How to use chi-square test for statistical analysis in Python?

As an important statistical method, Chi-Square Test is one of the commonly used testing methods for the relationship between categorical variables. In Python, the SciPy library provides the chisquare function for performing chi-square tests. This article will introduce the principle, usage and implementation examples of the chi-square test to help readers better understand and apply the chi-square test.

1. Principle of Chi-square test

The core idea of ​​the Chi-square test is to compare the difference between the actual observed value and the theoretical value. If the difference between the two is significant, it means that there is a difference between the two variables. relation. The chi-square test analyzes data in different dimensions differently. This article mainly introduces the principle of the two-dimensional chi-square test.

In the case of a two-dimensional table, the chi-square test first assumes that there is no relationship between the two variables, calculates the expected value E based on the assumption, then calculates the chi-square value based on the actual observed value O and the expected value E, and finally passes Look up tables or perform calculations to perform significance tests to determine whether the hypothesis is true.

The specific calculation formula is as follows:

Chi-square value χ²=(O-E)²/E

where O is the actual observed value and E is the expected value.

If the chi-square value is larger, the relationship between the two variables is more significant, and the hypothesis is rejected; conversely, if the chi-square value is smaller, the relationship is less significant, and the hypothesis is accepted.

2. Use of Chi-square test

1. Data preparation

Before performing the Chi-square test, you need to prepare the data. Generally speaking, data exists in the form of a two-dimensional table, including both the actual observed value O and the expected value E, as follows:

     类别A          类别B

Variable 1 70 30
Variable 2 40 60

Among them, 70 represents the number of intersections between variable 1 and category A.

2. Calculate the chi-square value based on data

Use the SciPy library in Python to easily calculate the chi-square value and the corresponding p-value. The code is as follows:

from scipy.stats import chisquare
import numpy as np

obs = np.array([[70, 30], [40, 60]])  #实际观测值
exp = np.array([[50, 50], [50, 50]])  #期望值

stat, pval = chisquare(obs.ravel(), f_exp=exp.ravel())
print(stat, pval)

Among them, the chisquare function is used to calculate the chi-square value and the corresponding p value, obs and exp represent the actual observed value and expected value respectively, and the ravel() function converts the two-dimensional array into a one-dimensional array , the f_exp parameter specifies the expected value. When set to None, obs.sum()/4 is used as the expected value.

3. Testing the hypothesis

After obtaining the chi-square value and p-value, you need to determine whether the hypothesis is true. Generally, the significance level α is set to 0.05. If the p value is less than or equal to α, the null hypothesis is rejected, indicating that there is a relationship between the two variables; otherwise, the null hypothesis is accepted, indicating that there is no relationship.

The code is as follows:

alpha = 0.05

if pval <= alpha:
    print("Reject null hypothesis, variables are related.")
else:
    print("Accept null hypothesis, variables are independent.")

3. Implementation example

The following is a simple example to demonstrate the use of the chi-square test. Suppose an A/B test is conducted on an e-commerce website to test whether the user's login time has an impact on the browsing time of the website. The data is as follows:

     浏览时长<10s      浏览时长>=10s

Login A 1000 2000
Login B 1500 2500

First, you need to calculate the expected value E. The expected value calculated based on the data is as follows:

     浏览时长<10s      浏览时长>=10s

Login A 1200 1800
Login B 1300 1900

Use Python code for calculation and hypothesis testing as follows:

obs = np.array([[1000, 2000], [1500, 2500]])  #实际观测值
exp = np.array([[1200, 1800], [1300, 1900]])  #期望值

stat, pval = chisquare(obs.ravel(), f_exp=exp.ravel())
print(stat, pval)

alpha = 0.05

if pval <= alpha:
    print("Reject null hypothesis, variables are related.")
else:
    print("Accept null hypothesis, variables are independent.")

The final result is: reject the null hypothesis, indicating that the user login method has an impact on the browsing time.

4. Summary

Chi-square test is a commonly used test method for the relationship between categorical variables, which can determine whether there is a relationship between two variables. In Python, the chi-square test can be easily performed using the chisquare function provided by the SciPy library. Through the introduction of this article, readers can better understand and use the chi-square test, and the statistical analysis of data can be more standardized and scientific.

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