Python, Pandas & Chi-Squared Test of Independence

16,202

A few corrections:

  • Your expected array is not correct. You must divide by observed.sum().sum(), which is 1284, not 1000.
  • For a 2x2 contingency table such as this, the degrees of freedom is 1, not 8.
  • Your calculation of chi_squared_stat does not include a continuity correction. (But it isn't necessarily wrong to not use it--that's a judgment call for the statistician.)

All the calculations that you perform (expected matrix, statistics, degrees of freedom, p-value) are computed by chi2_contingency:

In [65]: observed
Out[65]: 
                        Previously Successful  Previously Unsuccessful
Yes - changed strategy                  129.3                   260.17
No                                      182.7                   711.83

In [66]: from scipy.stats import chi2_contingency

In [67]: chi2, p, dof, expected = chi2_contingency(observed)

In [68]: chi2
Out[68]: 23.383138325890453

In [69]: p
Out[69]: 1.3273696199438626e-06

In [70]: dof
Out[70]: 1

In [71]: expected
Out[71]: 
array([[  94.63757009,  294.83242991],
       [ 217.36242991,  677.16757009]])

By default, chi2_contingency uses a continuity correction when the contingency table is 2x2. If you prefer to not use the correction, you can disable it with the argument correction=False:

In [73]: chi2, p, dof, expected = chi2_contingency(observed, correction=False)

In [74]: chi2
Out[74]: 24.072616672232893

In [75]: p
Out[75]: 9.2770200776879643e-07
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Mia
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Mia

Updated on August 08, 2022

Comments

  • Mia
    Mia over 1 year

    I am quite new to Python as well as Statistics. I'm trying to apply the Chi Squared Test to determine whether previous success affects the level of change of a person (percentage wise, this does seem to be the case, but I wanted to see whether my results were statistically significant).

    My question is: Did I do this correctly? My results say the p-value is 0.0, which means that there is a significant relationship between my variables (which is what I want of course...but 0 seems a little bit too perfect for a p-value, so I'm wondering whether I did it incorrectly coding wise).

    Here's what I did:

    import numpy as np
    import pandas as pd
    import scipy.stats as stats
    
    d = {'Previously Successful' : pd.Series([129.3, 182.7, 312], index=['Yes - changed strategy', 'No', 'col_totals']),
     'Previously Unsuccessful' : pd.Series([260.17, 711.83, 972], index=['Yes - changed strategy', 'No', 'col_totals']),
     'row_totals' : pd.Series([(129.3+260.17), (182.7+711.83), (312+972)], index=['Yes - changed strategy', 'No', 'col_totals'])}
    
    total_summarized = pd.DataFrame(d)
    
    observed = total_summarized.ix[0:2,0:2]
    

    Output: Observed

    expected =  np.outer(total_summarized["row_totals"][0:2],
                     total_summarized.ix["col_totals"][0:2])/1000
    
    expected = pd.DataFrame(expected)
    
    expected.columns = ["Previously Successful","Previously Unsuccessful"]
    expected.index = ["Yes - changed strategy","No"]
    
    chi_squared_stat = (((observed-expected)**2)/expected).sum().sum()
    
    print(chi_squared_stat)
    
    crit = stats.chi2.ppf(q = 0.95, # Find the critical value for 95% confidence*
                      df = 8)   # *
    
    print("Critical value")
    print(crit)
    
    p_value = 1 - stats.chi2.cdf(x=chi_squared_stat,  # Find the p-value
                             df=8)
    print("P value")
    print(p_value)
    
    stats.chi2_contingency(observed= observed)
    

    Output Statistics

  • Mia
    Mia over 6 years
    Warren, this is really helpful! 1) I was following along a tutorial for this and I did not realize that 1000 in their case was the observed number, I thought you always use 1000. 2) I actually do not know much about degrees of freedom. Is there always a specific number you can pick? Can't you use different ones? 3) But even with the contingency correction, the p=value looks very small...way less than 0.05?
  • Warren Weckesser
    Warren Weckesser over 6 years
    Regarding degrees of freedom: It is not something you can pick. These comments are not the place for a discussion of degrees of freedom. Maybe stats.stackexchange.com/questions/219617/… will help. Also look for tutorials on the chi-squared test, especially those about contingency tables. You could also ask over at stats.stackexchange.com
  • Warren Weckesser
    Warren Weckesser over 6 years
    Yes, the p value is small. That means your observed data is "far" from the expected table.
  • Mia
    Mia over 6 years
    You really helped me out! Thank you so much!!