Python Pandas find statistical difference between 2 distributions

Question

i have 2 columns with similar data. I plot them to compare their distributions and i want to quantify their difference.

df = pd.DataFrame({'a':['cat','dog','bird','cat','dog','dog','dog'],
             'b':['cat','cat','cat','bird','dog','dog','dog']})

I then plot the 2 columns of my data frame to compare their distributions:

ax = df['a'].value_counts().plot(kind='bar', color='blue', width=.75, legend=True, alpha=0.8)
df['b'].value_counts().plot(kind='bar', color='maroon', width=.5, alpha=1, legend=True)

How can i quantify the difference in the distributions statistically to say how similar they are?

would it be a simple t-test or something else?

Answer 1

It is very common to use the two-sided Kolmogorov-Smirnov test for this.

In Python, you can do so with scipy.stats.ks_2samp:

from scipy import stats

merged = pd.merge(
    df.a.value_counts().to_frame(),
    df.b.value_counts().to_frame(),
    left_index=True,
    right_index=True)

stats.ks_2samp(merged.a, merged.b)

Broadly speaking, if the second value of the returned tuple is small (say less than 0.05), you should reject the hypothesis that the distributions are the same.