DATA MATRIX:
21.0 19.0 22.0 24.0
19.0 30.0 40.0 20.0
22.0 42.0 29.0 17.0
20.0 82.0 65.0 22.0
23.0 60.0 80.0 19.0
EXPECTED FREQUENCIES:
13.36 29.64 30.02 12.98
16.93 37.57 38.05 16.45
17.09 37.91 38.40 16.60
29.36 65.14 65.98 28.52
28.27 62.73 63.54 27.46
X-SQUARE = 43.33 L-SQUARE = 41.94 D.O.F. = 12
p-value = 0.0
Model Diagnostics
=================
Warning : the model does not fit the data matrix, p-value smaler than 0.05
STANDARDIZED RESIDUALS MATRIX:
2.09 -1.95 -1.46 3.06
0.50 -1.23 0.32 0.88
1.19 0.66 -1.52 0.10
-1.73 2.09 -0.12 -1.22
-0.99 -0.34 2.07 -1.61
ANOAS for rows
Attempt 1: Rows 1 and 2
Analysis of row asociation
===========================
Sub L Statistics dF P-Value Interpretation
=== ============= == ======= ==============
S1 5.54 3 0.14 within {1,2}
Mk 36.40 9 0.0 betwen subsets
==============================================================
N 41.94 12 0.0 overal
Mk colapsed matrix:
(1,2) 40 49 62 4
(3) 2 42 29 17
(4) 0 82 65 2
(5) 23 60 80 19
STANDARDIZED RESIDUALS MATRIX:
1.76 -2.22 -0.74 2.69
1.19 0.66 -1.52 0.10
-1.73 2.09 -0.12 -1.22
-0.99 -0.34 2.07 -1.61
Number of significant residuals : 6
Attempt 2: rows 2 and 5
Analysis of row asociation
===========================
Sub L Statistics dF P-Value Interpretation
=== ============= == ======= ==============
S1 5.68 3 0.13 within {2,5}
Mk 36.25 9 0.0 betwen subsets
==============================================================
N 41.94 12 0.0 overal
Mk colapsed matrix:
(1) 21 19 2 24
(2,5) 4 0 10 39
(3) 2 42 29 17
(4) 0 8 65 2
STANDARDIZED RESIDUALS MATRIX:
2.09 -1.95 -1.46 3.06
-0.48 -1.03 1.83 -0.74
1.19 0.66 -1.52 0.10
-1.73 2.09 -0.12 -1.22
Number of significant residuals : 6
Attempt 3: rows 1,2,5
Analysis of row asociation
===========================
Sub L Statistics dF P-Value Interpretation
=== ============= == ======= ==============
S1 23.33 6 0.00 within {1,2,5}
Mk 18.60 6 0.0 betwen subsets
==============================================================
N 41.94 12 0.00 overall
Mk colapsed matrix:
(1,2,5) 63 109 142 63
(3) 2 42 29 17
(4) 20 82 65 2
STANDARDIZED RESIDUALS MATRIX:
0.58 -1.84 0.91 0.81
1.19 0.66 -1.52 0.10
-1.73 2.09 -0.12 -1.22
Number of significant residuals : 3
NOAS for columns : Cols 1 and 4
Analysis of column asociation
==============================
Sub L Statistics dF P-Value Interpretation
=== ============= == ======= ==============
S1 1.30 4 0.86 within {1,4}
Mk 40.63 8 0.0 betwen subsets
==============================================================
N 41.94 12 0.00 overall
Mk colapsed matrix:
(1,4) (2) (3)
45 19 22
39 30 40
39 42 29
42 82 65
42 60 80
STANDARDIZED RESIDUALS MATRIX:
3.64 -1.95 -1.46
0.97 -1.23 0.32
0.92 0.66 -1.52
-2.09 2.09 -0.12
-1.84 -0.34 2.07
Number of significant residuals : 6
**************************************************
FINALY COLAPSED TABLE: OVER ROWS 1 and 2 ONLY
ROW PRPORTIONS
MW W S B
(1,2) .205 .251 .318 .226
3 .200 .382 .264 .154
4 .106 .434 .344 .116
5 .126 .330 .440 .104
1. Selecting a model
Model With Lambda Coeficients : Independent 1 2 3 (2,1) (3,1) (3,2)
D.O.F = 2 L-Squared = 0. 19 p-value 0.52
Model Diagnostics
=================
The model fits the data matrix
Model With Lambda Coeficients : Independent 1 2 3 (3,1) (3,2)
D.O.F = 4 L-Squared = 0. 83 p-value 0.53
Model Diagnostics
=================
The model fits the data matrix
Model With Lambda Coeficients : Independent 1 2 3 (2,1) (3,2)
D.O.F = 3 L-Squared = 21.18 p-value 0.0
Model Diagnostics
=================
Warning : the model does not fit the data matrix, p-value smaller than 0.05
Model With Lambda Coeficients : Independent 1 2 3 (3,2)
D.O.F = 5 L-Squared = 21.92 p-value 0.0
Model Diagnostics
=================
Warning : the model does not fit the data matrix, p-value smaller than 0.05
Model With Lambda Coeficients : Independent 1 2 3 (2,1) (3,1)
D.O.F = 4 L-Squared = 6.55 p-value 0.35
Model Diagnostics
=================
The model fits the data matrix
Model With Lambda Coeficients : Independent 1 2 3 (3,1)
D.O.F = 6 L-Squared = 17.62 p-value 0.01
Model Diagnostics
=================
The model fits the data matrix
Model With Lambda Coeficients : Independent 1 2 3 (2,1)
D.O.F = 5 L-Squared = 21.36 p-value 0.0
Model Diagnostics
=================
Warning : the model does not fit the data matrix, p-value smaller than 0.05
Model With Lambda Coeficients : Independent 1 2 3
D.O.F = 7 L-Squared = 25.48 p-value 0.0
Model Diagnostics
=================
Warning : the model does not fit the data matrix, p-value smaller than 0.05
Conclusion:
The prefered model is
Model With Lambda Coeficients : Independent 1 2 3 (3,1) (3,2)
2. Analyzing two-way association
(a) Z vs. Y
Independence Results
=========================
DATA MATRIX:
X-SQUARE = 20.80 L-SQUARE = 21.17 D.O.F. = 1
p-value = 0.0
Model Diagnostics
=================
Warning : the model does not fit the data matrix, p-value smaller than 0.05
TAU(Y|X) = 0.10 TAU(X|Y) = 0.10
STANDARDIZED RESIDUALS MATRIX:
-2.36 2.39
2.17 -2.20
Number of significant residuals : 4
--------------------------------------------------------
(b) X vs. Y
Independence Results
=========================
DATA MATRIX:
Y
1 2
1 24.0 35.0
X 2 43.0 46.0
3 36.0 19.0
EXPECTED FREQUENCIES:
29.94 29.06
45.16 43.84
27.91 27.09
X-SQUARE = 7.36 L-SQUARE = 7.46 D.O.F. = 2
p-value = 0.02
Model Diagnostics
=================
Warning : the model does not fit the data matrix, p-value smaller than 0.05
TAU(Y|X) = 0.04 TAU(X|Y) = 0.02
STANDARDIZED RESIDUALS MATRIX:
-1.08 1.10
-0.32 0.33
1.53 -1.55
Number of significant residuals : 0