Topic: TwoWay Anova
Data: psych.sav
Example: Physical Therapy and Psychiatric Treatment
Goal: Determine if a difference in Physical Therapy Treatment affects time to recovery, determine if a difference in Psychiatric Therapy Treatment affects time to recovery, and determine if an interaction exists.
Researchers at a trauma center wished to develop a program to help
braindamaged trauma victims regain an acceptable level of independence. An
experiment involving 72 subjects with the same degree of brain damage was
conducted. The objective was to compare different combinations of psychiatric
treatment and physical therapy. Each subject was assigned to one of 24
different combinations of four types of psychiatric treatment and six physical
therapy programs. There were three subjects in each combination. The response
variable is the number of months elapsing between initiation of therapy and time
at which the patient was able to function independently. The results were as
follows:

Psychiatric Treatment 

Physical Therapy Program 
1 
2 
3 
4 
I 
11.0 
9.4 
12.5 
13.2 

9.6 
9.6 
11.5 
13.2 

10.8 
9.6 
10.5 
13.5 
II 
10.5 
10.8 
10.5 
15.0 

11.5 
10.5 
11.8 
14.6 

12.0 
10.5 
11.5 
14.0 
III 
12.0 
11.5 
11.8 
12.8 

11.5 
11.5 
11.8 
13.7 

11.8 
12.3 
12.3 
13.1 
IV 
11.5 
9.4 
13.7 
14.0 

11.8 
9.1 
13.5 
15.0 

10.5 
10.8 
12.5 
14.0 
V 
11.0 
11.2 
14.4 
13.0 

11.2 
11.8 
14.2 
14.2 

10.0 
10.2 
13.5 
13.7 
VI 
11.2 
10.8 
11.5 
11.8 

10.8 
11.5 
10.2 
12.8 

11.8 
10.2 
11.5 
12.0 
Can one conclude on the basis of these data that
the different psychiatric treatment programs have different effects? Can one
conclude that the physical therapy programs differ in effectiveness? Can one
conclude that there is interaction between psychiatric treatment programs and
physical therapy programs?
Take care to enter data carefully. Make sure the dependent variable, the
variable of interest, is in one column. Then make a column for each factor of
interest. These columns will have numbers indicating what category for each
factor. In the above example, the dependent variable is time (in
months). Then factor one is physical therapy program. So that column (physical)
will have numbers 16 in it. The third column is for psychiatric treatment (psych).
It will have 14 in it.
To view line graph, click on Graphs\Line\Multiple\Define. Click time over
to the circle labeled Other summary function. Click the first treatment
variable (in this case physical) over to the Category Axis: box
and then click the second treatment variable (in this case psych) over
to the Define Lines: by box. Then hit OK.
Conclusion: It appears a difference is going on.
a. Physical Therapy Treatments: H_{0}: m
_{1}=m _{2}=m _{3} v.s. H_{a}:
At least two of the means differ.
If rejected, level of physical therapy was affecting time to recovery.
b. Psychiatric Therapy Treatments: H_{0}: m _{1}=m _{2}=m _{3}=m
_{4 }v.s. H_{a}: At least two of the means differ
If rejected, level of psychiatric therapy was affecting time to recovery.
c. Interaction: H_{0}: Interaction does not exist v.s. H_{a}:
Interaction does exist.
Click on Analyze\General Linear Model\Univariate. Place the variable of
interest (time) in the Dependent Variable box. Put the factors of
interest (physical, psych) in the Fixed Factors box. If one hits OK
now, SPSS will test with interaction. That is okay. If the interaction is
significant then you are done. If it is not, the model must be refit without
the interaction term. To do this click the Model button. Place a check
in the Custom circle. Click the factor variables (physical, psych)
over to the Model box. In the Build terms box, click on Main
effects.
Without intercept:
With intercept:
Conclusions: We reject the Null Hypothesis for all three since the Pvalues for
PHYSICAL, PSYCH, and PHYSICAL*PSYCH (interaction) are below 0.05.
PSYCH
PHYSICAL
Homogeneous Subsets
Conclusion: For Psych, reject the null for all 6 pairs using SNK, Tukey HSD, and Duncan. For Physical, there are 15 pairs. Fail to reject for pairs 16, 23, 24, 25, 26, 34, 35, 45. There are three subgroups.
Exercise
Background: Suppose the USGA tests four different brands (A,B,C,D) of golf
balls and two different clubs (driver, fiveiron) in a completely randomized
design. Each of the eight BrandClub combinations is randomly and independently
assigned to four experimental units, each experimental unit consisting of a
specific position in the sequence of hits by Iron Byron. The distance response
is recorded for each of the 32 hits. The objective of this research to see if
there is any difference in using balls from different brands.

BRAND 

Club 
A 
B 
C 
D 
Driver 
226.4 
238.3 
240.5 
219.8 

232.6 
231.7 
246.9 
228.7 

234.0 
227.7 
240.3 
232.9 

220.7 
237.2 
244.7 
237.6 
Fiveiron 
163.8 
184.4 
179.0 
157.8 

179.4 
180.6 
168.0 
161.8 

168.6 
179.5 
165.2 
162.1 

173.4 
186.2 
156.5 
160.3 