beween group ariance python calculations code example

Example: how to performe anova on grouped variable in python

# load packages
import scipy.stats as stats
# stats f_oneway functions takes the groups as input and returns F and P-value
fvalue, pvalue = stats.f_oneway(d['A'], d['B'], d['C'], d['D'])
print(fvalue, pvalue)
# 17.492810457516338 2.639241146210922e-05

# get ANOVA table as R like output
import statsmodels.api as sm
from statsmodels.formula.api import ols
# reshape the d dataframe suitable for statsmodels package 
d_melt = pd.melt(d.reset_index(), id_vars=['index'], value_vars=['A', 'B', 'C', 'D'])
# replace column names
d_melt.columns = ['index', 'treatments', 'value']
# Ordinary Least Squares (OLS) model
model = ols('value ~ C(treatments)', data=d_melt).fit()
anova_table = sm.stats.anova_lm(model, typ=2)
anova_table

|                |  df   | sum_sq  | mean_sq  |  F       |  PR(>F)  |
|---------------|--------|---------|----------|----------|----------|
| C(treatments) | 3.0    | 3010.95 | 1003.650 | 17.49281 | 0.000026 |
| Residual      | 16.0   | 918.00  | 57.375   | NaN      | NaN      |

# note: if the data is balanced (equal sample size for each group), Type 1, 2, and 3 sums of squares
# (typ parameter) will produce similar results.