Chi square test with different sample sizes in Python

Question

I have two sets of data as shown below. Each data set have a different length

X_data1 and Y_data1 (black binned data) have a length of 40 whereas X_data2 and Y_data2 (red) have a length of 18k.

I would like to perform a Chi-Square Goodness of Fit Test on these two data as follows

from scipy import stats
stats.chisquare(f_obs=Y_data1, f_exp=Y_data2)

But I can not since the vector size is not the same and I receive an error.

~/opt/miniconda3/lib/python3.9/site-packages/scipy/stats/stats.py in chisquare(f_obs, f_exp, ddof, axis) 6850 6851 """ -> 6852 return power_divergence(f_obs, f_exp=f_exp, ddof=ddof, axis=axis, 6853 lambda_="pearson")
6854

~/opt/miniconda3/lib/python3.9/site-packages/scipy/stats/stats.py in power_divergence(f_obs, f_exp, ddof, axis, lambda_) 6676 if f_exp is not None: 6677 f_exp = np.asanyarray(f_exp) -> 6678 bshape = _broadcast_shapes(f_obs_float.shape, f_exp.shape) 6679 f_obs_float = _m_broadcast_to(f_obs_float, bshape) 6680 f_exp = _m_broadcast_to(f_exp, bshape)

~/opt/miniconda3/lib/python3.9/site-packages/scipy/stats/stats.py in _broadcast_shapes(shape1, shape2) 184 n = n1 185 else: --> 186 raise ValueError(f'shapes {shape1} and {shape2} could not be ' 187 'broadcast together') 188 shape.append(n)

ValueError: shapes (40,) and (18200,) could not be broadcast together

Is there a way in Python that I can compare these two data?

Answer 1

You can't do this unless both f_exp and f_obs have the same length. You can achieve your goal by interpolating Y_data2 on the x-axis of Y_data1 . You can do it as follows:

from scipy.interpolate import InterpolatedUnivariateSpline 
spl = InterpolatedUnivariateSpline(X_data2, Y_data2)
new_Y_data2 = spl(X_data1)

As both Y_data1 and new_Y_data2 have same lengths now, you can use them in stats.chisquare as follows:

from scipy import stats
stats.chisquare(f_obs=Y_data1, f_exp=new_Y_data2)