Question

M14. #14: Another type of painted ceramic vessel is called three-circle red-on-white ( Mimbres Mogollon Archaeology). At four different sites in an archaeological region, the number of such sherds was counted in local dwelling excavations.

Site I	Site II	Site III	Site IV
10	16	35	10
20	4	22	15
2	36	12	12
23	2	45	36
12	27		17
	15		19

A)  Find SS_TOT, SS_BET, and SS_W and check that SS_TOT = SS_BET + SS_W. (Use 3 decimal places.)

B) Find d.f._BET, d.f._W, MS_BET, and MS_W. (Use 4 decimal places for MS_BET, and MS_W.)

C) Find the value of the sample F statistic. (Use 2 decimal places.)

Answer 1

	Site I	Site II	Site III	Site IV	Total
Sum	67	100	114	109	390
Count	5	6	4	6	21
Mean, sum/n	13.4	16.6667	28.5	18.1667
Sum of square, Ʃ(xᵢ-x̅)²	279.2	859.333	629	434.833
Standard deviation	8.35464	13.1098	14.4799	9.32559

Number of treatment, k =        4
Total sample Size, N =        21
      
A) SS(between) = (Sum1)²/n1 + (Sum2)²/n2 + (Sum3)²/n3 + (Sum4)²/n4 - (Grand Sum)²/ N = 550.776
SS(within) = SS1 + SS2 + SS3 + SS4 = 2202.367
SS(total) = SS(between) + SS(within) =       2753.143

B) df(between) = k-1 =       3
df(within) = k(n-1) =       17
df(total) = N-1 =       20

MS(between) = SS(between)/df(between) =       183.5921
MS(within) = SS(within)/df(within) =       129.5510
      
C) F = MS(between)/MS(within) =       1.42