Question

(A) What is the corrected p-value for a 1-way ANOVA with 5 groups? Calculate the Bonferroni correction.

(B) What does the Bonferroni help us avoid?

Answer 1

The Bonferroni correction method is used as a correction factor for multiple comparisons between group means. Since the given alpha value may be applicable for individual comparisons. However, it may not hold while comparing different combinations

The Bonferroni corrected p-value is given by :

In the given example number of groups =5 and alpha =0.05. The number of tests performed will be given as

1. 1 to 2
2. 1 to 3
3. 2 to 3
4. 2 to 4
5. 3 to 4
6. 3 to 5
7. 4 to 5
8. 4 to 1
9. (1 to 2) and (3 to 4)
10. (1 to 2) and (4 to 5)

Thus, pvalue= 0.05/10 > 0.005

The Bonferroni help us avoid reducing the False positive rate ( rejecting the null hypothesis when is true) by reducing the alpha value