Understanding critical values for AXO1 For each of the follo

Understanding critical values for AXO?1. For each of the following, observe what effect the stated change has on the critical value of the test statistic (i.e., does it increase? decrease?) You can obtain these in R, but make sure you know how to read the F-table in your textbook as well! a. Increasing the number of groups (constant total sample size). Give the criticals value for an ANOVA with treatment groups each with 10 observations (for a total of 30 observations) and alpha = 0.05, an ANOVA with treatment groups each with 5 observations (for a totaI of 30 observations) and alpha = 0.05 b. Increasing the number of groups (constant per-group sample size). Give the criticals value for (1) an ANOVA with 3 treatment groups each with 10 observations (for a oral of 30 observations) and alpha = 0.05, an ANOVA with 6 treatment groups each with 10 observations (for a total of 60 observations) and alpha = 0.05 c. Increasing the sample size. Give the critical values for (1) an ANO VA with 3 treatment groups each with 10 observations (for a oral of 30 observations) and a = 0.05, an ANO VA with 3 treatment groups each with 20 observations (for a oral of 60 observations) and a = 0.05 d. Increasing the significance level. Give the critical values for (1) an ANO VA with 3 treatment groups each with 10 observations (for a total of 30 observations) and alpha = 0.05, an ANOVA with 3 treatment groups each with 10 observations (for a oral of 30 observations) and alpha = 0.10

Solution

a. Critical value decreases on increasing the number of groups (constant total sample size).

     1. F_2,27(0.05) = 3.354

     2. F_5,24(0.05) = 2.621

b. Critical value decreases on increasing the number of groups (constant pre-group sample size).

     1. F_2,27(0.05) = 3.354

     2. F_5,54(0.05) = 2.386

c. Critical value decreases on increasing the sample size.

     1. F_2,27(0.05) = 3.354

     2. F_2,57(0.05) = 3.159

d. Critical value decreases on increasing the significance level.

     1. F_2,27(0.05) = 3.354

     2. F_2,27(0.10) = 2.511