A researcher hypothesizes that there is a difference in fou

. A researcher hypothesizes that there is a difference in four autism treatments. She used analysis of variance to compare 4 treatment conditions with separate samples of n=4 participants in each treatment. Some results are below. Complete the table. There are 10 total points in this problem. Fill in the table first to help answer the questions posed here.

1 point a. Was at least one treatment different from the others at an alpha of .05? Give the critical F at .05.

1 point b. Was one treatment significantly different from the others at an alpha of .01? Give the critical F at .01.

1 point c. If there was a significant finding, what step would the researcher take to see which group or groups were specifically different from the others?

1 point for each number that has a question mark next to it, 7 points in the table.

Source

SS

Df

MS

Between Treatments

?

?

10

F=?

Within Treatments

48

?

?

Total

?

?

Solution

no. of treatments,k = 4
participants in each treatment,n = 4
N = nk = 16

df between treatment = k-1 = 3
df within treatment = N-k = 12
df total = N-1 = 15

SS total = SS between treatment + SS within treatment
SS total = 30+48 = 78

MS between treatment = SS between treatment / df between treatment
= 30 / 3 = 10

MS within treatment = SS within treatment / df within treatment
= 48 / 12 = 4

test statistic,F = MS between treatment / MS within treatment
F = 10/4 = 2.5