Practice Problem
Control
10
7
6
8
5
7.2
Mean
REBT
9
8
13
8
9
9.4
Cognitive
9
10
15
14
14
12.4
Psychoanalysis
16
14
19
15
16
16
IV = Depressed individuals were randomly assigned to receive either rational emotive behavioral
therapy (REBT), cognitive therapy, psychoanalysis or no therapy (control).
DV = number of weeks until depressive episode passed.
Questions: Is there a difference between the forms of treatment? Which treatment seems to be
the best?
1. On the last page, set up the columns you need (make sure the comparisons are
orthogonal)
2. Solve for SS y and x
SS (Y )   Y
2
SS ( X i )   X
Y 

2
N
2
i
 X 

SP(YX i )   YX i 
2
i
N
  Y   X 
SP( X i X j )   X i X j 
i
N
 Xi  X j 
N
3. Solve for SS regression, residual and total
SS(Total )  SS(Y )
SS( regression )  SS( reg . X i )  SS( reg . X j )

2
SP(YX i ) 2 SP(YX j )

SS ( X i )
SS ( X j )
SS( residual )  SS(Total )  SS( regression )
bi 
[ SP(YX i )][ SS ( X j )] [ SS ( X k )]  [ SP(YX j )] [ SP(YX k )]
[ SS ( X i )][ SS ( X j )] [ SS ( X k )]  [ SP( X i X j )]2 [ SP( X i X k )]2
a  Y  b1 ( X 1 )  b2 ( X 2 ) 
4. Solve for degrees of freedom
df (Total )  N  1 
df ( reg )  # predictors
df ( res )  N  a 
[ SP( X j X k )]2
5. Interpret the b’s we calculated
6. Fill out the ANOVA summary table
Source
SS
DF
Regression
Residual
Total
MS
F
7. For comparison the SPSS output gives us:
ANOVA
W EEKS
Between Groups
W ithin Groups
Total
Sum of
Squares
218.550
75.200
293.750
df
3
16
19
Mean Square
72.850
4.700
F
15.500
Sig.
.000
Control
REBT
Cognitive
Psychoanalysis
Y
10
7
6
8
5
9
8
13
8
9
9
10
15
14
14
16
14
19
15
16
Sum 225
X1
X2
X3
Y2 X12 X22 X32 Y*X1 Y*X2 Y*X3 X1*X2 X1*X3 X2*X3
100
49
36
64
25
81
64
169
64
81
81
100
225
196
196
256
196
361
225
256
2825