How to Check and Handle Violations of Chi-Square Test Assumptions

📚 Quick Study Guide

• 📊 The Chi-Square test is used to determine if there's a statistically significant association between categorical variables.
• 🤔 The key assumptions are: Independence of observations, data should be randomly selected, expected cell counts should be at least 5, and variables should be categorical.
• 🚫 Violation of Independence: Occurs when observations are not independent of each other. This is a serious violation.
• 📉 Low Expected Counts: If many cells have expected counts less than 5, the Chi-Square approximation may be poor.
• 🛠️ Corrective Actions: For independence violations, reconsider the study design. For low expected counts, combine categories or use Fisher's exact test.
• 🧮 The Chi-Square statistic is calculated as: $ \chi^2 = \sum \frac{(O_i - E_i)^2}{E_i} $, where $O_i$ is the observed frequency and $E_i$ is the expected frequency.

Practice Quiz

1. Question 1: Which of the following is a key assumption of the Chi-Square test?
   1. A) Data must be normally distributed.
   2. B) Observations must be independent.
   3. C) Variables must be continuous.
   4. D) Sample size must be less than 30.
2. Question 2: What is a common consequence of violating the assumption of independence in a Chi-Square test?
   1. A) Inflated Type I error rate.
   2. B) Deflated Type I error rate.
   3. C) No effect on error rates.
   4. D) Reduced statistical power.
3. Question 3: What is a common rule of thumb regarding expected cell counts in a Chi-Square test?
   1. A) All expected cell counts should be at least 10.
   2. B) At least 80% of expected cell counts should be greater than 5.
   3. C) All expected cell counts should be at least 5.
   4. D) Expected cell counts don't matter.
4. Question 4: If you have low expected cell counts, what is one potential solution?
   1. A) Increase the alpha level.
   2. B) Combine categories.
   3. C) Decrease the sample size.
   4. D) Use a t-test instead.
5. Question 5: Which test is often recommended as an alternative to the Chi-Square test when expected cell counts are low?
   1. A) ANOVA.
   2. B) Fisher's exact test.
   3. C) Regression analysis.
   4. D) Paired t-test.
6. Question 6: What type of variables are suitable for the Chi-Square test?
   1. A) Continuous variables.
   2. B) Ordinal variables.
   3. C) Categorical variables.
   4. D) Interval variables.
7. Question 7: How is the Chi-Square statistic calculated?
   1. A) $ \sum (O_i - E_i) $
   2. B) $ \sum \frac{(O_i - E_i)}{E_i} $
   3. C) $ \sum \frac{(O_i - E_i)^2}{E_i} $
   4. D) $ \sum (O_i - E_i)^2 $