Question

An article presents measurements of basal ionized calcium (Ca) levels for four groups of patients with differing levels of basal intact parathyroid hormone (PTH). The results are presented in the following table Group Ca levels (mM) 1.23 102 133 136 1.11 1.51 1.51 1.30 1.36 1.34 1.27 1.43 1.21 169 1.28 133 1.49 117 115 106 12125 136 1.08 1.27 1.32 0.97 0.98 1.23 1.11 125 126 1.25 1.32 1.25 1.31 1.04 132 1.29 0.95 1.38 108 165 1.14 1.44 1.37 1.11 0.82 131 109 1.46 1.35 167 138 105 1.32 0.95 1.21 1.21 1.22 1.13 1.51 072 1.33 1.46 Construct an ANOVA table. Source Group Error Total DF MS (Click to select)

Answer 1

	Group 1	Group 2	Group 3	Group 4	Total
Sum (T)	22.77	23.79	18.45	17.51	82.52
Count, n	17	20	15	14	66
Average	1.33941	1.1895	1.23	1.25071
Sum of square(SSi), Ʃ(xᵢ-x̅)²	0.40629	0.27050	0.68080	0.75569
Standard deviation	0.15935	0.11932	0.22052	0.24110

Number of treatment, k = 4

Total value, N = 66

df(between)	= k-1	3
df(within)	= k(n-1)	62
df(total)	= N-1	65
SS(between)	= (T1)²/n1 + (T2)²/n2 + (T3)²/n3 +(T4)²/n4 - (Grand Sum)²/ N	0.21511
SS(within)	= SS1 + SS2 + SS3 +SS4	2.11328
SS(total)	= SS(between) + SS(within)	2.32839
MS(between)	= SS(between)/df(between)	0.07170
MS(within)	= SS(within)/df(within)	0.03409
F	= MS(between)/MS(within)	2.10367
p-value	= F.DIST.RT(2.10367, 3, 62)	0.1088

ANOVA
Source of Variation	SS	df	MS	F	P-value
Between Groups	0.21511	3	0.07170	2.10367	0.1088
Within Groups	2.11328	62	0.03409
Total	2.32839	65

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