Chi Square χ² Distribution Explained Parametric vs Non Parametric Tests, Applications & Examples

Chi-Square (χ²) Distribution Explained: Parametric vs. Non-Parametric Tests, Applications & Examples

Description:
The Chi-square (χ²) distribution is a fundamental tool in statistics, used for both parametric and non-parametric hypothesis testing. Whether you're analyzing population variances or working with categorical data, the Chi-square test provides powerful insights.

🔹 What You’ll Learn:
✅ Parametric vs. Non-Parametric Tests – When to use each
✅ Key Applications – Goodness-of-fit, independence, homogeneity tests
✅ Real-World Examples – Testing fairness of coins, dice, survey data
✅ Degrees of Freedom (DOF) – How they shape the Chi-square distribution
✅ Limitations & Best Practices – Sample size requirements, assumptions

📊 Key Topics Covered:

Chi-square test for variance (parametric)

Goodness-of-fit test (does data match expected distribution?)

Contingency tables (testing independence between variables)

Homogeneity test (do different groups come from the same population?)

When to use Chi-square vs. other tests

📌 Examples & Case Studies:
✔ Is a coin fair? (Observed vs. expected frequencies)
✔ Is a die unbiased? (Uniform distribution test)
✔ Does income level affect university choice? (Independence test)
✔ Do students from different years have similar opinions? (Homogeneity test)

⚠ Limitations:

Requires larger sample sizes for accuracy

Less precise than parametric tests when assumptions are met

Not all non-parametric tests are supported in software like MINITAB

🔎 Why It Matters:
The Chi-square distribution is essential for researchers in fields like psychology, biology, marketing, and social sciences. It helps validate hypotheses when normal distribution assumptions fail or when dealing with categorical data.

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#ChiSquare #Statistics #HypothesisTesting #ParametricTests #NonParametric #GoodnessOfFit #ContingencyTable #HomogeneityTest #DOF #DegreesOfFreedom #DataAnalysis #VarianceTest #CategoricalData

📚 Resources & Software:

MINITAB (for some Chi-square tests)

Excel, R, Python (SciPy) for custom analyses

👍 Enjoyed the video? Check out our other tutorials on:

t-tests vs. z-tests

ANOVA explained

Regression analysis basics

Thanks for watching! 🚀
Chi-Square Test
Chi-Square Distribution
Parametric vs Non-Parametric Tests
Goodness-of-Fit Test
Contingency Table
Chi-Square Test for Independence
Chi-Square Test for Homogeneity
Hypothesis Testing in Statistics
Categorical Data Analysis
Degrees of Freedom (DOF) in Chi-Square
Chi-Square vs t-test
Chi-Square vs ANOVA
When to Use Chi-Square Test
Non-Parametric Statistical Tests
Testing Fairness of a Coin/Dice
Survey Data Analysis with Chi-Square
Chi-Square Test in Marketing Research
Chi-Square in Social Sciences
Chi-Square in Biostatistics
Chi-Square Test in Excel
Chi-Square Test in R/Python (SciPy)
Chi-Square in MINITAB
Assumptions of Chi-Square Test
Limitations of Chi-Square Test
Sample Size Requirements for Chi-Square
How to Perform a Chi-Square Test
Interpreting Chi-Square Results
Chi-Square Test Step-by-Step Guide

Видео Chi Square χ² Distribution Explained Parametric vs Non Parametric Tests, Applications & Examples канала BP International