# Chi-square test in Python

## Chi-square (χ2) test for independence (Pearson Chi-square test)

• Chi-square test is a non-parametric (distribution-free) method used to compare the relationship between the two categorical (nominal) variables in a contingency table
• For example, we have different treatments (treated and nontreated) and treatment outcomes (cured and noncured), here we could use the chi-square test for independence to check whether treatments are related to treatment outcomes.
• Note: Chi-square test for independence is different than the chi-square goodness of fit test

### Hypotheses

• Null hypotheses: The two categorical variables are independent (no association between the two variables)
• Alternative hypotheses: The two categorical variables are dependent (there is an association between the two variables)
• Note: There are no one or two-tailed P-value. Rejection region of the chi-square test is always on the right side of the distribution.

### Assumptions

• The two variables are categorical (nominal) and data is randomly sampled
• The levels of variables are mutually exclusive
• The expected frequency count for at least 80% of the cell in a contingency table is at least 5
• The expected frequency count should not be less than 1
• Observations should be independent of each other
• Observation data should be frequency counts and not percentages or transformed data

### Perform a chi-square test for independence

• We will use `bioinfokit` v0.9.5 or later
• Check bioinfokit documentation for installation and documentation
``````# I am using interactive python interpreter (Python 3.7.4)
>>> from bioinfokit.analys import stat, get_data
>>> df = get_data('drugdata').data
treatments  cured  noncured
0     treated     60        10
1  nontreated     30        25
# set treatments column as index
>>> df = df.set_index('treatments')
cured  noncured
treatments
treated        60        10
nontreated     30        25

# run chi-square test for independence
>>> res = stat()
>>> res.chisq(df=df)

# output
>>> print(res.summary)

Chi-squared test for independence

Test              Df    Chi-square      P-value
--------------  ----  ------------  -----------
Pearson            1       13.3365  0.000260291
Log-likelihood     1       13.4687  0.000242574

>>> print(res.expected_df)

Expected frequency counts

cured    noncured
--  -------  ----------
0     50.4        19.6
1     39.6        15.4

``````

### Interpretation

The P-value obtained from chi-square test for independence is significant (P<0.05), and therefore, we conclude that there is a significant association between treatments (treated and nontreated) with treatment outcome (cured and noncured)

## Chi-square (χ2) Goodness of Fit test

• Chi-square Goodness of Fit Test test is a non-parametric (distribution-free) method used to compare the observed and expected values from one categorical variable. The expected values are calculated based on the known theoretical expectation.
• For example, we have resistant (A) and susceptible (B) genotypes for some disease. The crosses between these two genotypes will produce offspring in 3:1 (75% A and 25% B genotype) as per Mendelian ratio assuming resistance to disease is a dominant trait. Here, we could use the chi-square Goodness of Fit Test test to check whether observed counts of A and B genotypes are similar to expected counts of A and B genotypes as per the Mendelian ratio.

### Hypotheses

• Null hypotheses: The observed and expected counts in each group are equal
• Alternative hypotheses: The observed and expected counts in each group are different

### Assumptions

• The variable should be categorical (nominal) and data is randomly sampled
• The groups of variables are mutually exclusive
• The expected count should be at least 5 for each group
• Observations should be independent of each other
• Observation data should be frequency counts and not percentages or transformed data

### Perform a Goodness of Fit test Python

• We will use `bioinfokit` v0.9.5 or later
• Check bioinfokit documentation for installation and documentation
``````# I am using interactive python interpreter (Python 3.7)
>>> from bioinfokit.analys import stat
>>> import pandas as pd
# create or import pandas dataframe of observed counts
>>> df = pd.DataFrame({'genotypes':['A', 'B'], 'observed':[155, 45]})
>>> df = df.set_index(['genotypes'])
observed
genotypes
A               155
B                45

# run chi-square test
>>> res = stat()
# p should be known theoretical expectation and must sum to 1
>>> res.chisq(df=df, p=(0.75, 0.25))

# output
>>> print(res.summary)

Chi-squared goodness of fit test

Chi-Square    Df    P-value    Sample size
------------  ----  ---------  -------------
0.666667     1   0.414216            200

# get expected counts
>>> print(res.expected_df)
observed  expected_counts
genotypes
A               155            150.0
B                45             50.0

``````

### Interpretation

The P-value obtained from the chi-square Goodness of Fit test is non-significant (P>0.05 and fail to reject the null hypothesis), and therefore, we conclude that the observed genotypes counts after crosses is similar to that of expected counts as per the Mendelian ratio.

### References

• Virtanen P, Gommers R, Oliphant TE, Haberland M, Reddy T, Cournapeau D, Burovski E, Peterson P, Weckesser W, Bright J, van der Walt SJ. SciPy 1.0: fundamental algorithms for scientific computing in Python. Nature methods. 2020 Mar;17(3):261-72.

How to cite?
Renesh Bedre.(2020, July 29). reneshbedre/bioinfokit: Bioinformatics data analysis and visualization toolkit (Version v0.9). Zenodo. http://doi.org/10.5281/zenodo.3965241

If you have any questions, comments or recommendations, please email me at reneshbe@gmail.com

Last updated: August 14, 2020