P-value from Chi sq test statistic in Python

Quick refresher here:

Probability Density Function: think of it as a point value; how dense is the probability at a given point?

Cumulative Distribution Function: this is the mass of probability of the function up to a given point; what percentage of the distribution lies on one side of this point?

In your case, you took the PDF, for which you got the correct answer. If you try 1 - CDF:

>>> 1 - stats.chi2.cdf(3.84, 1)
0.050043521248705147

PDF CDF

To calculate probability of null hypothesis given chisquared sum, and degrees of freedom you can also call chisqprob:

>>> from scipy.stats import chisqprob
>>> chisqprob(3.84, 1)
0.050043521248705189

---

Notice:

chisqprob is deprecated! stats.chisqprob is deprecated in scipy 0.17.0; use stats.distributions.chi2.sf instead

Update: as noted, chisqprob() is deprecated for scipy version 0.17.0 onwards. High accuracy chi-square values can now be obtained via scipy.stats.distributions.chi2.sf(), for example:

>>>from scipy.stats.distributions import chi2
>>>chi2.sf(3.84,1)
0.050043521248705189
>>>chi2.sf(1424,1)
1.2799986253099803e-311

---

While stats.chisqprob() and 1-stats.chi2.cdf() appear comparable for small chi-square values, for large chi-square values the former is preferable. The latter cannot provide a p-value smaller than machine epsilon,and will give very inaccurate answers close to machine epsilon. As shown by others, comparable values result for small chi-squared values with the two methods:

>>>from scipy.stats import chisqprob, chi2
>>>chisqprob(3.84,1)
0.050043521248705189
>>>1 - chi2.cdf(3.84,1)
0.050043521248705147

Using 1-chi2.cdf() breaks down here:

>>>1 - chi2.cdf(67,1)
2.2204460492503131e-16
>>>1 - chi2.cdf(68,1)
1.1102230246251565e-16
>>>1 - chi2.cdf(69,1)
1.1102230246251565e-16
>>>1 - chi2.cdf(70,1)
0.0

Whereas chisqprob() gives you accurate results for a much larger range of chi-square values, producing p-values nearly as small as the smallest float greater than zero, until it too underflows:

>>>chisqprob(67,1)
2.7150713219425247e-16
>>>chisqprob(68,1)
1.6349553217245471e-16
>>>chisqprob(69,1)
9.8463440314253303e-17    
>>>chisqprob(70,1)
5.9304458500824782e-17
>>>chisqprob(500,1)
9.505397766554137e-111
>>>chisqprob(1000,1)
1.7958327848007363e-219
>>>chisqprob(1424,1)
1.2799986253099803e-311
>>>chisqprob(1425,1)
0.0