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Update anova_documentation.rst
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Corey-Bryant committed Mar 8, 2022
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Expand Up @@ -124,9 +124,8 @@ Now let's get some quick information regarding the data set.
Now to take a look at the descriptive statistics of the univariate data. The output
indicates that all the columns are integers which is a discrete data type; however,
when we conduct the ANOVA the independent variables, drug and disease, will be
treated as categorical while the dependent variable will be treated as continuous.
indicates that there are no missing observations and that each variable is stored
as an integer.



Expand Down Expand Up @@ -155,14 +154,38 @@ treated as categorical while the dependent variable will be treated as continuou
<table border="1" class="dataframe"> <thead> <tr style="text-align: right;"> <th></th> <th>Variable</th> <th>Outcome</th> <th>Count</th> <th>Percent</th> </tr> </thead> <tbody> <tr> <th>0</th> <td>drug</td> <td>4</td> <td>16</td> <td>27.59</td> </tr> <tr> <th>1</th> <td></td> <td>2</td> <td>15</td> <td>25.86</td> </tr> <tr> <th>2</th> <td></td> <td>1</td> <td>15</td> <td>25.86</td> </tr> <tr> <th>3</th> <td></td> <td>3</td> <td>12</td> <td>20.69</td> </tr> <tr> <th>4</th> <td>disease</td> <td>3</td> <td>20</td> <td>34.48</td> </tr> <tr> <th>5</th> <td></td> <td>2</td> <td>19</td> <td>32.76</td> </tr> <tr> <th>6</th> <td></td> <td>1</td> <td>19</td> <td>32.76</td> </tr> </tbody></table>


Now to conduct the ANOVA; by default Type 3 sum of squares are used.
Now to conduct the ANOVA; by default Type 3 sum of squares are used. There are a few
ways one can conduct an ANOVA using Researchpy, the suggested approach is to assign
the ANOVA model to an object that way one can utilize the built-in methods. If
one does not want to do that, then running the model with and displaying the results
in one-line will work too; the output will be returned as a tuple. The suggested
approach will be shown in this example.


.. code:: python
mod = anova("systolic ~ C(drug) + C(disease) + C(drug):C(disease)", data = systolic, sum_of_squares = 3)
mod.results()
m = anova("systolic ~ C(drug) + C(disease) + C(drug):C(disease)", data = systolic, sum_of_squares = 3)
desc, table = m.results()
print(desc, table, sep = "\n"*2)
.. raw:: html

<p>Note: Effect size values for factors are partial.</p>

<table border="1" class="dataframe"><thead> <tr style="text-align: right;"> </tr> </thead> <tbody> <tr> <th>Number of obs =</th> <td>58.0000</td> </tr> <tr> <th>Root MSE =</th> <td>10.5096</td> </tr> <tr> <th>R-squared =</th> <td>0.4560</td> </tr> <tr> <th>Adj R-squared =</th> <td>0.3259</td> </tr> </tbody></table>

<table border="1" class="dataframe"> <thead> <tr style="text-align: right;"> <th>Source</th> <th>Sum of Squares</th> <th>Degrees of Freedom</th> <th>Mean Squares</th> <th>F value</th> <th>p-value</th> <th>Eta squared</th> <th>Omega squared</th> </tr> </thead> <tbody> <tr> <td>Model</td> <td>4,259.3385</td> <td>11</td> <td>387.2126</td> <td>3.5057</td> <td>0.0013</td> <td>0.4560</td> <td>0.3221</td> </tr> <tr> <td></td> <td></td> <td></td> <td></td> <td></td> <td></td> <td></td> <td></td> </tr> <tr> <td>drug</td> <td>2,997.4719</td> <td>3.0000</td> <td>999.1573</td> <td>9.0460</td> <td>0.0001</td> <td>0.3711</td> <td>0.2939</td> </tr> <tr> <td>disease</td> <td>415.8730</td> <td>2.0000</td> <td>207.9365</td> <td>1.8826</td> <td>0.1637</td> <td>0.0757</td> <td>0.0295</td> </tr> <tr> <td>drug:disease</td> <td>707.2663</td> <td>6.0000</td> <td>117.8777</td> <td>1.0672</td> <td>0.3958</td> <td>0.1222</td> <td>0.0069</td> </tr> <tr> <td></td> <td></td> <td></td> <td></td> <td></td> <td></td> <td></td> <td></td> </tr> <tr> <td>Residual</td> <td>5,080.8167</td> <td>46</td> <td>110.4525</td> <td></td> <td></td> <td></td> <td></td> </tr> <tr> <td>Total</td> <td>9,340.1552</td> <td>57</td> <td>163.8624</td> <td></td> <td></td> <td></td> <td></td> </tr> </tbody></table>


If it's of interest, one can also access the underlying regression table.


