PA 2 Paper - Advanced Statistical Concepts and Business Analytics
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PA2-SPSSOutput2.rtfDISCRIMINANT
/GROUPS=Group(0 1)
/VARIABLES=Test_1 Test_2
/ANALYSIS ALL
/PRIORS SIZE
/STATISTICS=MEAN STDDEV UNIVF BOXM RAW CORR TABLE CROSSVALID
/PLOT=COMBINED SEPARATE MAP
/CLASSIFY=NONMISSING POOLED.
Discriminant
Analysis Case Processing Summary
Unweighted Cases
N
Percent
Valid
43
100.0
Excluded
Missing or out-of-range group codes
0
.0
At least one missing discriminating variable
0
.0
Both missing or out-of-range group codes and at least one missing discriminating variable
0
.0
Total
0
.0
Total
43
100.0
Group Statistics : Look for the difference
Group
Mean
Std. Deviation
Valid N (listwise)
Unweighted
Weighted
.00
Test_1
84.7500
4.24109
20
20.000
Test_2
79.1000
4.38778
20
20.000
1.00
Test_1
92.4348
3.47492
23
23.000
Test_2
84.7826
6.23740
23
23.000
Total
Test_1
88.8605
5.43175
43
43.000
Test_2
82.1395
6.10847
43
43.000
Tests of Equality of Group Means
Wilks' Lambda
F
df1
df2
Sig.
Test_1
.490
42.644
1
41
.000
Test_2
.780
11.593
1
41
.001
Pooled Within-Groups Matrices
Test_1
Test_2
Correlation
Test_1
1.000
.187
Test_2
.187
1.000
Box's Test of Equality of Covariance Matrices
Log Determinants
Group
Rank
Log Determinant
.00
2
5.846
1.00
2
6.007
Pooled within-groups
2
6.055
The ranks and natural logarithms of determinants printed are those of the group covariance matrices.
Test Results
Box's M
5.014
F
Approx.
1.582
df1
3
df2
936960.353
Sig.(p value)
.191
Tests null hypothesis of equal population covariance matrices.
Summary of Canonical Discriminant Functions
Eigenvalues
Function
Eigenvalue
% of Variance
Cumulative %
Canonical Correlation
1
1.161a
100.0
100.0
.733
a. First 1 canonical discriminant functions were used in the analysis.
Coefficient of multiple correlation®. Calculate R-square and interpret it
Wilks' Lambda
Test of Function(s)
Wilks' Lambda
Chi-square
df
Sig.(p value)
1
.463
30.822
2
.000
Structure Matrix
Function
1
Test_1
.947
Test_2
.494
Pooled within-groups correlations between discriminating variables and standardized canonical discriminant functions
Variables ordered by absolute size of correlation within function.
Canonical Discriminant Function Coefficients
Function
1
Test_1
.230
Test_2
.060
(Constant)
-25.380
Unstandardized coefficients
Y = -25.380 + 0.230*Test 1 score + 0.06* Test 2 Score
Functions at Group Centroids
Group
Function
1
.00
-1.128
1.00
.981
Unstandardized canonical discriminant functions evaluated at group means
(Confusion Matrix) Classification Results a,c
Group
Predicted Group Membership
Total
.00
1.00
Original
Count
.00
16
4
20
1.00
4
19
23
%
.00
80.0
20.0
100.0
1.00
17.4
82.6
100.0
Cross-validatedb
Count
.00
16
4
20
1.00
5
18
23
%
.00
80.0
20.0
100.0
1.00
21.7
78.3
100.0
a. 81.4% of original grouped cases correctly classified.
b. Cross validation is done only for those cases in the analysis. In cross validation, each case is classified by the functions derived from all cases other than that case.
c. 79.1% of cross-validated grouped cases correctly classified.
