == \"M\"][\"height\"].mean()\n",
"print(\"Average height of men:\", male_mean)\n",
"female_mean = data.loc[data[\"gender\"] == \"F\"][\"height\"].mean()\n",
"print(\"Average height of women:\", female_mean)"
]
},
{
"cell_type": "code",
"execution_count": 67,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"T score: 1.711723, P score: 0.043815\n"
]
}
],
"source": [
"scores_men_tall = data.loc[np.logical_and(data[\"gender\"] == \"M\", data[\"height\"] >= male_mean)][\"points\"]\n",
"scores_men_short = data.loc[np.logical_and(data[\"gender\"] == \"M\", data[\"height\"] < male_mean)][\"points\"]\n",
"t, p = stats.ttest_ind(scores_men_tall, scores_men_short)\n",
"p = p/2 # Because 1 tailed T-Test\n",
"print(\"T score: %f, P score: %f\" % (t, p))"
]
},
{
"cell_type": "code",
"execution_count": 66,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"T score: 1.860241, P score: 0.032030\n"
]
}
],
"source": [
"scores_women_tall = data.loc[np.logical_and(data[\"gender\"] == \"F\", data[\"height\"] >= female_mean)][\"points\"]\n",
"scores_women_short = data.loc[np.logical_and(data[\"gender\"] == \"F\", data[\"height\"] < female_mean)][\"points\"]\n",
"t, p = stats.ttest_ind(scores_women_tall, scores_women_short)\n",
"p = p/2 # Because 1 tailed T-Test\n",
"print(\"T score: %f, P score: %f\" % (t, p))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Being left-handed is an advantage\n",
"\n",
"Initial investigation using simple data aggragation showed that left handed players hold higher ranks within the tennis board and on average they have more points than right handed players:"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Average rank of right-handed players: 215.72115384615384\n",
"Average score of right-handed players: 608.775641025641\n",
"\n",
"Average rank of left-handed players: 186.56578947368422\n",
@ -443,7 +513,7 @@
}
],
"source": [
"print(\"Average rank of right-handed players:\", data.loc[data[\"hand\"] == \"R\"][\"ranking\"].median())\n",
"print(\"Average rank of right-handed players:\", data.loc[data[\"hand\"] == \"R\"][\"ranking\"].mean())\n",
"print(\"Average score of right-handed players:\", data.loc[data[\"hand\"] == \"R\"][\"points\"].mean())\n",
"print(\"\\nAverage rank of left-handed players:\", data.loc[data[\"hand\"] == \"L\"][\"ranking\"].mean())\n",
"print(\"Average score of left-handed players:\", data.loc[data[\"hand\"] == \"L\"][\"points\"].mean())"
@ -458,7 +528,7 @@
},
{
"cell_type": "code",
"execution_count": 36,
"execution_count": 65,
"metadata": {},
"outputs": [
{
@ -472,7 +542,7 @@
"source": [
"scoresL = data.loc[data[\"hand\"] == \"L\"][\"points\"]\n",
"scoresR = data.loc[data[\"hand\"] == \"R\"][\"points\"]\n",
"t, p = stats.stats.ttest_ind(scoresL, scoresR)\n",
"t, p = stats.ttest_ind(scoresL, scoresR)\n",
"p = p/2 # Because 1 tailed T-Test\n",
"print(\"T score: %f, P score: %f\" % (t, p))"
]
@ -481,7 +551,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"Our $t$-Test reveals a $p$-score of $0.325815$. Generally we reject our null-hypothesis when this score is less that $0.05$. From this data is thus highly unlikely that left-handed players have a significant advantage over right-handed players."
"Our $t$-Test reveals a $p$-score of $0.325815$. Generally we reject our null-hypothesis when this score is less that $0.05$. From our data we can thus not conclude that left-handed players have a significant advantage over right-handed players."
]
},
{