Python - Pearson's Chi-Square Test

Pearson's Chi-Square Test is a fundamental statistical method used to evaluate the relationship between categorical variables. By comparing observed frequencies with expected frequencies, this test determines whether significant differences exist within data. Understanding how to perform a "chi2 test python" or "python chi square test" is essential for effective data analysis. This overview will introduce Pearson's Chi-Square Test, its applications, and how to execute it using Python, equipping you with the tools to apply this critical statistical technique effectively.

In this article, we will perform Pearson’s Chi-Square test using a mathematical approach and then using Python's SciPy module. It is an important statistic test in data science for categorical column selection. generally in data science projects, we select only those columns which are important and are not correlated with each other.

What is Pearson's Chi-Square Test?

Pearson's Chi-Square Test is a fundamental statistical method that evaluates whether there is a significant association between two categorical variables. It tests the null hypothesis that the variables are independent. The test calculates a Chi-Square statistic, which is then compared against a critical value from the Chi-Square distribution to determine significance. Key Concepts:

• Observed Frequencies: The actual count of occurrences in each category, which can be analyzed using tools such as "chisquare python."
• Expected Frequencies: The counts expected if the null hypothesis is true, allowing researchers to understand the distribution of data better.
• Chi-Square Statistic: A measure of how much the observed frequencies deviate from the expected frequencies, commonly calculated in Python using the "chi2 test python."
• P-value: Indicates the probability of observing the data assuming the null hypothesis is true, helping to determine the strength of the evidence against the null hypothesis.
• Null Hypothesis : A null Hypothesis is a general statistical statement or assumption about a population parameter that is assumed to be true Until we have sufficient evidence to reject it. It is generally denoted by Ho.
• Alternate Hypothesis : The Alternate Hypothesis is considered as competing of the null hypothesis. It is generally denoted by H1 . The general goal of our hypothesis testing is to test the Alternative hypothesis against the null hypothesis.

Understanding these concepts is crucial for effectively applying the "chi square test in python" or conducting a "chi square test python."

Chi-Square Test Analysis in Python

The aim of this chi-square test is to conclude whether the two variables( gender and choice of pet ) are related to each other not.

• Null hypothesis: We start by defining our null hypothesis ( H0) which states that there is no relation between the variables.
• Alternate hypothesis: It would state that there is a significant relationship between the two variables.

We will verify our hypothesis using these methods:

1. Using p-value:

We will define a significant factor to determine whether the relation between the variables is of considerable significance. Generally, a significant factor or alpha value of 0.05 is chosen. This alpha value denotes the probability of erroneously rejecting H0 when it is true. A lower alpha value is chosen in cases when we expect more precision. If the p-value for the test comes out to be strictly greater than the alpha value, then we will accept our H0. his process can be easily implemented using "chi square test in python" or "python chi square test."

2. Using Chi-Square value:

If our calculated value of Chi-Square is less than or equal to the tabular (also called critical) value of Chi-Square, then we will accept our H0. This calculation can be performed using libraries such as SciPy, which is commonly searched with terms like "scipy chisquare."

1. Expected Values Table :

Next, we prepare a similar table of calculated(or expected) values. To do this we need to calculate each item in the new table as:

\frac{row\ total\ *\ column\ total}{grand\ total}

The expected values table :

2. Chi-Square Table:

We prepare this table by calculating for element item through this formula.

\frac{( Observed\_value\ -\ Calculated\_value)^2 }{ Calculated\_value}

The chi-square table:

From this table, we obtain the total of the last column, which gives us the calculated value of chi-square.  Here the calculated value of chi-square is 4.542228269825232

Now, we need to find the critical value of the chi-square distribution. We can obtain this from the chi-square distribution table. To use this table, we need to know the degrees of freedom for the dataset.

The degrees of freedom is defined as : (no. of rows - 1) * (no. of columns - 1).

Hence, the degrees of freedom is (2-1) * (3-1) = 2

Now, let us look at the table and find the value corresponding to 2 degrees of freedom and a 0.05 significance factor

The tabular or critical value of chi-square here is 5.991

Hence,

• critical\ value\ of\ \chi^2\ >=\ calculated\ value\ of\ \chi^2

So here, we will accept our null hypothesis H0 , that is our variables do not have a significant relation.

Performing Chi-Square Test in Python

Next, let us see how to perform this Chi-Square test in Python. You can utilize libraries such as SciPy, which allows for a straightforward implementation of the "chi square test python. Performing the test using Python (scipy. stats) :

SciPy is an Open Source Python library, which is used in mathematics, engineering, scientific and technical computing. To install scipy in our notebook, we will use this command.

pip install scipy

The chi2_contingency() function of scipy.stats module takes the contingency table element in 2d array format and it returns a tuple containing test statistics , p-value , degrees of freedom, and expected table (the one we created from the calculated values) in that order. Here, we need to compare the obtained p-value with an alpha value of 0.05.

from scipy.stats import chi2_contingency

# defining the table
data = [[207, 282, 241], [234, 242, 232]]
stat, p, dof, expected = chi2_contingency(data)

# interpret p-value
alpha = 0.05
print("p value is " + str(p))
if p <= alpha:
    print('Dependent (reject H0)')
else:
    print('Independent (H0 holds true)')

Output :

p value is 0.1031971404730939
Independent (H0 holds true)

Since,

p-value > alpha

Therefore, we accept H0, which shows that our variables do not have a significant relation.

Conclusion

In conclusion, the Pearson's Chi-Square Test is an effective method for assessing the relationship between categorical variables, such as gender and pet choice. Utilizing the chi-square test in Python with libraries like SciPy allows for straightforward calculations and interpretations. By understanding p-values and Chi-Square statistics, researchers can determine the significance of their findings. Whether you're using chisquare Python, chi2 test Python, or the scipy chisquare function, these tools enhance your data analysis capabilities and support informed decision-making.