notebooks/04_Correlations.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Correlations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simple correlation\n",
    "Computing a correlation between two variables in Pingouin is done using the [corr](https://pingouin-stats.org/generated/pingouin.corr.html#pingouin.corr) function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>n</th>\n",
       "      <th>r</th>\n",
       "      <th>CI95%</th>\n",
       "      <th>p-val</th>\n",
       "      <th>BF10</th>\n",
       "      <th>power</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>pearson</th>\n",
       "      <td>8</td>\n",
       "      <td>0.185</td>\n",
       "      <td>[-0.6, 0.79]</td>\n",
       "      <td>0.661</td>\n",
       "      <td>0.468</td>\n",
       "      <td>0.072</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "         n      r         CI95%  p-val   BF10  power\n",
       "pearson  8  0.185  [-0.6, 0.79]  0.661  0.468  0.072"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import pingouin as pg\n",
    "\n",
    "# Set the default Pandas float precision to 3 decimals\n",
    "pd.set_option(\"display.precision\", 3)\n",
    "\n",
    "x = [4, 5, 7, 4, 5, 6, 8, 9]\n",
    "y = [3, 4, 5, 3, 4, 5, 4, 3]\n",
    "\n",
    "pg.corr(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The [corr](https://pingouin-stats.org/generated/pingouin.corr.html#pingouin.corr) function returns a pandas DataFrame with:\n",
    "\n",
    "1. The sample size `n` (after removal of NaN)\n",
    "2. the correlation coefficient (`r`)\n",
    "3. the parametric 95% confidence intervals of the coefficient (`CI95%`)\n",
    "4. the p-value (`p-unc`)\n",
    "5. the Bayes Factor for the alternative hypothesis (`BF10`)\n",
    "6. the achieved power of the test (`power`, = 1 - type 2 error)\n",
    "\n",
    "By default, the function returns the two-sided Pearson's correlation coefficients. This can be adjusted using the `tail` and `method` arguments:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
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       "      <th></th>\n",
       "      <th>n</th>\n",
       "      <th>r</th>\n",
       "      <th>CI95%</th>\n",
       "      <th>p-val</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>spearman</th>\n",
       "      <td>8</td>\n",
       "      <td>0.319</td>\n",
       "      <td>[-0.38, 1.0]</td>\n",
       "      <td>0.221</td>\n",
       "      <td>0.201</td>\n",
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      "text/plain": [
       "          n      r         CI95%  p-val  power\n",
       "spearman  8  0.319  [-0.38, 1.0]  0.221  0.201"
      ]
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   ],
   "source": [
    "pg.corr(x, y, method='spearman', alternative='greater')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***********************\n",
    "\n",
    "## Pairwise correlations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will now see how to compute pairwise correlations coefficients across columns of a pandas DataFrame using the [pairwise_corr](https://pingouin-stats.org/generated/pingouin.pairwise_corr.html#pingouin.pairwise_corr) function.\n",
    "\n",
    "To do so, we will first load an example dataset in which each row represents one subject and each columns represent a score on the well-known Big Five personality traits. There are 500 subjects in total."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Neuroticism</th>\n",
       "      <th>Extraversion</th>\n",
       "      <th>Openness</th>\n",
       "      <th>Agreeableness</th>\n",
       "      <th>Conscientiousness</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.479</td>\n",
       "      <td>4.208</td>\n",
       "      <td>3.938</td>\n",
       "      <td>3.958</td>\n",
       "      <td>3.458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.604</td>\n",
       "      <td>3.188</td>\n",
       "      <td>3.958</td>\n",
       "      <td>3.396</td>\n",
       "      <td>3.229</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.812</td>\n",
       "      <td>2.896</td>\n",
       "      <td>3.417</td>\n",
       "      <td>2.750</td>\n",
       "      <td>3.500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.896</td>\n",
       "      <td>3.562</td>\n",
       "      <td>3.521</td>\n",
       "      <td>3.167</td>\n",
       "      <td>2.792</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.021</td>\n",
       "      <td>3.333</td>\n",
       "      <td>4.021</td>\n",
       "      <td>3.208</td>\n",
       "      <td>2.854</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "   Neuroticism  Extraversion  Openness  Agreeableness  Conscientiousness\n",
       "0        2.479         4.208     3.938          3.958              3.458\n",
       "1        2.604         3.188     3.958          3.396              3.229\n",
       "2        2.812         2.896     3.417          2.750              3.500\n",
       "3        2.896         3.562     3.521          3.167              2.792\n",
       "4        3.021         3.333     4.021          3.208              2.854"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pg.read_dataset('pairwise_corr')\n",
    "\n",
    "# Remove the 'Subject' column\n",
    "df.drop(columns='Subject', inplace=True)\n",
    "\n",
    "# Print the first lines\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see if the personality dimensions are correlated or not. For that, we will compute the pairwise correlations between all the columns of the DataFrame:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>Y</th>\n",
       "      <th>method</th>\n",
       "      <th>alternative</th>\n",
       "      <th>n</th>\n",
       "      <th>r</th>\n",
       "      <th>CI95%</th>\n",
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       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Neuroticism</td>\n",
       "      <td>Extraversion</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
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       "      <th>1</th>\n",
       "      <td>Neuroticism</td>\n",
       "      <td>Openness</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
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       "      <td>0.058</td>\n",
       "      <td>0.056</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Neuroticism</td>\n",
       "      <td>Agreeableness</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>-0.134</td>\n",
       "      <td>[-0.22, -0.05]</td>\n",
       "      <td>2.615e-03</td>\n",
       "      <td>5.122</td>\n",
       "      <td>0.854</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Neuroticism</td>\n",
       "      <td>Conscientiousness</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>-0.368</td>\n",
       "      <td>[-0.44, -0.29]</td>\n",
       "      <td>1.759e-17</td>\n",
       "      <td>2.644e+14</td>\n",
       "      <td>1.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Extraversion</td>\n",
       "      <td>Openness</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>0.267</td>\n",
       "      <td>[0.18, 0.35]</td>\n",
       "      <td>1.288e-09</td>\n",
       "      <td>5.277e+06</td>\n",
       "      <td>1.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Extraversion</td>\n",
       "      <td>Agreeableness</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>0.055</td>\n",
       "      <td>[-0.03, 0.14]</td>\n",
       "      <td>2.234e-01</td>\n",
       "      <td>0.117</td>\n",
       "      <td>0.230</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Extraversion</td>\n",
       "      <td>Conscientiousness</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>0.065</td>\n",
       "      <td>[-0.02, 0.15]</td>\n",
       "      <td>1.492e-01</td>\n",
       "      <td>0.158</td>\n",
       "      <td>0.303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Openness</td>\n",
       "      <td>Agreeableness</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>0.159</td>\n",
       "      <td>[0.07, 0.24]</td>\n",
       "      <td>3.517e-04</td>\n",
       "      <td>32.635</td>\n",
       "      <td>0.948</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Openness</td>\n",
       "      <td>Conscientiousness</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>-0.013</td>\n",
       "      <td>[-0.1, 0.07]</td>\n",
       "      <td>7.642e-01</td>\n",
       "      <td>0.059</td>\n",
       "      <td>0.060</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Agreeableness</td>\n",
       "      <td>Conscientiousness</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>0.159</td>\n",
       "      <td>[0.07, 0.24]</td>\n",
       "      <td>3.685e-04</td>\n",
       "      <td>31.243</td>\n",
       "      <td>0.946</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "               X                  Y   method alternative    n      r  \\\n",
       "0    Neuroticism       Extraversion  pearson   two-sided  500 -0.350   \n",
       "1    Neuroticism           Openness  pearson   two-sided  500 -0.010   \n",
       "2    Neuroticism      Agreeableness  pearson   two-sided  500 -0.134   \n",
       "3    Neuroticism  Conscientiousness  pearson   two-sided  500 -0.368   \n",
       "4   Extraversion           Openness  pearson   two-sided  500  0.267   \n",
       "5   Extraversion      Agreeableness  pearson   two-sided  500  0.055   \n",
       "6   Extraversion  Conscientiousness  pearson   two-sided  500  0.065   \n",
       "7       Openness      Agreeableness  pearson   two-sided  500  0.159   \n",
       "8       Openness  Conscientiousness  pearson   two-sided  500 -0.013   \n",
       "9  Agreeableness  Conscientiousness  pearson   two-sided  500  0.159   \n",
       "\n",
       "            CI95%      p-unc       BF10  power  \n",
       "0  [-0.42, -0.27]  7.323e-16  6.765e+12  1.000  \n",
       "1    [-0.1, 0.08]  8.169e-01      0.058  0.056  \n",
       "2  [-0.22, -0.05]  2.615e-03      5.122  0.854  \n",
