Question

1. Below is an ANOVA table that is incomplete but has enough information provided to be completed.

Source SS df MS F

Between 910 2

Within 70

Total 59

a. (4 points) Complete the One-Way ANOVA table.

b. (2 points) Determine the critical F at =.05. Should we reject the null?

c. (2 points) How many different groups were in this study? Assuming equal numbers in each group, how many participants were in each group?

d. (4 points) Calculate eta-squared and omega-squared for this ANOVA.

Answer 1

a.

Source SS df MS F

Between (effect) 910 2 455 358.26

Within (error) 70 57 1.27

Total 980   59

df for within = df Total - df Between = 59 - 2 = 57

SS Total = SS Between + SS Error = 910 + 70 =980

MS = SS / df

b.

Critical values of F at = 0.05 and df = 2, 57 is 3.16

Since observed F is greater than critical value, we reject the null.

c.

Number of groups = df between + 1 = 2 + 1 = 3

Total participants = df Total + 1 = 59 + 1 = 60

Number of participants in each group = 60 / 3 = 20

d.

eta-squared = SS between / SS total = 910 / 980 = 0.9286

omega-squared = SS_effect-(df_effect)(MS_error) / (MS_error + SS_total)

= (910 - 2 * 1.27) / (1.27 + 980)

= 0.9248