Chi-Square Test

Chi-Square Test/dataset.csv

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+Gender,Preference
+Male,Sports
+Female,Reading
+Male,Sports
+Male,Sports
+Male,Reading
+Female,Sports
+Male,Reading
+Male,Reading
+Male,Reading
+Female,Sports
+Male,Sports
+Male,Sports
+Male,Sports
+Male,Sports
+Female,Sports
+Male,Sports
+Female,Reading
+Female,Sports
+Female,Reading
+Male,Sports
+Female,Sports
+Male,Sports
+Female,Reading
+Female,Reading
+Female,Reading
+Female,Reading
+Female,Sports
+Female,Reading
+Female,Sports
+Female,Sports
+Male,Reading
+Male,Reading
+Female,Reading
+Female,Reading
+Female,Reading
+Male,Reading
+Female,Reading
+Male,Reading
+Male,Sports
+Male,Reading
+Male,Reading
+Male,Sports
+Female,Reading
+Female,Sports
+Female,Sports
+Female,Reading
+Female,Sports
+Male,Sports
+Female,Sports
+Female,Sports
+Male,Reading
+Female,Sports
+Male,Reading
+Female,Sports
+Male,Sports
+Female,Sports
+Female,Sports
+Male,Reading
+Male,Reading
+Male,Sports
+Male,Sports
+Male,Reading
+Male,Sports
+Male,Sports
+Male,Sports
+Female,Reading
+Female,Reading
+Male,Reading
+Female,Sports
+Female,Sports
+Female,Reading
+Female,Reading
+Male,Reading
+Female,Reading
+Male,Sports
+Female,Reading
+Female,Sports
+Female,Reading
+Male,Sports
+Female,Reading
+Male,Reading
+Female,Reading
+Male,Reading
+Female,Sports
+Male,Reading
+Male,Sports
+Female,Sports
+Male,Sports
+Female,Sports
+Female,Reading
+Female,Sports
+Female,Sports
+Female,Sports
+Female,Reading
+Female,Reading
+Female,Reading
+Female,Reading
+Female,Sports
+Female,Sports
+Male,Reading
+Male,Sports
+Female,Sports
+Female,Sports
+Female,Reading
+Female,Reading
+Female,Sports
+Female,Reading
+Female,Reading
+Female,Reading
+Male,Reading
+Female,Reading
+Male,Sports
+Female,Reading
+Female,Sports
+Male,Sports
+Female,Reading
+Male,Sports
+Female,Sports
+Female,Sports
+Male,Reading
+Female,Reading
+Male,Sports
+Female,Reading
+Male,Reading
+Male,Reading
+Female,Reading
+Female,Sports
+Male,Sports
+Female,Reading
+Female,Reading
+Female,Sports
+Male,Sports
+Male,Reading
+Male,Sports
+Male,Reading
+Male,Reading
+Male,Sports
+Male,Sports
+Male,Reading
+Male,Reading
+Female,Sports
+Male,Reading
+Female,Sports
+Female,Reading
+Female,Sports
+Male,Sports
+Male,Sports
+Male,Reading
+Male,Reading
+Female,Sports
+Male,Reading
+Male,Sports
+Male,Sports
+Male,Reading
+Male,Reading
+Female,Sports
+Male,Reading
+Female,Reading
+Male,Sports
+Female,Sports
+Male,Reading
+Male,Sports
+Female,Sports
+Female,Reading
+Female,Sports
+Male,Sports
+Female,Reading
+Male,Reading
+Male,Sports
+Female,Sports
+Female,Reading
+Male,Reading
+Male,Reading
+Female,Reading
+Female,Sports
+Female,Reading
+Male,Reading
+Male,Sports
+Male,Reading
+Male,Sports
+Male,Reading
+Male,Reading
+Female,Reading
+Male,Sports
+Male,Sports
+Male,Reading
+Female,Sports
+Male,Sports
+Male,Sports
+Female,Sports
+Male,Sports
+Male,Sports
+Male,Reading
+Male,Reading
+Male,Sports
+Female,Reading
+Female,Reading
+Female,Reading
+Male,Reading
+Male,Sports

