Question

1.6) Mention the business implications of performing ANOVA for this particular case study.

A	B	Volunteer	Relief
1	1	1	2.4
1	1	2	2.7
1	1	3	2.3
1	1	4	2.5
1	2	1	4.6
1	2	2	4.2
1	2	3	4.9
1	2	4	4.7
1	3	1	4.8
1	3	2	4.5
1	3	3	4.4
1	3	4	4.6
2	1	1	5.8
2	1	2	5.2
2	1	3	5.5
2	1	4	5.3
2	2	1	8.9
2	2	2	9.1
2	2	3	8.7
2	2	4	9
2	3	1	9.1
2	3	2	9.3
2	3	3	8.7
2	3	4	9.4
3	1	1	6.1
3	1	2	5.7
3	1	3	5.9
3	1	4	6.2
3	2	1	9.9
3	2	2	10.5
3	2	3	10.6
3	2	4	10.1
3	3	1	13.5
3	3	2	13
3	3	3	13.3
3	3	4	13.2

Answer 1

1.6)

Perform in Minitab software:

Factorial Fit: Relief versus A, B, Volunteer

Estimated Effects and Coefficients for Relief:

Term	Effect	Coef SE	Coef	t	P
Constant		7.18333	0.1477	48.63	0.000
A	5.95000	2.97500	0.1809	16.44	0.000
B	4.35000	2.17500	0.1809	12.02	0.000
Volunteer	-0.00667	-0.00333	0.1982	-0.02	0.987
A*B	2.58750	1.29375	0.2216	5.84	0.000
A*Volunteer	0.02000	0.01000	0.2427	0.04	0.967
B*Volunteer	-0.01000	-0.00500	0.2427	-0.02	0.984
A*B*Volunteer	-0.03750	-0.011875	0.2973	-0.06	0.950

S = 0.886292; PRESS = 34.4507; R-Sq = 94.13%; R-Sq(pred) = 90.81%; R-Sq(adj) = 92.66%

Analysis of Variance for Relief:

Source	DF	Seq SS	Adj SS	Adj MS	F	P
Main Effects	3	325.950	325.950	108.650	138.32	0.000
A	1	212.415	212.415	212.415	270.42	0.000
B	1	113.535	113.535	113.535	144.54	0.000
Volunteer	1	0.000	0.000	0.000	0.000	0.987
2-Way Interactions	3	26.782	26.782	8.927	11.37	0.000
A*B	1	26.781	26.781	26.781	34.09	0.000
A*Volenteer	1	0.001	0.001	0.001	0.00	0.967
B*Volenteer	1	0.000	0.000	0.000	0.00	0.984
3-Way Interactions	1	0.003	0.003	0.003	0.00	0.950
A*B*Volunteer	1	0.003	0.003	0.003	0.00	0.950
Residual Error	28	21.994	21.994	0.786
Total	35	374.730

Unusual Observations for Relief:

Obs	StdOrder	Relief	Fit	SE Fit	Residual	St Resid
17	17	8.9	7.1867	0.2472	1.7133	2.01R
18	18	9.1	7.1844	0.1618	1.9156	2.20R
20	20	9.0	7.1800	0.2472	1.8200	2.14R

R denotes an observation with a large standardized residual.

Estimated Coefficients for Relief using data in uncoded units

Term	Coef
Constant	2.20556
A	0.30833
B	-0.46667
Volunteer	-0.058889
A*B	1.32500
A*Volunteer	0.031667
B*Volunteer	0.021667
A*B*Volunteer	-0.012500

Residual Plots for Relief: