The algorithm begins with one large cluster encompassing all objects to be clustered. In this case, the error sum of squares is 0. The program searches objects that can be grouped together while minimizing the increase in error sum of squares. Error sum of squares is computed as:
SSe = x²i - 1/n(Sxi)²
Ward's method creates clusters of near equal size, having hyperspherical shapes.
The WARD program begins in standard PC-MDS fashion, requesting a title, name of the input file and name of the output file. Following this input, the user provides information about four parameter values:
|
ENTER THE NUMBER OF VARIABLES TO BE INCLUDED IN THE ANALYSIS. (MAXIMUM=300) |
|
ENTER THE MAXIMUM NUMBER OF CLUSTERS TO BE PRINTED IN THE SOLUTION (MAXIMUM = 100) |
|
YOUR DATA WILL BE STANDARDIZED ON EACH VARIABLE BEFORE GROUPING | ||
| Press ENTER to STANDARDIZE data |
OR | Type 1 to NOT STANDARDIZE |
|
YOUR DATA MAY BE TRANSPOSED TO GROUP THE COLUMNS RATHER THAN THE ROWS | ||
| Press ENTER to NOT TRANSPOSE |
OR | Type 1 to TRANSPOSE DATA |
The first three options specifying the number of variables to be included in the analysis, the number of clusters to be printed, and the variable standardization option are straight forward. The option to transform the data simply allows clustering to be performed on the rows rather than on the columns.
The WARD program analyzes an objects by variables matrix of maximum size 300 x 300. The input for this data matrix is standard, excepting that WARD requires the user to specify an identification code for each row of the data matrix.
The first line of the data file must contain the format for reading the identification code and the variables.
The identification code is to be read as a variable 6 columns wide, followed by each variable, which is read in according to the user specified format.
In the sample data file, the FORTRAN format statement uses T and A editing to perform the required task. First, the program tabs (T58) over to column 58 where it starts reading the identification code as six columns of alphanumeric (A6) formatted data. Next, the program will tab back to column 1 (T1), where it will read the 20 variables at the locations specified in the format statement.
Input, therefore requires
(1) Format for reading Identification code: 6 columns maximum, followed by the format for reading the variables
(2) The data file
(T58,A6,T1,F3.0,6F2.0,F3.0,4F2.0,F4.0,F2.0,2F3.0,F4.0,2F3.0,F4.0)
125 0 1 2 0 0 4 08 1 0 0 1 300 5 38 46 184 72 53 350 1 ASTON MARTIN SALOON
110 0 1 2 0 0 2 12 1 1 0 1 380 5 39 37 177 78 45 354 2 FERRARI TESTAROSA
118 0 1 2 0 0 2 12 1 1 0 1 420 5 39 33 165 79 42 341 3 LAMBORGHINI CONTACH
057 0 1 2 0 0 2 04 1 1 0 1 215 4 36 27 169 73 45 194 4 LOTUS TURBO ESPIRIT
059 0 1 2 0 0 2 08 1 0 0 1 316 5 38 35 178 72 51 317 5 PORSCHE 928
........
........
........ REMAINDER OF 90 RESPONDENT'S DATA
........
........