       "3  [-0.44, -0.29]  1.759e-17  2.644e+14  1.000  \n",
       "4    [0.18, 0.35]  1.288e-09  5.277e+06  1.000  \n",
       "5   [-0.03, 0.14]  2.234e-01      0.117  0.230  \n",
       "6   [-0.02, 0.15]  1.492e-01      0.158  0.303  \n",
       "7    [0.07, 0.24]  3.517e-04     32.635  0.948  \n",
       "8    [-0.1, 0.07]  7.642e-01      0.059  0.060  \n",
       "9    [0.07, 0.24]  3.685e-04     31.243  0.946  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pg.pairwise_corr(df)  # Similar to df.pairwise_corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the example above, we can see that the highest correlation between personality dimensions is between `Neuroticism` and `Conscientiousness`, as indicated by the correlation coefficient (-0.368), the p-value (1.75e-17) and the Bayes Factor (1.80e14)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Non-parametric correlations\n",
    "If your data do not follow a normal distribution or contains outliers, you may want to use a non-parametric method such as the Spearman rank-correlation.\n",
    "\n",
    "In the example below, we compute the one-sided Spearman pairwise correlations between a subset of columns. Note that the Bayes Factor is only computed when using the Pearson method and is therefore not present in the table above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Neuroticism</td>\n",
       "      <td>Extraversion</td>\n",
       "      <td>spearman</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>-0.325</td>\n",
       "      <td>[-0.4, -0.24]</td>\n",
       "      <td>8.385e-14</td>\n",
       "      <td>1.0</td>\n",
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       "             X             Y    method alternative    n      r          CI95%  \\\n",
       "0  Neuroticism  Extraversion  spearman   two-sided  500 -0.325  [-0.4, -0.24]   \n",
       "\n",
       "       p-unc  power  \n",
       "0  8.385e-14    1.0  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
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    }
   ],
   "source": [
    "pg.pairwise_corr(data=df, columns=['Neuroticism', 'Extraversion'], method='spearman')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Robust correlations\n",
    "If you believe that your dataset contains outliers, you can use a robust correlation method. Learn more on the documentation of the [corr](https://pingouin-stats.org/generated/pingouin.corr.html#pingouin.corr) function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>Y</th>\n",
       "      <th>method</th>\n",
       "      <th>alternative</th>\n",
       "      <th>n</th>\n",
       "      <th>r</th>\n",
       "      <th>CI95%</th>\n",
       "      <th>p-unc</th>\n",
       "      <th>power</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Neuroticism</td>\n",
       "      <td>Extraversion</td>\n",
       "      <td>bicor</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>-0.343</td>\n",
       "      <td>[-0.42, -0.26]</td>\n",
       "      <td>2.908e-15</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             X             Y method alternative    n      r           CI95%  \\\n",
       "0  Neuroticism  Extraversion  bicor   two-sided  500 -0.343  [-0.42, -0.26]   \n",
       "\n",
       "       p-unc  power  \n",
       "0  2.908e-15    1.0  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Introduce two outliers in variable X\n",
    "df.loc[[5, 12, 24, 58], 'Neuroticism'] = 18\n",
    "\n",
    "# Biweight midcorrelation\n",
    "pg.pairwise_corr(data=df, columns=['Neuroticism', 'Extraversion'], method='bicor')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>Y</th>\n",
       "      <th>method</th>\n",
       "      <th>alternative</th>\n",
       "      <th>n</th>\n",
       "      <th>r</th>\n",
       "      <th>CI95%</th>\n",
       "      <th>p-unc</th>\n",
       "      <th>power</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Neuroticism</td>\n",
       "      <td>Extraversion</td>\n",
       "      <td>percbend</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>-0.327</td>\n",
       "      <td>[-0.4, -0.25]</td>\n",
       "      <td>5.985e-14</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             X             Y    method alternative    n      r          CI95%  \\\n",
       "0  Neuroticism  Extraversion  percbend   two-sided  500 -0.327  [-0.4, -0.25]   \n",
       "\n",
       "       p-unc  power  \n",
       "0  5.985e-14    1.0  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Percentage bend correlation\n",
    "pg.pairwise_corr(data=df, columns=['Neuroticism', 'Extraversion'], method='percbend')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>Y</th>\n",
       "      <th>method</th>\n",
       "      <th>alternative</th>\n",
       "      <th>n</th>\n",
       "      <th>outliers</th>\n",
       "      <th>r</th>\n",
       "      <th>CI95%</th>\n",
       "      <th>p-unc</th>\n",
       "      <th>power</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Neuroticism</td>\n",
       "      <td>Extraversion</td>\n",
       "      <td>shepherd</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>16.0</td>\n",
       "      <td>-0.319</td>\n",
       "      <td>[-0.4, -0.24]</td>\n",
       "      <td>6.791e-13</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             X             Y    method alternative    n  outliers      r  \\\n",
       "0  Neuroticism  Extraversion  shepherd   two-sided  500      16.0 -0.319   \n",
       "\n",
       "           CI95%      p-unc  power  \n",
       "0  [-0.4, -0.24]  6.791e-13    1.0  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Shepherd's correlation\n",
    "pg.pairwise_corr(data=df, columns=['Neuroticism', 'Extraversion'], method='shepherd')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Correction for multiple comparisons\n",
    "Finally, if you are computing a large number of correlation coefficients, you might want to correct the p-values for multiple comparisons. This can be done with `padjust` argument:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>Y</th>\n",
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       "      <th>r</th>\n",
       "      <th>CI95%</th>\n",
       "      <th>p-unc</th>\n",
       "      <th>p-corr</th>\n",
       "      <th>p-adjust</th>\n",
       "      <th>power</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Neuroticism</td>\n",
       "      <td>Extraversion</td>\n",
       "      <td>spearman</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>-0.330</td>\n",
       "      <td>[-0.41, -0.25]</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>holm</td>\n",
       "      <td>1.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Neuroticism</td>\n",
       "      <td>Openness</td>\n",
       "      <td>spearman</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>-0.020</td>\n",
       "      <td>[-0.11, 0.07]</td>\n",
       "      <td>0.662</td>\n",
       "      <td>1.000</td>\n",
       "      <td>holm</td>\n",
       "      <td>0.072</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Neuroticism</td>\n",
       "      <td>Agreeableness</td>\n",
       "      <td>spearman</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>-0.132</td>\n",
       "      <td>[-0.22, -0.04]</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.015</td>\n",
       "      <td>holm</td>\n",
       "      <td>0.843</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Neuroticism</td>\n",
       "      <td>Conscientiousness</td>\n",
       "      <td>spearman</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>-0.365</td>\n",
       "      <td>[-0.44, -0.29]</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>holm</td>\n",
       "      <td>1.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Extraversion</td>\n",
       "      <td>Openness</td>\n",
       "      <td>spearman</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>0.243</td>\n",
       "      <td>[0.16, 0.32]</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>holm</td>\n",
       "      <td>1.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Extraversion</td>\n",
       "      <td>Agreeableness</td>\n",
       "      <td>spearman</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>0.062</td>\n",
       "      <td>[-0.03, 0.15]</td>\n",
       "      <td>0.166</td>\n",
       "      <td>0.666</td>\n",
       "      <td>holm</td>\n",
       "      <td>0.283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Extraversion</td>\n",
       "      <td>Conscientiousness</td>\n",
       "      <td>spearman</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>0.056</td>\n",
       "      <td>[-0.03, 0.14]</td>\n",
       "      <td>0.213</td>\n",
       "      <td>0.666</td>\n",
       "      <td>holm</td>\n",
       "      <td>0.238</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Openness</td>\n",
       "      <td>Agreeableness</td>\n",
       "      <td>spearman</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>0.170</td>\n",
       "      <td>[0.08, 0.25]</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.001</td>\n",
       "      <td>holm</td>\n",
       "      <td>0.969</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Openness</td>\n",
       "      <td>Conscientiousness</td>\n",
       "      <td>spearman</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>-0.007</td>\n",
       "      <td>[-0.09, 0.08]</td>\n",
       "      <td>0.880</td>\n",
       "      <td>1.000</td>\n",
       "      <td>holm</td>\n",
       "      <td>0.053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Agreeableness</td>\n",
       "      <td>Conscientiousness</td>\n",
       "      <td>spearman</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>0.161</td>\n",
       "      <td>[0.07, 0.24]</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.002</td>\n",
       "      <td>holm</td>\n",
       "      <td>0.951</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               X                  Y    method alternative    n      r  \\\n",
