One-Way ANOVA vs t-test: Key differences and when to use each

📚 Quick Study Guide

• 🔢 T-test: Used to compare the means of two groups. Can be independent samples or paired samples.
• ➗ Independent Samples T-test: Compares the means of two independent groups (e.g., treatment vs. control).
• 🤝 Paired Samples T-test: Compares the means of two related groups (e.g., before and after treatment on the same individuals).
• 📈 One-Way ANOVA: Used to compare the means of three or more groups.
• 🧪 Assumptions of ANOVA: Data should be normally distributed, variances should be equal across groups (homogeneity of variance), and observations should be independent.
• 📊 Null Hypothesis (T-test & ANOVA): There is no significant difference between the means of the groups being compared.
• 📝 Formula Considerations:
  • T-test: $t = \frac{\bar{x}_1 - \bar{x}_2}{s_{\text{p}} \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}$
  • ANOVA: $F = \frac{\text{Variance between groups}}{\text{Variance within groups}}$

Practice Quiz

1. Which test is appropriate for comparing the means of three independent groups?
   1. T-test
   2. One-Way ANOVA
   3. Chi-Square Test
   4. Correlation
2. When should you use a paired samples t-test?
   1. To compare two independent groups.
   2. To compare three or more independent groups.
   3. To compare two related groups.
   4. To compare variances between groups.
3. What is a key assumption of ANOVA?
   1. Non-normal distribution of data
   2. Unequal variances between groups
   3. Homogeneity of variance
   4. Dependent observations
4. If you want to compare the average test scores of students in two different classrooms, which test should you use?
   1. One-Way ANOVA
   2. Paired Samples T-test
   3. Independent Samples T-test
   4. Regression Analysis
5. The F-statistic is associated with which test?
   1. T-test
   2. Z-test
   3. One-Way ANOVA
   4. Chi-Square Test
6. What does the null hypothesis typically state in both t-tests and ANOVA?
   1. There is a significant difference between group means.
   2. There is no significant difference between group means.
   3. The variances are equal.
   4. The data is normally distributed.
7. If you are comparing the pre-test and post-test scores of the same group of students, which test is most appropriate?
   1. Independent Samples T-test
   2. One-Way ANOVA
   3. Paired Samples T-test
   4. Correlation