Question

What are the corresponding degrees of freedom and critical value for a within-subjects ANOVA with 3 conditions, 5 subjects in each condition, and =

0.01
α=0.01?

a) BG: 2, BS: 12, Error: 12, Total: 23, critical value: 11.771

b) BG: 2, BS: 12, Error: 12, Total: 23, critical value: 9.709

c) BG: 2, BS: 12, Error: 8, Total: 23, critical value: 13.361

d) BG: 2, BS: 8, Error: 12, Total: 23, critical value: 9.709

Answer 1

The corresponding degrees of freedom for a within-subjects ANOVA with 3 conditions and 5 subjects in each condition are BG: 2, BS: 12, Error: 8, and Total: 23. The critical value for α = 0.01 is 13.361.

Step-by-step explanation:

The corresponding degrees of freedom for a within-subjects ANOVA are calculated as follows:

• Between Groups (BG): k - 1 = 3 - 1 = 2
• Between Subjects (BS): (k - 1)(n - 1) = (3 - 1)(5 - 1) = 12
• Error: (k - 1)(n - 1) = (3 - 1)(5 - 1) = 12
• Total: kn - 1 = 3(5) - 1 = 14

The critical value for a within-subjects ANOVA with α = 0.01 can be found using the degrees of freedom table. The critical value for α = 0.01 and df = 11 is 13.28. Therefore, the answer is option c) BG: 2, BS: 12, Error: 8, Total: 23, critical value: 13.361.