       "0    Neuroticism       Extraversion  spearman   two-sided  500 -0.330   \n",
       "1    Neuroticism           Openness  spearman   two-sided  500 -0.020   \n",
       "2    Neuroticism      Agreeableness  spearman   two-sided  500 -0.132   \n",
       "3    Neuroticism  Conscientiousness  spearman   two-sided  500 -0.365   \n",
       "4   Extraversion           Openness  spearman   two-sided  500  0.243   \n",
       "5   Extraversion      Agreeableness  spearman   two-sided  500  0.062   \n",
       "6   Extraversion  Conscientiousness  spearman   two-sided  500  0.056   \n",
       "7       Openness      Agreeableness  spearman   two-sided  500  0.170   \n",
       "8       Openness  Conscientiousness  spearman   two-sided  500 -0.007   \n",
       "9  Agreeableness  Conscientiousness  spearman   two-sided  500  0.161   \n",
       "\n",
       "            CI95%  p-unc  p-corr p-adjust  power  \n",
       "0  [-0.41, -0.25]  0.000   0.000     holm  1.000  \n",
       "1   [-0.11, 0.07]  0.662   1.000     holm  0.072  \n",
       "2  [-0.22, -0.04]  0.003   0.015     holm  0.843  \n",
       "3  [-0.44, -0.29]  0.000   0.000     holm  1.000  \n",
       "4    [0.16, 0.32]  0.000   0.000     holm  1.000  \n",
       "5   [-0.03, 0.15]  0.166   0.666     holm  0.283  \n",
       "6   [-0.03, 0.14]  0.213   0.666     holm  0.238  \n",
       "7    [0.08, 0.25]  0.000   0.001     holm  0.969  \n",
       "8   [-0.09, 0.08]  0.880   1.000     holm  0.053  \n",
       "9    [0.07, 0.24]  0.000   0.002     holm  0.951  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pg.pairwise_corr(df, method='spearman', padjust=\"holm\").round(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Advanced columns selection\n",
    "\n",
    "One of the advantages of the [pairwise_corr](https://pingouin-stats.org/generated/pingouin.pairwise_corr.html#pingouin.pairwise_corr) function is that it allows for almost unlimited flexibility with regards to columns indexing. To understand this, we'll first start by adding some fake columns to our dataframe:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Neuroticism</th>\n",
       "      <th>Extraversion</th>\n",
       "      <th>Openness</th>\n",
       "      <th>Agreeableness</th>\n",
       "      <th>Conscientiousness</th>\n",
       "      <th>Age</th>\n",
       "      <th>BMI</th>\n",
       "      <th>Gender</th>\n",
       "      <th>Ethnicity</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.479</td>\n",
       "      <td>4.208</td>\n",
       "      <td>3.938</td>\n",
       "      <td>3.958</td>\n",
       "      <td>3.458</td>\n",
       "      <td>63</td>\n",
       "      <td>28</td>\n",
       "      <td>1</td>\n",
       "      <td>Caucasian</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.604</td>\n",
       "      <td>3.188</td>\n",
       "      <td>3.958</td>\n",
       "      <td>3.396</td>\n",
       "      <td>3.229</td>\n",
       "      <td>20</td>\n",
       "      <td>36</td>\n",
       "      <td>0</td>\n",
       "      <td>Caucasian</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.812</td>\n",
       "      <td>2.896</td>\n",
       "      <td>3.417</td>\n",
       "      <td>2.750</td>\n",
       "      <td>3.500</td>\n",
       "      <td>46</td>\n",
       "      <td>25</td>\n",
       "      <td>0</td>\n",
       "      <td>Caucasian</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.896</td>\n",
       "      <td>3.562</td>\n",
       "      <td>3.521</td>\n",
       "      <td>3.167</td>\n",
       "      <td>2.792</td>\n",
       "      <td>52</td>\n",
       "      <td>27</td>\n",
       "      <td>0</td>\n",
       "      <td>Caucasian</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.021</td>\n",
       "      <td>3.333</td>\n",
       "      <td>4.021</td>\n",
       "      <td>3.208</td>\n",
       "      <td>2.854</td>\n",
       "      <td>56</td>\n",
       "      <td>33</td>\n",
       "      <td>0</td>\n",
       "      <td>Caucasian</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Neuroticism  Extraversion  Openness  Agreeableness  Conscientiousness  Age  \\\n",
       "0        2.479         4.208     3.938          3.958              3.458   63   \n",
       "1        2.604         3.188     3.958          3.396              3.229   20   \n",
       "2        2.812         2.896     3.417          2.750              3.500   46   \n",
       "3        2.896         3.562     3.521          3.167              2.792   52   \n",
       "4        3.021         3.333     4.021          3.208              2.854   56   \n",
       "\n",
       "   BMI  Gender  Ethnicity  \n",
       "0   28       1  Caucasian  \n",
       "1   36       0  Caucasian  \n",
       "2   25       0  Caucasian  \n",
       "3   27       0  Caucasian  \n",
       "4   33       0  Caucasian  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "np.random.seed(123)\n",
    "df['Age'] = np.random.randint(18, 70, size=df.shape[0])\n",
    "df['BMI'] = np.random.randint(18, 45, size=df.shape[0])\n",
    "df['Gender'] = np.random.randint(0, 2, size=df.shape[0])\n",
    "df['Ethnicity'] = 'Caucasian'\n",
    "\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's assume that I am interested in looking only at the correlation between `Age` on the one hand and all the other variables on the other hand. This can be done very easily:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <td>0.078</td>\n",
       "      <td>0.128</td>\n",
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       "    <tr>\n",
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       "      <td>Age</td>\n",
       "      <td>Extraversion</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>-0.004</td>\n",
       "      <td>[-0.09, 0.08]</td>\n",
       "      <td>0.921</td>\n",
       "      <td>0.056</td>\n",
       "      <td>0.051</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Age</td>\n",
       "      <td>Openness</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
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       "      <td>[-0.05, 0.12]</td>\n",
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       "      <td>0.076</td>\n",
       "      <td>0.121</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Age</td>\n",
       "      <td>Agreeableness</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
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       "      <td>[-0.13, 0.04]</td>\n",
       "      <td>0.313</td>\n",
       "      <td>0.093</td>\n",
       "      <td>0.172</td>\n",
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       "      <th>4</th>\n",
       "      <td>Age</td>\n",
       "      <td>Conscientiousness</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
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       "      <td>0.132</td>\n",
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       "      <td>0.114</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
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       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>-0.023</td>\n",
       "      <td>[-0.11, 0.06]</td>\n",
       "      <td>0.611</td>\n",
       "      <td>0.064</td>\n",
       "      <td>0.080</td>\n",
       "    </tr>\n",
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      ],
      "text/plain": [
       "     X                  Y   method alternative    n      r          CI95%  \\\n",
       "0  Age        Neuroticism  pearson   two-sided  500 -0.036  [-0.12, 0.05]   \n",
       "1  Age       Extraversion  pearson   two-sided  500 -0.004  [-0.09, 0.08]   \n",
       "2  Age           Openness  pearson   two-sided  500  0.035  [-0.05, 0.12]   \n",
       "3  Age      Agreeableness  pearson   two-sided  500 -0.045  [-0.13, 0.04]   \n",
       "4  Age  Conscientiousness  pearson   two-sided  500  0.059  [-0.03, 0.15]   \n",
       "5  Age                BMI  pearson   two-sided  500 -0.053  [-0.14, 0.03]   \n",
       "6  Age             Gender  pearson   two-sided  500 -0.023  [-0.11, 0.06]   \n",
       "\n",
       "   p-unc   BF10  power  \n",
       "0  0.418  0.078  0.128  \n",
       "1  0.921  0.056  0.051  \n",
       "2  0.438  0.076  0.121  \n",
       "3  0.313  0.093  0.172  \n",
       "4  0.191  0.132  0.258  \n",
       "5  0.233  0.114  0.222  \n",
       "6  0.611  0.064  0.080  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pg.pairwise_corr(df, columns='Age')  # Age versus all the other numeric columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Great! What about if I am interested in looking at `Age` and `Gender` on the one hand and the personality dimensions on the other hand? That's also very easy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "        X                  Y   method alternative    n      r          CI95%  \\\n",
       "0     Age        Neuroticism  pearson   two-sided  500 -0.036  [-0.12, 0.05]   \n",
       "1     Age       Extraversion  pearson   two-sided  500 -0.004  [-0.09, 0.08]   \n",
       "2     Age           Openness  pearson   two-sided  500  0.035  [-0.05, 0.12]   \n",
       "3     Age      Agreeableness  pearson   two-sided  500 -0.045  [-0.13, 0.04]   \n",
       "4     Age  Conscientiousness  pearson   two-sided  500  0.059  [-0.03, 0.15]   \n",
       "5  Gender        Neuroticism  pearson   two-sided  500  0.007  [-0.08, 0.09]   \n",
       "6  Gender       Extraversion  pearson   two-sided  500  0.011   [-0.08, 0.1]   \n",
       "7  Gender           Openness  pearson   two-sided  500 -0.046  [-0.13, 0.04]   \n",
       "8  Gender      Agreeableness  pearson   two-sided  500  0.020  [-0.07, 0.11]   \n",
       "9  Gender  Conscientiousness  pearson   two-sided  500  0.029  [-0.06, 0.12]   \n",
       "\n",
       "   p-unc   BF10  power  \n",
       "0  0.418  0.078  0.128  \n",
       "1  0.921  0.056  0.051  \n",
       "2  0.438  0.076  0.121  \n",
       "3  0.313  0.093  0.172  \n",
       "4  0.191  0.132  0.258  \n",
       "5  0.879  0.057  0.053  \n",