.. code:: python
m.regression_table()
.. raw:: html

<table border="1" class="dataframe"> <thead> <tr style="text-align: right;"> <th></th> <th>Source</th> <th>Sum of Squares</th> <th>Degrees of Freedom</th> <th>Mean Squares</th> <th>F value</th> <th>p-value</th> </tr> </thead> <tbody> <tr> <th>0</th> <td>Model</td> <td>4259.34</td> <td>11</td> <td>387.213</td> <td>3.5057</td> <td>0.0013</td> </tr> <tr> <th>1</th> <td></td> <td></td> <td></td> <td></td> <td></td> <td></td> </tr> <tr> <th>2</th> <td>drug</td> <td>2997.47</td> <td>3</td> <td>999.157</td> <td>9.046</td> <td>0.0001</td> </tr> <tr> <th>3</th> <td>disease</td> <td>415.873</td> <td>2</td> <td>207.936</td> <td>1.8826</td> <td>0.1637</td> </tr> <tr> <th>4</th> <td>drug:disease</td> <td>707.266</td> <td>6</td> <td>117.878</td> <td>1.0672</td> <td>0.3958</td> </tr> <tr> <th>5</th> <td></td> <td></td> <td></td> <td></td> <td></td> <td></td> </tr> <tr> <th>6</th> <td>Residual</td> <td>5080.82</td> <td>46</td> <td>110.453</td> <td></td> <td></td> </tr> <tr> <th>7</th> <td>Total</td> <td>9340.16</td> <td>57</td> <td>163.862</td> <td></td> <td></td> </tr> </tbody></table>
<table border="1" class="dataframe"> <thead> <tr style="text-align: right;"> <th>systolic</th> <th>Coef.</th> <th>Std. Err.</th> <th>t</th> <th>p-value</th> <th>95% Conf. Interval</th> </tr> </thead> <tbody> <tr> <td>Intercept</td> <td>29.3333</td> <td>4.2905</td> <td>6.8367</td> <td>0.0000</td> <td>[20.6969, 37.9697]</td> </tr> <tr> <td>drug</td> <td></td> <td></td> <td></td> <td></td> <td></td> </tr> <tr> <td>1</td> <td>(reference)</td> <td></td> <td></td> <td></td> <td></td> </tr> <tr> <td>2</td> <td>-1.3333</td> <td>6.3639</td> <td>-0.2095</td> <td>0.8350</td> <td>[-14.1432, 11.4765]</td> </tr> <tr> <td>3</td> <td>-13.0000</td> <td>7.4314</td> <td>-1.7493</td> <td>0.0869</td> <td>[-27.9587, 1.9587]</td> </tr> <tr> <td>4</td> <td>-15.7333</td> <td>6.3639</td> <td>-2.4723</td> <td>0.0172</td> <td>[-28.5432, -2.9235]</td> </tr> <tr> <td>disease</td> <td></td> <td></td> <td></td> <td></td> <td></td> </tr> <tr> <td>1</td> <td>(reference)</td> <td></td> <td></td> <td></td> <td></td> </tr> <tr> <td>2</td> <td>-1.0833</td> <td>6.7839</td> <td>-0.1597</td> <td>0.8738</td> <td>[-14.7387, 12.572]</td> </tr> <tr> <td>3</td> <td>-8.9333</td> <td>6.3639</td> <td>-1.4038</td> <td>0.1671</td> <td>[-21.7432, 3.8765]</td> </tr> <tr> <td>drug:disease</td> <td></td> <td></td> <td></td> <td></td> <td></td> </tr> <tr> <td>2:3</td> <td>-0.9000</td> <td>8.9999</td> <td>-0.1000</td> <td>0.9208</td> <td>[-19.0159, 17.2159]</td> </tr> <tr> <td>2:2</td> <td>6.5833</td> <td>9.7839</td> <td>0.6729</td> <td>0.5044</td> <td>[-13.1107, 26.2774]</td> </tr> <tr> <td>2:3</td> <td>-0.9000</td> <td>8.9999</td> <td>-0.1000</td> <td>0.9208</td> <td>[-19.0159, 17.2159]</td> </tr> <tr> <td>3:2</td> <td>-10.8500</td> <td>10.2435</td> <td>-1.0592</td> <td>0.2950</td> <td>[-31.4692, 9.7692]</td> </tr> <tr> <td>3:3</td> <td>1.1000</td> <td>10.2435</td> <td>0.1074</td> <td>0.9150</td> <td>[-19.5192, 21.7192]</td> </tr> <tr> <td>4:2</td> <td>0.3167</td> <td>9.3017</td> <td>0.0340</td> <td>0.9730</td> <td>[-18.4066, 19.04]</td> </tr> <tr> <td>4:3</td> <td>9.5333</td> <td>9.2022</td> <td>1.0360</td> <td>0.3056</td> <td>[-8.9897, 28.0564]</td> </tr> <tr> <td>2:3</td> <td>-0.9000</td> <td>8.9999</td> <td>-0.1000</td> <td>0.9208</td> <td>[-19.0159, 17.2159]</td> </tr> </tbody></table>

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