3.1.6.1.2.1. Relating Gender and IQ

Going back to the brain size + IQ data, test if the VIQ of male and female are different after removing the effect of brain size, height and weight.

Notice that here ‘Gender’ is a categorical value. As it is a non-float data type, statsmodels is able to automatically infer this.

Python source code: plot_brain_size.py

import pandas
from statsmodels.formula.api import ols

data = pandas.read_csv('../brain_size.csv', sep=';', na_values='.')

model = ols('VIQ ~ Gender + MRI_Count + Height', data).fit()
print(model.summary())

# Here, we don't need to define a contrast, as we are testing a single
# coefficient of our model, and not a combination of coefficients.
# However, defining a contrast, which would then be a 'unit contrast',
# will give us the same results
print(model.f_test([0, 1, 0, 0]))

###############################################################################
# Here we plot a scatter matrix to get intuitions on our results.
# This goes beyond what was asked in the exercise

# This plotting is useful to get an intuitions on the relationships between
# our different variables

from pandas.tools import plotting
import matplotlib.pyplot as plt

# Fill in the missing values for Height for plotting
data['Height'].fillna(method='pad', inplace=True)

# The parameter 'c' is passed to plt.scatter and will control the color
# The same holds for parameters 'marker', 'alpha' and 'cmap', that
# control respectively the type of marker used, their transparency and
# the colormap
plotting.scatter_matrix(data[['VIQ', 'MRI_Count', 'Height']],
                        c=(data['Gender'] == 'Female'), marker='o',
                        alpha=1, cmap='winter')

fig = plt.gcf()
fig.suptitle("blue: male, green: female", size=13)

plt.show()