Question

CH13 Q5

The following observations were obtained when conducting a two-way ANOVA experiment with no interaction. Factor A X for Factor B 2.500 8.000 13.750 Factor B 15 9.667 13 8.000 16 8.333 Xi for Factor A 6.000 X 8.083 a. Calculate SST, SSA, SSB, and SSE. (Round intermediate calculations to at least 4 decimal places. Round your answers to 2 decimal places.) SST SSA SSB SSE

Answer 1

using excel data analysis tool for two way anova without replication

Anova: Two-Factor Without Replication
SUMMARY	Count	Sum	Average	Variance
factor B                                                          1	4	10	2.500	3.000
2	4	32	8.000	2.000
3	4	55	13.750	4.917
Factor A                                                       1	3	29	9.667	25.333
2	3	19	6.333	20.333
3	3	24	8.000	31.000
4	3	25	8.333	56.333
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Rows	253.17	2	126.58	59.182	0.000	5.14325285
Columns	16.92	3	5.64	2.636	0.144	4.757062663
Error	12.83	6	2.14
Total	282.92	11

a) using above table

SST = 282.92
SSA=16.92
SSB=253.17
SSE=12.83

b) MSA=5.64
MSB=126.58
MSE=2.14

c)

ANOVA
Source of Variation	SS	df	MS	F	P-value
Rows	253.17	2	126.583	59.182	0.000
Columns	16.92	3	5.639	2.636	0.144
Error	12.83	6	2.139
Total	282.92	11