       "6  0.814  0.058  0.056  \n",
       "7  0.300  0.096  0.179  \n",
       "8  0.654  0.062  0.073  \n",
       "9  0.518  0.069  0.099  "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "subj = ['Age', 'Gender']\n",
    "personality = ['Neuroticism', 'Extraversion', 'Openness', 'Agreeableness', 'Conscientiousness']\n",
    "pg.pairwise_corr(df, columns=[subj, personality])  # Cartesian product between the first and second list"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Also great...but what if I don't want to have to write all the columns names, and let's say that I am just interested in looking at `Age` and `Gender` versus all the other columns in the dataframe?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
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       "      <td>0.099</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>Gender</td>\n",
       "      <td>BMI</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>0.071</td>\n",
       "      <td>[-0.02, 0.16]</td>\n",
       "      <td>0.111</td>\n",
       "      <td>0.199</td>\n",
       "      <td>0.358</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         X                  Y   method alternative    n      r          CI95%  \\\n",
       "0      Age        Neuroticism  pearson   two-sided  500 -0.036  [-0.12, 0.05]   \n",
       "1      Age       Extraversion  pearson   two-sided  500 -0.004  [-0.09, 0.08]   \n",
       "2      Age           Openness  pearson   two-sided  500  0.035  [-0.05, 0.12]   \n",
       "3      Age      Agreeableness  pearson   two-sided  500 -0.045  [-0.13, 0.04]   \n",
       "4      Age  Conscientiousness  pearson   two-sided  500  0.059  [-0.03, 0.15]   \n",
       "5      Age                BMI  pearson   two-sided  500 -0.053  [-0.14, 0.03]   \n",
       "6   Gender        Neuroticism  pearson   two-sided  500  0.007  [-0.08, 0.09]   \n",
       "7   Gender       Extraversion  pearson   two-sided  500  0.011   [-0.08, 0.1]   \n",
       "8   Gender           Openness  pearson   two-sided  500 -0.046  [-0.13, 0.04]   \n",
       "9   Gender      Agreeableness  pearson   two-sided  500  0.020  [-0.07, 0.11]   \n",
       "10  Gender  Conscientiousness  pearson   two-sided  500  0.029  [-0.06, 0.12]   \n",
       "11  Gender                BMI  pearson   two-sided  500  0.071  [-0.02, 0.16]   \n",
       "\n",
       "    p-unc   BF10  power  \n",
       "0   0.418  0.078  0.128  \n",
       "1   0.921  0.056  0.051  \n",
       "2   0.438  0.076  0.121  \n",
       "3   0.313  0.093  0.172  \n",
       "4   0.191  0.132  0.258  \n",
       "5   0.233  0.114  0.222  \n",
       "6   0.879  0.057  0.053  \n",
       "7   0.814  0.058  0.056  \n",
       "8   0.300  0.096  0.179  \n",
       "9   0.654  0.062  0.073  \n",
       "10  0.518  0.069  0.099  \n",
       "11  0.111  0.199  0.358  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pg.pairwise_corr(df, columns=[subj, None])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### MultiIndex columns\n",
    "\n",
    "The [pairwise_corr](https://pingouin-stats.org/generated/pingouin.pairwise_corr.html#pingouin.pairwise_corr) function also works with two-dimensional columns. To illustrate this, let's create a fake multi-level dataframe:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"2\" halign=\"left\">Behavior</th>\n",
       "      <th colspan=\"2\" halign=\"left\">Physio</th>\n",
       "      <th>Psycho</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>Rating</th>\n",
       "      <th>ReactionTime</th>\n",
       "      <th>PupilDilation</th>\n",
       "      <th>BPM</th>\n",
       "      <th>Sleepiness</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>66</td>\n",
       "      <td>273</td>\n",
       "      <td>-3</td>\n",
       "      <td>66</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>92</td>\n",
       "      <td>232</td>\n",
       "      <td>-1</td>\n",
       "      <td>75</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>98</td>\n",
       "      <td>424</td>\n",
       "      <td>3</td>\n",
       "      <td>72</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>17</td>\n",
       "      <td>311</td>\n",
       "      <td>-5</td>\n",
       "      <td>79</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>83</td>\n",
       "      <td>453</td>\n",
       "      <td>2</td>\n",
       "      <td>78</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>57</td>\n",
       "      <td>296</td>\n",
       "      <td>4</td>\n",
       "      <td>57</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>86</td>\n",
       "      <td>408</td>\n",
       "      <td>-2</td>\n",
       "      <td>85</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>97</td>\n",
       "      <td>268</td>\n",
       "      <td>-1</td>\n",
       "      <td>48</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>96</td>\n",
       "      <td>202</td>\n",
       "      <td>1</td>\n",
       "      <td>87</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>47</td>\n",
       "      <td>239</td>\n",
       "      <td>-4</td>\n",
       "      <td>50</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Behavior                     Physio         Psycho\n",
       "    Rating ReactionTime PupilDilation BPM Sleepiness\n",
       "0       66          273            -3  66          1\n",
       "1       92          232            -1  75          4\n",
       "2       98          424             3  72          3\n",
       "3       17          311            -5  79          3\n",
       "4       83          453             2  78          3\n",
       "5       57          296             4  57          6\n",
       "6       86          408            -2  85          3\n",
       "7       97          268            -1  48          5\n",
       "8       96          202             1  87          4\n",
       "9       47          239            -4  50          4"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from numpy.random import randint as rdint\n",
    "np.random.seed(123)\n",
    "\n",
    "# Create MultiIndex dataframe\n",
    "columns = pd.MultiIndex.from_tuples([('Behavior', 'Rating'),\n",
    "                                     ('Behavior', 'ReactionTime'),\n",
    "                                     ('Physio', 'PupilDilation'),\n",
    "                                     ('Physio', 'BPM'),\n",
    "                                     ('Psycho', 'Sleepiness')])\n",
    "\n",
    "data = pd.DataFrame(dict(Rating=rdint(0, 100, size=10),\n",
    "                         RT=rdint(200, 500, size=10),\n",
    "                         PupilDilation=rdint(-5, 5, size=10),\n",
    "                         HR=rdint(45, 90, size=10),\n",
    "                         Sleepiness=rdint(1, 7, size=10)))\n",
    "\n",
    "data.columns = columns\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To compute the correlation on the combination of all the columns, one can simply use:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>Y</th>\n",
       "      <th>method</th>\n",
       "      <th>alternative</th>\n",
       "      <th>n</th>\n",
       "      <th>r</th>\n",
       "      <th>CI95%</th>\n",
       "      <th>p-unc</th>\n",
       "      <th>BF10</th>\n",
       "      <th>power</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>(Behavior, Rating)</td>\n",
       "      <td>(Behavior, ReactionTime)</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>10</td>\n",
       "      <td>0.135</td>\n",
       "      <td>[-0.54, 0.7]</td>\n",
       "      <td>0.711</td>\n",
       "      <td>0.411</td>\n",
       "      <td>0.065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>(Behavior, Rating)</td>\n",
       "      <td>(Physio, PupilDilation)</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>10</td>\n",
       "      <td>0.542</td>\n",
       "      <td>[-0.13, 0.87]</td>\n",
       "      <td>0.106</td>\n",
       "      <td>1.234</td>\n",
       "      <td>0.388</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>(Behavior, Rating)</td>\n",
       "      <td>(Physio, BPM)</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>10</td>\n",
       "      <td>0.160</td>\n",
       "      <td>[-0.52, 0.72]</td>\n",
       "      <td>0.660</td>\n",
       "      <td>0.422</td>\n",
       "      <td>0.072</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>(Behavior, Rating)</td>\n",
       "      <td>(Psycho, Sleepiness)</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>10</td>\n",
       "      <td>0.076</td>\n",
       "      <td>[-0.58, 0.67]</td>\n",
       "      <td>0.836</td>\n",
       "      <td>0.394</td>\n",
       "      <td>0.054</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>(Behavior, ReactionTime)</td>\n",
       "      <td>(Physio, PupilDilation)</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>10</td>\n",
       "      <td>0.327</td>\n",
       "      <td>[-0.38, 0.79]</td>\n",
       "      <td>0.356</td>\n",
       "      <td>0.566</td>\n",
       "      <td>0.155</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>(Behavior, ReactionTime)</td>\n",
       "      <td>(Physio, BPM)</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>10</td>\n",
       "      <td>0.300</td>\n",
       "      <td>[-0.41, 0.78]</td>\n",
       "      <td>0.401</td>\n",
       "      <td>0.53</td>\n",
       "      <td>0.136</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>(Behavior, ReactionTime)</td>\n",
       "      <td>(Psycho, Sleepiness)</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>10</td>\n",
       "      <td>-0.294</td>\n",
       "      <td>[-0.78, 0.41]</td>\n",
       "      <td>0.410</td>\n",
       "      <td>0.524</td>\n",
       "      <td>0.132</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>(Physio, PupilDilation)</td>\n",
       "      <td>(Physio, BPM)</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>10</td>\n",
       "      <td>0.050</td>\n",
       "      <td>[-0.6, 0.66]</td>\n",
