#!/usr/bin/env python
# coding: utf-8

# # Two-way ANOVA

# ANOVA with interaction: 
# 
# *Measurement of fetal head circumference, by four observers in three fetuses, from a study investigating the
# reproducibility of ultrasonic fetal head circumference data.*
# 
# Author:  Thomas Haslwanter, Date:    June-2014

# In[3]:


get_ipython().run_line_magic('pylab', 'inline')
import pandas as pd
import urllib
from statsmodels.formula.api import ols
from statsmodels.stats.anova import anova_lm


# ## Get and format the data

# In[4]:


inFile = 'altman_12_6.txt'
url_base = 'https://raw.githubusercontent.com/thomas-haslwanter/statsintro_python/master/ipynb/Data/data_altman/'
url = url_base + inFile
data = genfromtxt(urllib.request.urlopen(url), delimiter=',')

# Bring them in dataframe-format
df = pd.DataFrame(data, columns=['hs', 'fetus', 'observer'])


# ## ANOVA with interaction

# In[5]:


formula = 'hs ~ C(fetus) + C(observer) + C(fetus):C(observer)'
lm = ols(formula, df).fit()
print(anova_lm(lm))