Chi-Square
The chi-square test is a key method in hypothesis testing for analyzing categorical data. It helps you determine whether the observed frequencies in your data differ significantly from what you would expect under a specific hypothesis.
When to Use the Chi-Square Test
- Use the chi-square test with categorical variables, where data are sorted into distinct groups or categories;
- Do not use it for continuous data or paired measurements.
Types of Chi-Square Tests
- Test of independence: Checks if two categorical variables are related or independent;
- Goodness of fit test: Determines if the distribution of a single categorical variable matches an expected distribution.
Both tests compare observed frequencies to expected frequencies under your hypothesis.
Example Scenario
Suppose you want to know whether there is an association between two categorical variables, such as gender and preference for a new product. You collect data in a contingency table, which shows the frequency counts for each combination of categories. The chi-square test of independence helps you decide if the distribution of preferences is independent of gender, or if there is a statistically significant relationship between them.
How to Perform a Chi-Square Test in Python
Use the scipy.stats library, which provides the chi2_contingency function. This function calculates the test statistic and p-value based on your contingency table.
1234567891011121314151617import numpy as np from scipy.stats import chi2_contingency # Example contingency table: rows = gender, columns = product preference # Prefer A Prefer B Prefer C # Male 20 15 25 # Female 30 25 15 table = np.array([[20, 15, 25], [30, 25, 15]]) chi2, p, dof, expected = chi2_contingency(table) print("Chi-square statistic:", chi2) print("p-value:", p) print("Degrees of freedom:", dof) print("Expected frequencies:\n", expected)
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The chi-square test is a key method in hypothesis testing for analyzing categorical data. It helps you determine whether the observed frequencies in your data differ significantly from what you would expect under a specific hypothesis.
When to Use the Chi-Square Test
- Use the chi-square test with categorical variables, where data are sorted into distinct groups or categories;
- Do not use it for continuous data or paired measurements.
Types of Chi-Square Tests
- Test of independence: Checks if two categorical variables are related or independent;
- Goodness of fit test: Determines if the distribution of a single categorical variable matches an expected distribution.
Both tests compare observed frequencies to expected frequencies under your hypothesis.
Example Scenario
Suppose you want to know whether there is an association between two categorical variables, such as gender and preference for a new product. You collect data in a contingency table, which shows the frequency counts for each combination of categories. The chi-square test of independence helps you decide if the distribution of preferences is independent of gender, or if there is a statistically significant relationship between them.
How to Perform a Chi-Square Test in Python
Use the scipy.stats library, which provides the chi2_contingency function. This function calculates the test statistic and p-value based on your contingency table.
1234567891011121314151617import numpy as np from scipy.stats import chi2_contingency # Example contingency table: rows = gender, columns = product preference # Prefer A Prefer B Prefer C # Male 20 15 25 # Female 30 25 15 table = np.array([[20, 15, 25], [30, 25, 15]]) chi2, p, dof, expected = chi2_contingency(table) print("Chi-square statistic:", chi2) print("p-value:", p) print("Degrees of freedom:", dof) print("Expected frequencies:\n", expected)
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