       "      <td>0.890</td>\n",
       "      <td>0.39</td>\n",
       "      <td>0.051</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>(Physio, PupilDilation)</td>\n",
       "      <td>(Psycho, Sleepiness)</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>10</td>\n",
       "      <td>0.424</td>\n",
       "      <td>[-0.28, 0.83]</td>\n",
       "      <td>0.222</td>\n",
       "      <td>0.753</td>\n",
       "      <td>0.240</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>(Physio, BPM)</td>\n",
       "      <td>(Psycho, Sleepiness)</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>10</td>\n",
       "      <td>-0.420</td>\n",
       "      <td>[-0.83, 0.29]</td>\n",
       "      <td>0.227</td>\n",
       "      <td>0.741</td>\n",
       "      <td>0.235</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                          X                         Y   method alternative  \\\n",
       "0        (Behavior, Rating)  (Behavior, ReactionTime)  pearson   two-sided   \n",
       "1        (Behavior, Rating)   (Physio, PupilDilation)  pearson   two-sided   \n",
       "2        (Behavior, Rating)             (Physio, BPM)  pearson   two-sided   \n",
       "3        (Behavior, Rating)      (Psycho, Sleepiness)  pearson   two-sided   \n",
       "4  (Behavior, ReactionTime)   (Physio, PupilDilation)  pearson   two-sided   \n",
       "5  (Behavior, ReactionTime)             (Physio, BPM)  pearson   two-sided   \n",
       "6  (Behavior, ReactionTime)      (Psycho, Sleepiness)  pearson   two-sided   \n",
       "7   (Physio, PupilDilation)             (Physio, BPM)  pearson   two-sided   \n",
       "8   (Physio, PupilDilation)      (Psycho, Sleepiness)  pearson   two-sided   \n",
       "9             (Physio, BPM)      (Psycho, Sleepiness)  pearson   two-sided   \n",
       "\n",
       "    n      r          CI95%  p-unc   BF10  power  \n",
       "0  10  0.135   [-0.54, 0.7]  0.711  0.411  0.065  \n",
       "1  10  0.542  [-0.13, 0.87]  0.106  1.234  0.388  \n",
       "2  10  0.160  [-0.52, 0.72]  0.660  0.422  0.072  \n",
       "3  10  0.076  [-0.58, 0.67]  0.836  0.394  0.054  \n",
       "4  10  0.327  [-0.38, 0.79]  0.356  0.566  0.155  \n",
       "5  10  0.300  [-0.41, 0.78]  0.401   0.53  0.136  \n",
       "6  10 -0.294  [-0.78, 0.41]  0.410  0.524  0.132  \n",
       "7  10  0.050   [-0.6, 0.66]  0.890   0.39  0.051  \n",
       "8  10  0.424  [-0.28, 0.83]  0.222  0.753  0.240  \n",
       "9  10 -0.420  [-0.83, 0.29]  0.227  0.741  0.235  "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pg.pairwise_corr(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All the previously-mentionned advanced column selection tricks work just as fine here. For example, to compute the one versus all:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>Y</th>\n",
       "      <th>method</th>\n",
       "      <th>alternative</th>\n",
       "      <th>n</th>\n",
       "      <th>r</th>\n",
       "      <th>CI95%</th>\n",
       "      <th>p-unc</th>\n",
       "      <th>BF10</th>\n",
       "      <th>power</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>(Behavior, Rating)</td>\n",
       "      <td>(Behavior, ReactionTime)</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>10</td>\n",
       "      <td>0.135</td>\n",
       "      <td>[-0.54, 0.7]</td>\n",
       "      <td>0.711</td>\n",
       "      <td>0.411</td>\n",
       "      <td>0.065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>(Behavior, Rating)</td>\n",
       "      <td>(Physio, PupilDilation)</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>10</td>\n",
       "      <td>0.542</td>\n",
       "      <td>[-0.13, 0.87]</td>\n",
       "      <td>0.106</td>\n",
       "      <td>1.234</td>\n",
       "      <td>0.388</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>(Behavior, Rating)</td>\n",
       "      <td>(Physio, BPM)</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>10</td>\n",
       "      <td>0.160</td>\n",
       "      <td>[-0.52, 0.72]</td>\n",
       "      <td>0.660</td>\n",
       "      <td>0.422</td>\n",
       "      <td>0.072</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>(Behavior, Rating)</td>\n",
       "      <td>(Psycho, Sleepiness)</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>10</td>\n",
       "      <td>0.076</td>\n",
       "      <td>[-0.58, 0.67]</td>\n",
       "      <td>0.836</td>\n",
       "      <td>0.394</td>\n",
       "      <td>0.054</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    X                         Y   method alternative   n  \\\n",
       "0  (Behavior, Rating)  (Behavior, ReactionTime)  pearson   two-sided  10   \n",
       "1  (Behavior, Rating)   (Physio, PupilDilation)  pearson   two-sided  10   \n",
       "2  (Behavior, Rating)             (Physio, BPM)  pearson   two-sided  10   \n",
       "3  (Behavior, Rating)      (Psycho, Sleepiness)  pearson   two-sided  10   \n",
       "\n",
       "       r          CI95%  p-unc   BF10  power  \n",
       "0  0.135   [-0.54, 0.7]  0.711  0.411  0.065  \n",
       "1  0.542  [-0.13, 0.87]  0.106  1.234  0.388  \n",
       "2  0.160  [-0.52, 0.72]  0.660  0.422  0.072  \n",
       "3  0.076  [-0.58, 0.67]  0.836  0.394  0.054  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pg.pairwise_corr(data, columns=('Behavior', 'Rating'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or between multiple columns:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
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       "      <th>0</th>\n",
       "      <td>(Behavior, ReactionTime)</td>\n",
       "      <td>(Psycho, Sleepiness)</td>\n",
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       "                          X                     Y   method alternative   n  \\\n",
       "0  (Behavior, ReactionTime)  (Psycho, Sleepiness)  pearson   two-sided  10   \n",
       "\n",
       "       r          CI95%  p-unc   BF10  power  \n",
       "0 -0.294  [-0.78, 0.41]   0.41  0.524  0.132  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pg.pairwise_corr(data, columns=[('Behavior', 'ReactionTime'), ('Psycho', 'Sleepiness')])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
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       "      <td>0.388</td>\n",
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       "      <th>1</th>\n",
       "      <td>(Behavior, Rating)</td>\n",
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       "      <td>0.660</td>\n",
       "      <td>0.422</td>\n",
       "      <td>0.072</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>(Behavior, Rating)</td>\n",
       "      <td>(Psycho, Sleepiness)</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>10</td>\n",
       "      <td>0.076</td>\n",
       "      <td>[-0.58, 0.67]</td>\n",
       "      <td>0.836</td>\n",
       "      <td>0.394</td>\n",
       "      <td>0.054</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>(Behavior, ReactionTime)</td>\n",
       "      <td>(Physio, PupilDilation)</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>10</td>\n",
       "      <td>0.327</td>\n",
       "      <td>[-0.38, 0.79]</td>\n",
       "      <td>0.356</td>\n",
       "      <td>0.566</td>\n",
       "      <td>0.155</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>(Behavior, ReactionTime)</td>\n",
       "      <td>(Physio, BPM)</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>10</td>\n",
       "      <td>0.300</td>\n",
       "      <td>[-0.41, 0.78]</td>\n",
       "      <td>0.401</td>\n",
       "      <td>0.53</td>\n",
       "      <td>0.136</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>(Behavior, ReactionTime)</td>\n",
       "      <td>(Psycho, Sleepiness)</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>10</td>\n",
       "      <td>-0.294</td>\n",
       "      <td>[-0.78, 0.41]</td>\n",
       "      <td>0.410</td>\n",
       "      <td>0.524</td>\n",
       "      <td>0.132</td>\n",
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       "  </tbody>\n",
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       "</div>"
      ],
      "text/plain": [
       "                          X                        Y   method alternative   n  \\\n",
       "0        (Behavior, Rating)  (Physio, PupilDilation)  pearson   two-sided  10   \n",
       "1        (Behavior, Rating)            (Physio, BPM)  pearson   two-sided  10   \n",
       "2        (Behavior, Rating)     (Psycho, Sleepiness)  pearson   two-sided  10   \n",
       "3  (Behavior, ReactionTime)  (Physio, PupilDilation)  pearson   two-sided  10   \n",
       "4  (Behavior, ReactionTime)            (Physio, BPM)  pearson   two-sided  10   \n",
       "5  (Behavior, ReactionTime)     (Psycho, Sleepiness)  pearson   two-sided  10   \n",
       "\n",
       "       r          CI95%  p-unc   BF10  power  \n",
       "0  0.542  [-0.13, 0.87]  0.106  1.234  0.388  \n",
       "1  0.160  [-0.52, 0.72]  0.660  0.422  0.072  \n",
       "2  0.076  [-0.58, 0.67]  0.836  0.394  0.054  \n",
       "3  0.327  [-0.38, 0.79]  0.356  0.566  0.155  \n",
       "4  0.300  [-0.41, 0.78]  0.401   0.53  0.136  \n",
       "5 -0.294  [-0.78, 0.41]  0.410  0.524  0.132  "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pg.pairwise_corr(data, columns=[[('Behavior', 'Rating'), ('Behavior', 'ReactionTime')], None])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And finally between levels, using the [pandas.xs](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.xs.html) function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "All columns in level \"Behavior\" [('Behavior', 'Rating'), ('Behavior', 'ReactionTime')]\n",
      "All columns in level \"Physio\" [('Physio', 'PupilDilation'), ('Physio', 'BPM')]\n"
     ]
    },
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       "      <th>3</th>\n",
       "      <td>(Behavior, ReactionTime)</td>\n",
       "      <td>(Physio, BPM)</td>\n",
       "      <td>pearson</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>10</td>\n",
