Question 1088675
a)The independent-measures design F-ratio has df = {{{highlight(2)}}}, {{{highlight(57)}}}
df(between treatments) = k-1 = 3 – 1 = 2
df(Total) = N-1 = 60 – 1 = 59
df(error) = df(Total) - df(between treatments) = 59 - 2 = 57
Hence, the independent-measures design F-ratio has df = 2, 57
60 individuals were needed for the study

b) The repeated-measures F-ratio has df = {{{highlight(2)}}}, {{{highlight(38)}}}
df(between subjects) = n-1 = 20 – 1 = 19
df(within treatments) = Σ df inside each treatment = 19 + 19 + 19 = 57  

df(between treatments) = k-1 = 3 – 1 = 2
df(error) = df(within treatments) - df(between subjects) = 57 - 19 = 38

Hence, the repeated-measures F-ratio has df = 2, 38
20 individuals were needed for the study (same subjects for each treatment)