Understanding the Parametric Test Selection Framework in Statistics

📚 Quick Study Guide

• 📏 Parametric Tests: Assume data follows a specific distribution (usually normal) and require interval or ratio data.
• 📊 Normality Assumption: Many parametric tests require that the data are approximately normally distributed. This can be checked using tests like the Shapiro-Wilk test or visually with histograms and Q-Q plots.
• 👯 Independent Samples T-test: Used to compare the means of two independent groups. Assumes normality and equal variances.
• 🧑‍🤝‍🧑 Paired Samples T-test: Used to compare the means of two related groups (e.g., before and after measurements). Assumes normality of the differences.
• ANOVA ANOVA (Analysis of Variance): Used to compare the means of three or more groups. Assumes normality and equal variances.
• ⚠️ Equal Variance Assumption: Often checked using Levene's test. If variances are unequal, adjustments like Welch's t-test (for two groups) or Welch's ANOVA (for multiple groups) can be used.
• 🔢 Pearson Correlation: Measures the linear relationship between two continuous variables. Assumes normality for both variables. The correlation coefficient, $r$, ranges from -1 to 1.

Practice Quiz

1. Which of the following is a key assumption of parametric tests?
   1. A. Data are categorical
   2. B. Data are normally distributed
   3. C. Data are skewed
   4. D. Data have unequal variances
2. Which test is appropriate for comparing the means of two independent groups when data is normally distributed?
   1. A. Chi-square test
   2. B. Independent samples t-test
   3. C. Paired samples t-test
   4. D. ANOVA
3. You want to compare the effectiveness of a new drug on a group of patients by measuring their symptoms before and after treatment. Which test is most appropriate?
   1. A. Independent samples t-test
   2. B. Paired samples t-test
   3. C. ANOVA
   4. D. Pearson correlation
4. Which test is used to compare the means of three or more independent groups?
   1. A. T-test
   2. B. Chi-square test
   3. C. ANOVA
   4. D. Regression analysis
5. Levene's test is used to check which assumption?
   1. A. Normality
   2. B. Independence
   3. C. Equal variances
   4. D. Linearity
6. Which test measures the linear relationship between two continuous variables?
   1. A. T-test
   2. B. ANOVA
   3. C. Chi-square test
   4. D. Pearson correlation
7. If the assumption of equal variances is violated in an independent samples t-test, which alternative test can be used?
   1. A. Paired t-test
   2. B. Welch's t-test
   3. C. ANOVA
   4. D. Chi-square test