       "      <td>0.300</td>\n",
       "      <td>[-0.41, 0.78]</td>\n",
       "      <td>0.401</td>\n",
       "      <td>0.53</td>\n",
       "      <td>0.136</td>\n",
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      "text/plain": [
       "                          X                        Y   method alternative   n  \\\n",
       "0        (Behavior, Rating)  (Physio, PupilDilation)  pearson   two-sided  10   \n",
       "1        (Behavior, Rating)            (Physio, BPM)  pearson   two-sided  10   \n",
       "2  (Behavior, ReactionTime)  (Physio, PupilDilation)  pearson   two-sided  10   \n",
       "3  (Behavior, ReactionTime)            (Physio, BPM)  pearson   two-sided  10   \n",
       "\n",
       "       r          CI95%  p-unc   BF10  power  \n",
       "0  0.542  [-0.13, 0.87]  0.106  1.234  0.388  \n",
       "1  0.160  [-0.52, 0.72]  0.660  0.422  0.072  \n",
       "2  0.327  [-0.38, 0.79]  0.356  0.566  0.155  \n",
       "3  0.300  [-0.41, 0.78]  0.401   0.53  0.136  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "col_behavior = data.xs('Behavior', axis=1, level=0, drop_level=False).columns.to_list()\n",
    "col_physio = data.xs('Physio', axis=1, level=0, drop_level=False).columns.to_list()\n",
    "\n",
    "print('All columns in level \"Behavior\"', col_behavior)\n",
    "print('All columns in level \"Physio\"', col_physio)\n",
    "\n",
    "# pairwise_corr(data, columns=col_behavior + col_physio)  # All possible correlations\n",
    "pg.pairwise_corr(data, columns=[col_behavior, col_physio])   # Between-list correlations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "## Partial correlation\n",
    "\n",
    "In some cases, you will want to measure the correlation between two variables whilst controlling for the potential influence of other variables (also known as covariates). This can be done easily using the [partial_corr](https://pingouin-stats.org/generated/pingouin.partial_corr.html#pingouin.partial_corr) function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      <th></th>\n",
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       "      <th>r</th>\n",
       "      <th>CI95%</th>\n",
       "      <th>p-val</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>pearson</th>\n",
       "      <td>500</td>\n",
       "      <td>0.267</td>\n",
       "      <td>[0.18, 0.35]</td>\n",
       "      <td>1.277e-09</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           n      r         CI95%      p-val\n",
       "pearson  500  0.267  [0.18, 0.35]  1.277e-09"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Correlation between extraversion and openess whilst controlling for age:\n",
    "# Pandas-style: df.partial_corr(x='Extraversion', y='Openness', covar='Age')\n",
    "pg.partial_corr(data=df, x='Extraversion', y='Openness', covar='Age', method='pearson')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>n</th>\n",
       "      <th>r</th>\n",
       "      <th>CI95%</th>\n",
       "      <th>p-val</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>pearson</th>\n",
       "      <td>500</td>\n",
       "      <td>0.266</td>\n",
       "      <td>[0.18, 0.35]</td>\n",
       "      <td>1.652e-09</td>\n",
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      ],
      "text/plain": [
       "           n      r         CI95%      p-val\n",
       "pearson  500  0.266  [0.18, 0.35]  1.652e-09"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Correlation between extraversion and openess whilst controlling for age and BMI:\n",
    "pg.partial_corr(data=df, x='Extraversion', y='Openness', covar=['Age', 'BMI'], method='pearson')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cherry on the cake, the [pairwise_corr](https://pingouin-stats.org/generated/pingouin.pairwise_corr.html#pingouin.pairwise_corr) function also supports partial correlation with the `covar` argument!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>Y</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Neuroticism</td>\n",
       "      <td>Extraversion</td>\n",
       "      <td>spearman</td>\n",
       "      <td>['Age', 'Gender', 'BMI']</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>-0.329</td>\n",
       "      <td>[-0.41, -0.25]</td>\n",
       "      <td>5.247e-14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Neuroticism</td>\n",
       "      <td>Openness</td>\n",
       "      <td>spearman</td>\n",
       "      <td>['Age', 'Gender', 'BMI']</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>-0.016</td>\n",
       "      <td>[-0.1, 0.07]</td>\n",
       "      <td>7.287e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Neuroticism</td>\n",
       "      <td>Agreeableness</td>\n",
       "      <td>spearman</td>\n",
       "      <td>['Age', 'Gender', 'BMI']</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>-0.135</td>\n",
       "      <td>[-0.22, -0.05]</td>\n",
       "      <td>2.495e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Neuroticism</td>\n",
       "      <td>Conscientiousness</td>\n",
       "      <td>spearman</td>\n",
       "      <td>['Age', 'Gender', 'BMI']</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>-0.365</td>\n",
       "      <td>[-0.44, -0.29]</td>\n",
       "      <td>4.280e-17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Extraversion</td>\n",
       "      <td>Openness</td>\n",
       "      <td>spearman</td>\n",
       "      <td>['Age', 'Gender', 'BMI']</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>0.241</td>\n",
       "      <td>[0.16, 0.32]</td>\n",
       "      <td>5.700e-08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Extraversion</td>\n",
       "      <td>Agreeableness</td>\n",
       "      <td>spearman</td>\n",
       "      <td>['Age', 'Gender', 'BMI']</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>0.063</td>\n",
       "      <td>[-0.02, 0.15]</td>\n",
       "      <td>1.591e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Extraversion</td>\n",
       "      <td>Conscientiousness</td>\n",
       "      <td>spearman</td>\n",
       "      <td>['Age', 'Gender', 'BMI']</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>0.058</td>\n",
       "      <td>[-0.03, 0.14]</td>\n",
       "      <td>2.001e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Openness</td>\n",
       "      <td>Agreeableness</td>\n",
       "      <td>spearman</td>\n",
       "      <td>['Age', 'Gender', 'BMI']</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>0.174</td>\n",
       "      <td>[0.09, 0.26]</td>\n",
       "      <td>9.949e-05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Openness</td>\n",
       "      <td>Conscientiousness</td>\n",
       "      <td>spearman</td>\n",
       "      <td>['Age', 'Gender', 'BMI']</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>-0.006</td>\n",
       "      <td>[-0.09, 0.08]</td>\n",
       "      <td>8.999e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Agreeableness</td>\n",
       "      <td>Conscientiousness</td>\n",
       "      <td>spearman</td>\n",
       "      <td>['Age', 'Gender', 'BMI']</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>500</td>\n",
       "      <td>0.163</td>\n",
       "      <td>[0.08, 0.25]</td>\n",
       "      <td>2.718e-04</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               X                  Y    method                     covar  \\\n",
       "0    Neuroticism       Extraversion  spearman  ['Age', 'Gender', 'BMI']   \n",
       "1    Neuroticism           Openness  spearman  ['Age', 'Gender', 'BMI']   \n",
       "2    Neuroticism      Agreeableness  spearman  ['Age', 'Gender', 'BMI']   \n",
       "3    Neuroticism  Conscientiousness  spearman  ['Age', 'Gender', 'BMI']   \n",
       "4   Extraversion           Openness  spearman  ['Age', 'Gender', 'BMI']   \n",
       "5   Extraversion      Agreeableness  spearman  ['Age', 'Gender', 'BMI']   \n",
       "6   Extraversion  Conscientiousness  spearman  ['Age', 'Gender', 'BMI']   \n",
       "7       Openness      Agreeableness  spearman  ['Age', 'Gender', 'BMI']   \n",
       "8       Openness  Conscientiousness  spearman  ['Age', 'Gender', 'BMI']   \n",
       "9  Agreeableness  Conscientiousness  spearman  ['Age', 'Gender', 'BMI']   \n",
       "\n",
       "  alternative    n      r           CI95%      p-unc  \n",
       "0   two-sided  500 -0.329  [-0.41, -0.25]  5.247e-14  \n",
       "1   two-sided  500 -0.016    [-0.1, 0.07]  7.287e-01  \n",
       "2   two-sided  500 -0.135  [-0.22, -0.05]  2.495e-03  \n",
       "3   two-sided  500 -0.365  [-0.44, -0.29]  4.280e-17  \n",
       "4   two-sided  500  0.241    [0.16, 0.32]  5.700e-08  \n",
       "5   two-sided  500  0.063   [-0.02, 0.15]  1.591e-01  \n",
       "6   two-sided  500  0.058   [-0.03, 0.14]  2.001e-01  \n",
       "7   two-sided  500  0.174    [0.09, 0.26]  9.949e-05  \n",
       "8   two-sided  500 -0.006   [-0.09, 0.08]  8.999e-01  \n",
       "9   two-sided  500  0.163    [0.08, 0.25]  2.718e-04  "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Pandas-style: df.pairwise_corr(covar=['Age', 'Gender', 'BMI'], method='spearman')\n",
    "pg.pairwise_corr(data=df, covar=['Age', 'Gender', 'BMI'], method='spearman')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you are only interested in the partial correlation matrix (and not the p-values, CI..), an alternative is to use the [pandas.DataFrame.pcorr()](https://pingouin-stats.org/generated/pingouin.pcorr.html#pingouin.pcorr) method that is implemented in Pingouin. This returns the pairwise correlation matrix between two variables while controlling for all the other variables:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Neuroticism</th>\n",
       "      <th>Extraversion</th>\n",
       "      <th>Openness</th>\n",
       "      <th>Agreeableness</th>\n",
       "      <th>Conscientiousness</th>\n",
       "      <th>Age</th>\n",
       "      <th>BMI</th>\n",
       "      <th>Gender</th>\n",