Chi-Square Test/readme.md

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+# Chi-Square Test for Independence
+
+## Overview
+The Chi-Square Test for Independence is a statistical test used to determine whether there is a significant association between two categorical variables. It is based on the comparison of observed frequencies in the data with the frequencies that would be expected if the variables were independent.
+
+## Mathematical Logic
+The Chi-Square statistic (χ²) is calculated using the following formula:
+
+$$
+χ² = Σ((O_i - E_i)² / E_i)
+$$
+
+Where:
+- **O_i**: Observed frequency for the i-th category
+- **E_i**: Expected frequency for the i-th category
+
+The expected frequency (E_i) for each category is calculated under the assumption of independence between the variables, using:
+
+$$
+E_i = \frac{(Row \, Total \, * \, Column \, Total)}{Grand \, Total}
+$$
+
+## Steps to Perform Chi-Square Test
+1. **Create a Contingency Table**: Summarize the frequencies of the two categorical variables in a matrix format.
+2. **Calculate Expected Frequencies**: Compute the expected frequencies for each cell of the table assuming the variables are independent.
+3. **Compute the Chi-Square Statistic**: Use the formula to calculate the χ² value.
+4. **Determine the Degrees of Freedom (df)**: Calculated as (number of rows - 1) * (number of columns - 1).
+5. **Find the P-Value**: Compare the χ² value with the Chi-Square distribution table to find the p-value.
+6. **Interpret the Result**: If the p-value is less than the significance level (typically 0.05), reject the null hypothesis of independence.
+
+## Example Calculation
+Consider a dataset with two variables: Gender (Male, Female) and Preference (Sports, Reading). Suppose we have the following observed frequencies in a contingency table:
+
+|             | Sports | Reading | Row Total |
+|-------------|--------|---------|-----------|
+| Male        | 30     | 20      | 50        |
+| Female      | 20     | 30      | 50        |
+| Column Total| 50     | 50      | 100       |
+
+1. **Expected Frequencies**:
+    - E(Male, Sports) = (50 * 50) / 100 = 25
+    - E(Male, Reading) = (50 * 50) / 100 = 25
+    - E(Female, Sports) = (50 * 50) / 100 = 25
+    - E(Female, Reading) = (50 * 50) / 100 = 25
+
+2. **Chi-Square Statistic**:
+$$
+χ² = Σ((O_i - E_i)² / E_i) = ((30 - 25)² / 25) + ((20 - 25)² / 25) + ((20 - 25)² / 25) + ((30 - 25)² / 25)
+$$
+
+$$
+χ² = (5² / 25) + ((-5)² / 25) + ((-5)² / 25) + (5² / 25) = 4
+$$
+
+3. **Degrees of Freedom**:
+    - df = (2-1)(2-1) = 1
+
+4. **P-Value**: Using the Chi-Square distribution table or a calculator, find the p-value corresponding to χ² = 4 and df = 1.
+
+## Uses of Chi-Square Test
+The Chi-Square Test for Independence is widely used in various fields, including:
+1. **Biology**: To determine if there is an association between different genetic traits.
+2. **Social Sciences**: To analyze survey data and examine relationships between demographic variables.
+3. **Market Research**: To evaluate consumer preferences and behaviors based on categorical variables like gender, age group, etc.
+4. **Medical Research**: To investigate the relationship between risk factors and health outcomes.
+
+## Interpretation
+- **P-Value < 0.05**: Reject the null hypothesis; there is a significant association between the variables.
+- **P-Value ≥ 0.05**: Fail to reject the null hypothesis; no significant association exists between the variables.
+
+This test allows researchers and analysts to make informed decisions based on the relationships between categorical variables in their data.
+
+## Coding Implementation
+### 1. Generate Dataset
+First, we generate a dataset with 200 samples, each having two categorical variables: Gender and Preference. The dataset is saved to a CSV file for further analysis.
+
+```python
+import pandas as pd
+import numpy as np
+
+# Seed for reproducibility
+np.random.seed(42)
+
+# Generate sample data
+n_samples = 200
+genders = np.random.choice(['Male', 'Female'], size=n_samples)
+preferences = np.random.choice(['Sports', 'Reading'], size=n_samples)
+
+# Create a DataFrame
+data = {
+    'Gender': genders,
+    'Preference': preferences
+}
+df = pd.DataFrame(data)
+
+# Save DataFrame to CSV in the current environment
+csv_file_path = 'large_sample_data.csv'
+df.to_csv(csv_file_path, index=False)
+print(f"CSV file created at: {csv_file_path}")

Chi-Square Test/requirement.txt

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+pandas==1.5.3
+numpy==1.24.2
+scipy==1.10.0
+matplotlib==3.7.1
+seaborn==0.12.2