A one-way ANOVA only involves one factor or independent variable, whereas there are two independent variables in a two-way ANOVA.

A one-way ANOVA only involves one factor or independent variable, whereas there are two independent variables in a two-way ANOVA. 3. In a one-way ANOVA, the one factor or independent variable analyzed has three or more categorical groups. A two-way ANOVA instead compares multiple groups of two factors.

1. Test of difference MURIEL N. CACERES, PhD Student Anova oNe-way and two-way 1

2. Questions to consider.. 2 What is ANOVA ONE-WAY AND TWO-WAY? How can I calculate it? How do I interpret the results? 2

3. 3 What is ANOVA ONE-WAY AND TWO-WAY? Questions to consider.. 3

4. 4 What is ANOVA ONE-WAY? - is a statistical method used to compare means among three or more groups. One-way ANOVA specifically deals with the comparison of means across different levels of a single independent variable. 4

5. HOW ONE-WAY ANOVA WORKS: 1. Null Hypothesis (H0) : Assumes that there is no significant difference between the group means. 2. Alternative Hypothesis (H1) : Assumes that there is a significant difference between at least two group means. 5

6. HOW ONE-WAY ANOVA WORKS: 3. Data Collection : Gather data from multiple groups. Each group should be independent, meaning that the data points in one group are not related to the data points in another group. 4. Calculate Group Means : Find the mean of each group. This is done by adding up all the values in each group and dividing by the number of values in that group. 6

7. HOW ONE-WAY ANOVA WORKS: 5. Calculate Overall Mean (Grand Mean) : Find the mean of all the data points from all the groups combined. 6. Calculate Sum of Squares (SS) : Determine the variability within each group and the overall variability. 7

8. HOW ONE-WAY ANOVA WORKS: 7. Degrees of Freedom : Calculate degrees of freedom for between groups ( dfB ) and within groups ( dfW ). 8. Mean Squares : Calculate mean squares for between groups (MSB) and within groups (MSW). 8

9. HOW ONE-WAY ANOVA WORKS: 9. F-ratio : Compute the F-ratio by dividing MSB by MSW. 10. Critical Value and Decision : Compare the calculated F-ratio with the critical value from the F-distribution table for a given significance level (e.g., 0.05). If the calculated F-ratio is greater than the critical value, reject the null hypothesis. 9

10. HOW ONE-WAY ANOVA WORKS: 11. Post-Hoc Tests (optional) : If the null hypothesis is rejected, perform post-hoc tests (e.g., Tukey's HSD) to identify which specific group means are significantly different from each other. 10

11. IN SUMMARY… one-way ANOVA helps determine if there are any significant differences in means between groups, providing a more comprehensive analysis than comparing pairs of groups individually. 11

12. 12 What is ANOVA tWO-WAY ? - is a statistical method used to analyze the variance between two independent variables (factors) and their interaction on a dependent variable. 12

13. HOW TWO-WAY ANOVA WORKS: 1. Factors : 13

14. HOW TWO-WAY ANOVA WORKS: 2. Null Hypotheses : 14

15. HOW TWO-WAY ANOVA WORKS: 3. Data Collection : Data is collected for each combination of levels of Factor A and Factor B. 4. Calculate Group Means : Calculate means for each combination of levels of Factor A and Factor B. 15 5. Calculate Overall Mean (Grand Mean) : Find the mean of all data points across all combinations of levels.

16. HOW TWO-WAY ANOVA WORKS: 16 6. Calculate Sum of Squares (SS) : 7. Degrees of Freedom :

17. HOW TWO-WAY ANOVA WORKS: 17 8. Mean Squares : 9. F-ratios :

18. HOW TWO-WAY ANOVA WORKS: 10. Critical Value and Decision : 18 11. Post-Hoc Tests (optional) :

19. IN SUMMARY… Two-way ANOVA is powerful in situations where there are two independent variables, and researchers want to understand the effects of each variable individually as well as their interaction. This method is commonly used in experimental designs where multiple factors may influence the outcome. 19

20. example… 20 One-way anova

21. example… 21 One-way anova

22. example… 22 One-way anova

23. example… 23 twO-way anova

24. example… 24 twO-way anova

25. example… 25 twO-way anova