       "      <th>Ethnicity</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.479</td>\n",
       "      <td>4.208</td>\n",
       "      <td>3.938</td>\n",
       "      <td>3.958</td>\n",
       "      <td>3.458</td>\n",
       "      <td>63</td>\n",
       "      <td>28</td>\n",
       "      <td>1</td>\n",
       "      <td>Caucasian</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.604</td>\n",
       "      <td>3.188</td>\n",
       "      <td>3.958</td>\n",
       "      <td>3.396</td>\n",
       "      <td>3.229</td>\n",
       "      <td>20</td>\n",
       "      <td>36</td>\n",
       "      <td>0</td>\n",
       "      <td>Caucasian</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.812</td>\n",
       "      <td>2.896</td>\n",
       "      <td>3.417</td>\n",
       "      <td>2.750</td>\n",
       "      <td>3.500</td>\n",
       "      <td>46</td>\n",
       "      <td>25</td>\n",
       "      <td>0</td>\n",
       "      <td>Caucasian</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.896</td>\n",
       "      <td>3.562</td>\n",
       "      <td>3.521</td>\n",
       "      <td>3.167</td>\n",
       "      <td>2.792</td>\n",
       "      <td>52</td>\n",
       "      <td>27</td>\n",
       "      <td>0</td>\n",
       "      <td>Caucasian</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.021</td>\n",
       "      <td>3.333</td>\n",
       "      <td>4.021</td>\n",
       "      <td>3.208</td>\n",
       "      <td>2.854</td>\n",
       "      <td>56</td>\n",
       "      <td>33</td>\n",
       "      <td>0</td>\n",
       "      <td>Caucasian</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>495</th>\n",
       "      <td>3.062</td>\n",
       "      <td>3.438</td>\n",
       "      <td>3.329</td>\n",
       "      <td>3.042</td>\n",
       "      <td>3.125</td>\n",
       "      <td>53</td>\n",
       "      <td>25</td>\n",
       "      <td>1</td>\n",
       "      <td>Caucasian</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>496</th>\n",
       "      <td>3.083</td>\n",
       "      <td>3.396</td>\n",
       "      <td>4.000</td>\n",
       "      <td>3.229</td>\n",
       "      <td>3.104</td>\n",
       "      <td>57</td>\n",
       "      <td>38</td>\n",
       "      <td>0</td>\n",
       "      <td>Caucasian</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>497</th>\n",
       "      <td>3.521</td>\n",
       "      <td>2.417</td>\n",
       "      <td>3.062</td>\n",
       "      <td>3.562</td>\n",
       "      <td>3.000</td>\n",
       "      <td>44</td>\n",
       "      <td>43</td>\n",
       "      <td>0</td>\n",
       "      <td>Caucasian</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>498</th>\n",
       "      <td>2.083</td>\n",
       "      <td>3.667</td>\n",
       "      <td>3.583</td>\n",
       "      <td>3.458</td>\n",
       "      <td>3.396</td>\n",
       "      <td>59</td>\n",
       "      <td>19</td>\n",
       "      <td>0</td>\n",
       "      <td>Caucasian</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>499</th>\n",
       "      <td>2.542</td>\n",
       "      <td>3.562</td>\n",
       "      <td>3.146</td>\n",
       "      <td>3.458</td>\n",
       "      <td>2.896</td>\n",
       "      <td>45</td>\n",
       "      <td>25</td>\n",
       "      <td>0</td>\n",
       "      <td>Caucasian</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>500 rows × 9 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     Neuroticism  Extraversion  Openness  Agreeableness  Conscientiousness  \\\n",
       "0          2.479         4.208     3.938          3.958              3.458   \n",
       "1          2.604         3.188     3.958          3.396              3.229   \n",
       "2          2.812         2.896     3.417          2.750              3.500   \n",
       "3          2.896         3.562     3.521          3.167              2.792   \n",
       "4          3.021         3.333     4.021          3.208              2.854   \n",
       "..           ...           ...       ...            ...                ...   \n",
       "495        3.062         3.438     3.329          3.042              3.125   \n",
       "496        3.083         3.396     4.000          3.229              3.104   \n",
       "497        3.521         2.417     3.062          3.562              3.000   \n",
       "498        2.083         3.667     3.583          3.458              3.396   \n",
       "499        2.542         3.562     3.146          3.458              2.896   \n",
       "\n",
       "     Age  BMI  Gender  Ethnicity  \n",
       "0     63   28       1  Caucasian  \n",
       "1     20   36       0  Caucasian  \n",
       "2     46   25       0  Caucasian  \n",
       "3     52   27       0  Caucasian  \n",
       "4     56   33       0  Caucasian  \n",
       "..   ...  ...     ...        ...  \n",
       "495   53   25       1  Caucasian  \n",
       "496   57   38       0  Caucasian  \n",
       "497   44   43       0  Caucasian  \n",
       "498   59   19       0  Caucasian  \n",
       "499   45   25       0  Caucasian  \n",
       "\n",
       "[500 rows x 9 columns]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Neuroticism</th>\n",
       "      <th>Extraversion</th>\n",
       "      <th>Openness</th>\n",
       "      <th>Agreeableness</th>\n",
       "      <th>Conscientiousness</th>\n",
       "      <th>Age</th>\n",
       "      <th>BMI</th>\n",
       "      <th>Gender</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Neuroticism</th>\n",
       "      <td>1.000</td>\n",
       "      <td>-0.140</td>\n",
       "      <td>0.074</td>\n",
       "      <td>0.057</td>\n",
       "      <td>-0.169</td>\n",
       "      <td>-0.026</td>\n",
       "      <td>0.016</td>\n",
       "      <td>0.014</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Extraversion</th>\n",
       "      <td>-0.140</td>\n",
       "      <td>1.000</td>\n",
       "      <td>0.272</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.046</td>\n",
       "      <td>-0.023</td>\n",
       "      <td>-0.018</td>\n",
       "      <td>0.025</td>\n",
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       "    <tr>\n",
       "      <th>Openness</th>\n",
       "      <td>0.074</td>\n",
       "      <td>0.272</td>\n",
       "      <td>1.000</td>\n",
       "      <td>0.156</td>\n",
       "      <td>-0.043</td>\n",
       "      <td>0.046</td>\n",
       "      <td>-0.056</td>\n",
       "      <td>-0.049</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Agreeableness</th>\n",
       "      <td>0.057</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.156</td>\n",
       "      <td>1.000</td>\n",
       "      <td>0.172</td>\n",
       "      <td>-0.060</td>\n",
       "      <td>-0.001</td>\n",
       "      <td>0.021</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Conscientiousness</th>\n",
       "      <td>-0.169</td>\n",
       "      <td>0.046</td>\n",
       "      <td>-0.043</td>\n",
       "      <td>0.172</td>\n",
       "      <td>1.000</td>\n",
       "      <td>0.067</td>\n",
       "      <td>0.043</td>\n",
       "      <td>0.023</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Age</th>\n",
       "      <td>-0.026</td>\n",
       "      <td>-0.023</td>\n",
       "      <td>0.046</td>\n",
       "      <td>-0.060</td>\n",
       "      <td>0.067</td>\n",
       "      <td>1.000</td>\n",
       "      <td>-0.052</td>\n",
       "      <td>-0.017</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BMI</th>\n",
       "      <td>0.016</td>\n",
       "      <td>-0.018</td>\n",
       "      <td>-0.056</td>\n",
       "      <td>-0.001</td>\n",
       "      <td>0.043</td>\n",
       "      <td>-0.052</td>\n",
       "      <td>1.000</td>\n",
       "      <td>0.067</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Gender</th>\n",
       "      <td>0.014</td>\n",
       "      <td>0.025</td>\n",
       "      <td>-0.049</td>\n",
       "      <td>0.021</td>\n",
       "      <td>0.023</td>\n",
       "      <td>-0.017</td>\n",
       "      <td>0.067</td>\n",
       "      <td>1.000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   Neuroticism  Extraversion  Openness  Agreeableness  \\\n",
       "Neuroticism              1.000        -0.140     0.074          0.057   \n",
       "Extraversion            -0.140         1.000     0.272          0.007   \n",
       "Openness                 0.074         0.272     1.000          0.156   \n",
       "Agreeableness            0.057         0.007     0.156          1.000   \n",
       "Conscientiousness       -0.169         0.046    -0.043          0.172   \n",
       "Age                     -0.026        -0.023     0.046         -0.060   \n",
       "BMI                      0.016        -0.018    -0.056         -0.001   \n",
       "Gender                   0.014         0.025    -0.049          0.021   \n",
       "\n",
       "                   Conscientiousness    Age    BMI  Gender  \n",
       "Neuroticism                   -0.169 -0.026  0.016   0.014  \n",
       "Extraversion                   0.046 -0.023 -0.018   0.025  \n",
       "Openness                      -0.043  0.046 -0.056  -0.049  \n",
       "Agreeableness                  0.172 -0.060 -0.001   0.021  \n",
       "Conscientiousness              1.000  0.067  0.043   0.023  \n",
       "Age                            0.067  1.000 -0.052  -0.017  \n",
       "BMI                            0.043 -0.052  1.000   0.067  \n",
       "Gender                         0.023 -0.017  0.067   1.000  "
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.pcorr().round(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Semi-partial correlation\n",
    "\n",
    "With partial correlation, we find the correlation between $x$ and $y$ holding $C$ constant for both $x$ and $y$. Sometimes, however, we want to hold $C$ constant for just $x$ or just $y$. In that case, we compute a semi-partial correlation. While a partial correlation is computed between two residuals, a semi-partial correlation is computed between one residual and another raw (or unresidualized) variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
