Question

Using excel and the data in chapter 14 data set 2, complete the analysis and interpret the results. It is a 2 x 3 experiment: There are two levels of severity, where the Level 1 is severe and Level 2 is mild, and there are three levels of treatment, where Level 1 is Drug #1, Level 2 is Drug #2, and Level 3 is Placebo. This is an ANOVA with replication because each participant received all three levels of treatment, which are represented by the columns of data; severity is represented by the rows.

  
Severity 1  

6   6   2
   6   5   1
   7   4   3
   7   5   4
   7   4   5
   6   3   4
   5   3   3
   6   3   3
   7   4   3
   8   5   4
   7   5   5
   6   5   3
   5   6   1
   6   6   2
   7   7   4
   8   6   5
   9   5   3
   8   7   4
   7   6   2
7   8   3

Severity 2  

7   7   4
   8   5   5
   8   4   6
   9   3   5
   8   4   4
   7   5   4
   6   4   6
   6   4   5
   6   3   4
   7   3   2
   7   4   1
   6   5   3
   7   6   2
   8   7   2
   8   7   3
   8   6   4
   9   5   3
   0   4   2
   9   4   2
   8   5   1

Answer 1

Here first the data need to be entered in this way in excel

Then using the data solver we select two factor anova with replication

The analysis table so obtained is

Anova: Two-Factor With Replication
SUMMARY	drug1	drug2	placebo	Total
level1
Count	20	20	20	60
Sum	135	103	64	302
Average	6.75	5.15	3.2	5.033333
Variance	1.039474	1.923684	1.431579	3.558192
level2
Count	20	20	20	60
Sum	142	95	68	305
Average	7.1	4.75	3.4	5.083333
Variance	3.778947	1.671053	2.357895	4.891243
Total
Count	40	40	40
Sum	277	198	132
Average	6.925	4.95	3.3
Variance	2.378846	1.792308	1.85641
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	0.075	1	0.075	0.036877	0.848057	3.92433
Columns	263.5167	2	131.7583	64.78521	1.61E-19	3.075853
Interaction	3.15	2	1.575	0.774423	0.463379	3.075853
Within	231.85	114	2.033772
Total	498.5917	119

From the ANOVA table we can easily say that treatment effects are significant since p-value for columns is very small while the two levels of severity are insignificant given by sample value above. The interaction between severity level and treatment is also proving to be insignificant given by interaction term above.

It is to be noted that replication is not studied separately here since already replication which is a error term is included in the within source of variation or residuals.