Chi-Square Association/Fisher’s exact

Introduction

The chi-square test is a non-parametric statistical test used to determine whether there is a significant association within the categorical variables. It compares the observed frequencies in a contingency table with the frequency we would expect if the variables were independent. The chi-square test calculates a test statistic, often denoted as χ² (chi-square), which follows chi-square distribution, we can determine whether the association between the variables are statistically significant.

The chi-squared test and Fisher’s exact test can assess for independence between two variables when the comparing groups are independent and not correlated. The chi-squared test applies an approximation assuming the sample is large, while the Fisher’s exact test runs an exact procedure especially for small-sized samples.

Data used

To perform the analysis the data used is: Loprinzi CL. Laurie JA. Wieand HS. Krook JE. Novotny PJ. Kugler JW. Bartel J. Law M. Bateman M. Klatt NE. et al. Prospective evaluation of prognostic variables from patient-completed questionnaires. North Central Cancer Treatment Group. Journal of Clinical Oncology. 12(3):601-7, 1994.

Implementing Chi-Square test in Python

We can use crosstab() function to create contingency table of two selected variables.

import pandas as pd 
import numpy as np
import scipy.stats as stats 

# Read the sample data
data = pd.read_csv("../data/lung_cancer.csv") 

# Removing undesired rows
df= data.dropna(subset=['ph.ecog','wt.loss']) 

# Converting numerical variable into categorical variable

df['ecog_grp']= np.where(df['ph.ecog']>0, "fully active","symptomatic")
print(df['ecog_grp'])
df['wt_grp'] = np.where(df['wt.loss']>0, "weight loss", "weight gain")

contingency_table= pd.crosstab(df['ecog_grp'],df['wt_grp'])
contingency_table
1       symptomatic
2       symptomatic
3      fully active
4       symptomatic
5      fully active
           ...     
223    fully active
224     symptomatic
225    fully active
226    fully active
227    fully active
Name: ecog_grp, Length: 213, dtype: object
/tmp/ipykernel_24370/2909872460.py:13: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame.
Try using .loc[row_indexer,col_indexer] = value instead

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  df['ecog_grp']= np.where(df['ph.ecog']>0, "fully active","symptomatic")
/tmp/ipykernel_24370/2909872460.py:15: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame.
Try using .loc[row_indexer,col_indexer] = value instead

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  df['wt_grp'] = np.where(df['wt.loss']>0, "weight loss", "weight gain")
wt_grp weight gain weight loss
ecog_grp
fully active 39 113
symptomatic 22 39

Furthermore, the chi2_contingency() function in scipy.stats library in Python can be used to implement Chi-square test.

# Parsing the values from the contingency table
value = np.array([contingency_table.iloc[0][0:5].values,
                  contingency_table.iloc[1][0:5].values])

statistic, p, dof, expected = stats.chi2_contingency(value)

print("The chi2 value is:", statistic)
print("The p value is:", p)
print("The degree of freedom is:", dof)
print("The expected values are:", expected)
The chi2 value is: 1.8260529076055192
The p value is: 0.17659446865934614
The degree of freedom is: 1
The expected values are: [[ 43.53051643 108.46948357]
 [ 17.46948357  43.53051643]]

Implementing Fisher exact test in Python

To implement Fischer’s exact test in Python, we can use the fischer_exact() function from the stats module in SciPy library. It returns SignificanceResult object with statistic and pvalue as it’s attributes.

stats.fisher_exact(value, alternative="two-sided")
SignificanceResult(statistic=np.float64(0.6118262268704746), pvalue=np.float64(0.13500579984749855))