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       "      <th>p-val</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>pearson</th>\n",
       "      <td>500</td>\n",
       "      <td>0.267</td>\n",
       "      <td>[0.18, 0.35]</td>\n",
       "      <td>1.307e-09</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           n      r         CI95%      p-val\n",
       "pearson  500  0.267  [0.18, 0.35]  1.307e-09"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Correlation between extraversion and openess whilst controlling \n",
    "# Extraversion for age:\n",
    "df.partial_corr(x='Extraversion', y='Openness', x_covar='Age')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "## Correlation matrix\n",
    "\n",
    "If you have a lot of variables, it can be difficult to read the output of the [pairwise_corr](https://pingouin-stats.org/generated/pingouin.pairwise_corr.html#pingouin.pairwise_corr) function. An alternative is to use the [rcorr](https://pingouin-stats.org/generated/pingouin.rcorr.html#pingouin.rcorr) function, which works directly as a Pandas DataFrame method, to obtain a correlation matrix with the r-values on the lower triangle and the p-values on the upper triangle."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/raphael/GitHub/pingouin/pingouin/correlation.py:1116: FutureWarning: DataFrame.applymap has been deprecated. Use DataFrame.map instead.\n",
      "  mat_upper = mat_upper.applymap(replace_pval)\n"
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       "      <th>Neuroticism</th>\n",
       "      <th>Extraversion</th>\n",
       "      <th>Openness</th>\n",
       "      <th>Agreeableness</th>\n",
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       "      <td>-</td>\n",
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       "      <td></td>\n",
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       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Extraversion</th>\n",
       "      <td>-0.131</td>\n",
       "      <td>-</td>\n",
       "      <td>***</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
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       "      <th>Age</th>\n",
       "      <td>-0.036</td>\n",
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       "      <td>0.035</td>\n",
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       "      <td>0.011</td>\n",
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       "      <td>-0.069</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>0.039</td>\n",
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       "      <th>Gender</th>\n",
       "      <td>0.007</td>\n",
       "      <td>0.011</td>\n",
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       "      <td>0.02</td>\n",
       "      <td>0.029</td>\n",
       "      <td>-0.023</td>\n",
       "      <td>0.071</td>\n",
       "      <td>-</td>\n",
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       "                  Neuroticism Extraversion Openness Agreeableness  \\\n",
       "Neuroticism                 -           **                          \n",
       "Extraversion           -0.131            -      ***                 \n",
       "Openness                0.046        0.267        -           ***   \n",
       "Agreeableness           0.036        0.055    0.159             -   \n",
       "Conscientiousness      -0.171        0.065   -0.013         0.159   \n",
       "Age                    -0.036       -0.004    0.035        -0.045   \n",
       "BMI                     0.011       -0.033   -0.069          -0.0   \n",
       "Gender                  0.007        0.011   -0.046          0.02   \n",
       "\n",
       "                  Conscientiousness     Age    BMI Gender  \n",
       "Neuroticism                     ***                        \n",
       "Extraversion                                               \n",
       "Openness                                                   \n",
       "Agreeableness                   ***                        \n",
       "Conscientiousness                 -                        \n",
       "Age                           0.059       -                \n",
       "BMI                           0.039  -0.053      -         \n",
       "Gender                        0.029  -0.023  0.071      -  "
      ]
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     "execution_count": 26,
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   "source": [
    "df.rcorr()"
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   "cell_type": "code",
   "execution_count": 27,
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    {
     "name": "stderr",
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     "text": [
      "/Users/raphael/GitHub/pingouin/pingouin/correlation.py:1116: FutureWarning: DataFrame.applymap has been deprecated. Use DataFrame.map instead.\n",
      "  mat_upper = mat_upper.applymap(replace_pval)\n"
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       "      <td>0.021</td>\n",
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       "      <td>0.016</td>\n",
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       "      <td>0.072</td>\n",
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       "                  Neuroticism Extraversion Openness Agreeableness  \\\n",
       "Neuroticism                 -          ***                          \n",
       "Extraversion            -0.33            -      ***                 \n",
       "Openness                -0.02        0.243        -            **   \n",
       "Agreeableness          -0.132        0.062     0.17             -   \n",
       "Conscientiousness      -0.365        0.056   -0.007         0.161   \n",
       "Age                    -0.045        0.003    0.032        -0.048   \n",
       "BMI                     0.031       -0.054    -0.07         0.017   \n",
       "Gender                  0.021       -0.014   -0.043         0.017   \n",
       "\n",
       "                  Conscientiousness     Age    BMI Gender  \n",
       "Neuroticism                     ***                        \n",
       "Extraversion                                               \n",
       "Openness                                                   \n",
       "Agreeableness                    **                        \n",
       "Conscientiousness                 -                        \n",
       "Age                           0.044       -                \n",
       "BMI                           0.027  -0.053      -         \n",
       "Gender                        0.016  -0.025  0.072      -  "
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     "execution_count": 27,
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   "source": [
    "# Using Spearman correlation and adjusting the p-values for multiple comparisons\n",
    "df.rcorr(method='spearman', padjust='holm')"
   ]
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  {
   "cell_type": "code",
   "execution_count": 28,
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     "text": [
      "/Users/raphael/GitHub/pingouin/pingouin/correlation.py:1118: FutureWarning: DataFrame.applymap has been deprecated. Use DataFrame.map instead.\n",
      "  mat_upper = mat_upper.applymap(lambda x: ffp(x, precision=decimals))\n"
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       "      <td>-0.13</td>\n",
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       "      <td>-0.36</td>\n",
       "      <td>0.06</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>0.16</td>\n",
       "      <td>-</td>\n",
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       "      <td>1.</td>\n",
       "      <td>1.</td>\n",
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       "      <th>Age</th>\n",
       "      <td>-0.04</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.03</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>0.04</td>\n",
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       "      <td>0.03</td>\n",
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       "      <td>0.02</td>\n",
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       "                  Neuroticism Extraversion Openness Agreeableness  \\\n",
       "Neuroticism                 -         0.00       1.          0.07   \n",
       "Extraversion            -0.33            -     0.00            1.   \n",
       "Openness                -0.02         0.24        -          0.00   \n",
       "Agreeableness           -0.13         0.06     0.17             -   \n",
       "Conscientiousness       -0.36         0.06    -0.01          0.16   \n",
       "Age                     -0.04          0.0     0.03         -0.05   \n",
       "BMI                      0.03        -0.05    -0.07          0.02   \n",
       "Gender                   0.02        -0.01    -0.04          0.02   \n",
       "\n",
       "                  Conscientiousness    Age   BMI Gender  \n",
       "Neuroticism                    0.00     1.    1.     1.  \n",
       "Extraversion                     1.     1.    1.     1.  \n",
       "Openness                         1.     1.    1.     1.  \n",
       "Agreeableness                  0.01     1.    1.     1.  \n",
       "Conscientiousness                 -     1.    1.     1.  \n",
       "Age                            0.04      -    1.     1.  \n",
       "BMI                            0.03  -0.05     -     1.  \n",
       "Gender                         0.02  -0.02  0.07      -  "
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     },
     "execution_count": 28,
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   "source": [
    "# Showing the raw p-values (with 2 decimals) instead of stars\n",
    "df.rcorr(method='spearman', stars=False, padjust='holm', decimals=2)"
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