Question

Suppose we collected three groups of exam scores: each group has 10 persons, the exam average score within each group is 15, 20, 25 respectively, and the sample standard deviation within each group is always 5. Using ANOVA and F-test, compute the p-value for testing H0 : miu1 = miu2 = miu3 for the three groups

Answer 1

	Group 1	Group 2	Group 3	Total
Count, n	10	10	10	30
Average	15	20	25
Sum = n*average	150	200	250	600
Standard deviation, s	5	5	5

Number of treatment, k =        3
Total sample Size, N =       30
      
df(between) = k-1 =       2
df(within) = N-k =       27
df(total) = N-1 =       29
      
SS(between) = (Sum1)²/n1 + (Sum2)²/n2 + (Sum3)²/n3 - (Grand Sum)²/ N =       500
SS(within) = s1²(n-1) + s2²(n-1) + s3²​​​​​​​(n-1) =        675
SS(total) = SS(between) + SS(within) =       1175
      
MS(between) = SS(between)/df(between) =       250
MS(within) = SS(within)/df(within) =       25
      
F = MS(between)/MS(within) =    10
p-value = F.DIST.RT(10, 2, 27 ) =  0.00056

Source of variation	SS	df	MS	F	P-value
Between Groups	500	2	250	10	0.00056
Within Groups	675	27	25
Total	1175	29