Parametric Assumptions and Robustness Quiz: Test Your Statistics Knowledge

📚 Quick Study Guide

• 🔢 Parametric Assumptions: These are assumptions about the population distribution that must be met to ensure the validity of parametric statistical tests (e.g., t-tests, ANOVA). Common assumptions include normality, homogeneity of variance, and independence of observations.
• 📊 Normality: Data should be approximately normally distributed. Tests like the Shapiro-Wilk test or visual inspection of histograms and Q-Q plots can assess normality.
• ⚖️ Homogeneity of Variance (Homoscedasticity): The variance should be equal across different groups. Levene's test is commonly used to check this assumption.
• 🌱 Independence: Observations should be independent of each other. This is often ensured through proper experimental design.
• 💪 Robustness: Refers to the ability of a statistical test to provide accurate results even when its assumptions are violated. Some tests are more robust than others.
• 💡 Central Limit Theorem: Helps in achieving normality when dealing with sample means, even if the population isn't normally distributed, especially with larger sample sizes.
• 🛠️ Data Transformations: Techniques like log transformation or Box-Cox transformation can be applied to make the data meet the assumptions of normality or homogeneity of variance.
• 🚫 Non-Parametric Tests: Used when parametric assumptions are severely violated. Examples include Mann-Whitney U test, Kruskal-Wallis test, and Wilcoxon signed-rank test.

Practice Quiz

1. Which of the following is a key assumption of parametric tests?
   1. A. Non-normality of data
   2. B. Heterogeneity of variance
   3. C. Independence of observations
   4. D. Dependence of observations
2. What test is commonly used to assess the assumption of homogeneity of variance?
   1. A. Shapiro-Wilk test
   2. B. Levene's test
   3. C. T-test
   4. D. Chi-square test
3. What does 'robustness' in statistics refer to?
   1. A. The ability of a test to always be significant
   2. B. The ability of a test to handle large datasets
   3. C. The ability of a test to provide accurate results even when its assumptions are violated
   4. D. The ability of a test to only work with normal data
4. Which of the following can help achieve normality when dealing with sample means, even if the population isn't normally distributed?
   1. A. Law of Large Numbers
   2. B. Central Limit Theorem
   3. C. Bayes' Theorem
   4. D. Empirical Rule
5. What type of data transformation can be applied to make data meet the assumptions of normality?
   1. A. Subtraction
   2. B. Multiplication
   3. C. Log transformation
   4. D. Division
6. When are non-parametric tests typically used?
   1. A. When parametric assumptions are met
   2. B. When sample sizes are very large
   3. C. When parametric assumptions are severely violated
   4. D. When data is normally distributed
7. Which of the following is an example of a non-parametric test?
   1. A. T-test
   2. B. ANOVA
   3. C. Mann-Whitney U test
   4. D. F-test