.. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_packages_statistics_auto_examples_plot_wage_education_gender.py: Test for an education/gender interaction in wages ================================================== Wages depend mostly on education. Here we investigate how this dependence is related to gender: not only does gender create an offset in wages, it also seems that wages increase more with education for males than females. Does our data support this last hypothesis? We will test this using statsmodels' formulas (http://statsmodels.sourceforge.net/stable/example_formulas.html). Load and massage the data .. code-block:: python import pandas import urllib import os if not os.path.exists('wages.txt'): # Download the file if it is not present urllib.urlretrieve('http://lib.stat.cmu.edu/datasets/CPS_85_Wages', 'wages.txt') # EDUCATION: Number of years of education # SEX: 1=Female, 0=Male # WAGE: Wage (dollars per hour) data = pandas.read_csv('wages.txt', skiprows=27, skipfooter=6, sep=None, header=None, names=['education', 'gender', 'wage'], usecols=[0, 2, 5], ) # Convert genders to strings (this is particulary useful so that the # statsmodels formulas detects that gender is a categorical variable) import numpy as np data['gender'] = np.choose(data.gender, ['male', 'female']) # Log-transform the wages, because they typically are increased with # multiplicative factors data['wage'] = np.log10(data['wage']) simple plotting .. code-block:: python import seaborn # Plot 2 linear fits for male and female. seaborn.lmplot(y='wage', x='education', hue='gender', data=data) .. image:: /packages/statistics/auto_examples/images/sphx_glr_plot_wage_education_gender_001.png :class: sphx-glr-single-img statistical analysis .. code-block:: python import statsmodels.formula.api as sm # Note that this model is not the plot displayed above: it is one # joined model for male and female, not separate models for male and # female. The reason is that a single model enables statistical testing result = sm.ols(formula='wage ~ education + gender', data=data).fit() print(result.summary()) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none OLS Regression Results ============================================================================== Dep. Variable: wage R-squared: 0.193 Model: OLS Adj. R-squared: 0.190 Method: Least Squares F-statistic: 63.42 Date: Thu, 18 Aug 2022 Prob (F-statistic): 2.01e-25 Time: 10:40:01 Log-Likelihood: 86.654 No. Observations: 534 AIC: -167.3 Df Residuals: 531 BIC: -154.5 Df Model: 2 Covariance Type: nonrobust ================================================================================== coef std err t P>|t| [0.025 0.975] ---------------------------------------------------------------------------------- Intercept 0.4053 0.046 8.732 0.000 0.314 0.496 gender[T.male] 0.1008 0.018 5.625 0.000 0.066 0.136 education 0.0334 0.003 9.768 0.000 0.027 0.040 ============================================================================== Omnibus: 4.675 Durbin-Watson: 1.792 Prob(Omnibus): 0.097 Jarque-Bera (JB): 4.876 Skew: -0.147 Prob(JB): 0.0873 Kurtosis: 3.365 Cond. No. 69.7 ============================================================================== Warnings: [1] Standard Errors assume that the covariance matrix of the errors is correctly specified. The plots above highlight that there is not only a different offset in wage but also a different slope We need to model this using an interaction .. code-block:: python result = sm.ols(formula='wage ~ education + gender + education * gender', data=data).fit() print(result.summary()) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none OLS Regression Results ============================================================================== Dep. Variable: wage R-squared: 0.198 Model: OLS Adj. R-squared: 0.194 Method: Least Squares F-statistic: 43.72 Date: Thu, 18 Aug 2022 Prob (F-statistic): 2.94e-25 Time: 10:40:01 Log-Likelihood: 88.503 No. Observations: 534 AIC: -169.0 Df Residuals: 530 BIC: -151.9 Df Model: 3 Covariance Type: nonrobust ============================================================================================ coef std err t P>|t| [0.025 0.975] -------------------------------------------------------------------------------------------- Intercept 0.2998 0.072 4.173 0.000 0.159 0.441 gender[T.male] 0.2750 0.093 2.972 0.003 0.093 0.457 education 0.0415 0.005 7.647 0.000 0.031 0.052 education:gender[T.male] -0.0134 0.007 -1.919 0.056 -0.027 0.000 ============================================================================== Omnibus: 4.838 Durbin-Watson: 1.825 Prob(Omnibus): 0.089 Jarque-Bera (JB): 5.000 Skew: -0.156 Prob(JB): 0.0821 Kurtosis: 3.356 Cond. No. 194. ============================================================================== Warnings: [1] Standard Errors assume that the covariance matrix of the errors is correctly specified. Looking at the p-value of the interaction of gender and education, the data does not support the hypothesis that education benefits males more than female (p-value > 0.05). .. code-block:: python import matplotlib.pyplot as plt plt.show() **Total running time of the script:** ( 0 minutes 0.513 seconds) .. _sphx_glr_download_packages_statistics_auto_examples_plot_wage_education_gender.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: sphx-glr-download :download:`Download Python source code: plot_wage_education_gender.py ` .. container:: sphx-glr-download :download:`Download Jupyter notebook: plot_wage_education_gender.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_