Question

CH13 Q8

A two-way analysis of variance experiment with interaction was conducted. Factor A had three levels (columns), factor B had five levels (rows), and six observations were obtained for each combination. The results include the following sum of squares terms: SST 1548 SSA 1022 SSB 390 SSAB 26 a. Construct an ANOVA table. (Round intermediate calculations to at least 4 decimal places. Round "MS" to 4 decimal places and "F' to 3 decimal places.) Answer is not complete. ANOVA Source of Variation Rows Columns Interaction Error Total p- 0.000 0.000 0.035 df MS value

Answer 1

Solution :-

Given data :

SST = 1548

SSA = 1022

SSB = 390

SSAB = 26

Factor A had three levels (columns), factor B had five levels (rows), and six observations were obtained for each combination.

Here we need to construct the ANOVA table.

ANOVA
Source of variation	SS	DF	MS	F	P-Value
Rows ( B )	390	=(5 - 1) = 4	= (395 / 4) = 98.75	= (98.75 /1.467) = 67.314	0.000
Columns ( A )	1022	=(3 - 1) = 2	= (1022 / 2) = 511	= (511 / 1.467) =348.321	0.000
Interaction ( A * B )	26	=(4 * 2) = 8	= (26 / 8) = 3.25	= (3.25 / 1.467) = 2.215	0.035
Error	=(1548-(390+1022+26)) =110	=(5 * 3 * (6-1)) = (5 * 3 * 5) = 75	= (110 / 75) =1.467
Total	1548	89