012 1 0 3 1 0 5 04 1 0 1 1 085 2 34 29 165 71 63 132 85 JEEP CHEROKEE
010 1 0 2 0 0 4 04 1 0 1 1 085 3 36 29 121 66 72 141 86 JEEP WRANGLER
011 1 1 5 1 0 5 04 1 0 1 1 096 3 35 32 175 65 70 125 87 ISUZU TROOPER
010 1 1 2 0 0 4 04 1 0 1 1 109 3 34 33 157 66 71 142 88 MITSUBISHI MONTERRO
017 1 1 5 1 0 5 04 1 0 1 1 125 3 41 42 184 71 70 200 89 TOYOTA LANDCRUSER
007 1 1 2 0 0 4 04 1 0 1 1 063 3 33 21 135 60 66 074 90 SUZUKI SAMURAI
Sample Output
W A R D
HIERARCHICAL GROUPING USING WARDS METHOD
MATHEMATICAL ALGORITHM BY D. J. VELDMAN
PC - MDS VERSION
ANALYSIS TITLE:
AUTOMOBILE TEST DATA
DATA IS READ FROM FILE: WARD.DAT
OUTPUT FILE IS: TEST.PRN
INPUT FORMAT: (T58,A6,T1,F3.0,6F2.0,F3.0,4F2.0,F4.0,F2.0,2F3.0,F4.0,2F3.0,F4.0)
89 GROUPS AFTER COMBINING G 28 (N= 1) AND G 39 (N= 1). ERROR = .0081
88 GROUPS AFTER COMBINING G 56 (N= 1) AND G 58 (N= 1). ERROR = .1120
87 GROUPS AFTER COMBINING G 35 (N= 1) AND G 46 (N= 1). ERROR = .1238
86 GROUPS AFTER COMBINING G 27 (N= 1) AND G 32 (N= 1). ERROR = .1727
85 GROUPS AFTER COMBINING G 38 (N= 1) AND G 61 (N= 1). ERROR = .1798
84 GROUPS AFTER COMBINING G 74 (N= 1) AND G 80 (N= 1). ERROR = .2192
83 GROUPS AFTER COMBINING G 36 (N= 1) AND G 53 (N= 1). ERROR = .2312
82 GROUPS AFTER COMBINING G 35 (N= 2) AND G 40 (N= 1). ERROR = .2329
81 GROUPS AFTER COMBINING G 55 (N= 1) AND G 59 (N= 1). ERROR = .3160
80 GROUPS AFTER COMBINING G 28 (N= 2) AND G 35 (N= 3). ERROR = .4183
79 GROUPS AFTER COMBINING G 74 (N= 2) AND G 76 (N= 1). ERROR = .4664
78 GROUPS AFTER COMBINING G 78 (N= 1) AND G 79 (N= 1). ERROR = .5226
77 GROUPS AFTER COMBINING G 16 (N= 1) AND G 62 (N= 1). ERROR = .5355
76 GROUPS AFTER COMBINING G 55 (N= 2) AND G 57 (N= 1). ERROR = .6271
75 GROUPS AFTER COMBINING G 2 (N= 1) AND G 3 (N= 1). ERROR = .7033
74 GROUPS AFTER COMBINING G 66 (N= 1) AND G 68 (N= 1). ERROR = .7923
73 GROUPS AFTER COMBINING G 28 (N= 5) AND G 44 (N= 1). ERROR = 1.0049
72 GROUPS AFTER COMBINING G 28 (N= 6) AND G 38 (N= 2). ERROR = 1.1194
71 GROUPS AFTER COMBINING G 7 (N= 1) AND G 23 (N= 1). ERROR = 1.1472
70 GROUPS AFTER COMBINING G 74 (N= 3) AND G 78 (N= 2). ERROR = 1.1530
69 GROUPS AFTER COMBINING G 33 (N= 1) AND G 42 (N= 1). ERROR = 1.6070
68 GROUPS AFTER COMBINING G 55 (N= 3) AND G 60 (N= 1). ERROR = 1.6869
67 GROUPS AFTER COMBINING G 10 (N= 1) AND G 30 (N= 1). ERROR = 1.7874
66 GROUPS AFTER COMBINING G 8 (N= 1) AND G 22 (N= 1). ERROR = 1.8110
65 GROUPS AFTER COMBINING G 81 (N= 1) AND G 82 (N= 1). ERROR = 1.8197
64 GROUPS AFTER COMBINING G 74 (N= 5) AND G 77 (N= 1). ERROR = 1.9330
63 GROUPS AFTER COMBINING G 48 (N= 1) AND G 49 (N= 1). ERROR = 2.0177
62 GROUPS AFTER COMBINING G 83 (N= 1) AND G 84 (N= 1). ERROR = 2.1996
61 GROUPS AFTER COMBINING G 47 (N= 1) AND G 52 (N= 1). ERROR = 2.2140
60 GROUPS AFTER COMBINING G 26 (N= 1) AND G 54 (N= 1). ERROR = 2.2842
59 GROUPS AFTER COMBINING G 28 (N= 8) AND G 37 (N= 1). ERROR = 2.2853
58 GROUPS AFTER COMBINING G 12 (N= 1) AND G 15 (N= 1). ERROR = 2.4542
57 GROUPS AFTER COMBINING G 6 (N= 1) AND G 21 (N= 1). ERROR = 2.5476
56 GROUPS AFTER COMBINING G 7 (N= 2) AND G 29 (N= 1). ERROR = 2.5785
55 GROUPS AFTER COMBINING G 75 (N= 1) AND G 81 (N= 2). ERROR = 2.6287
54 GROUPS AFTER COMBINING G 63 (N= 1) AND G 64 (N= 1). ERROR = 2.6615
53 GROUPS AFTER COMBINING G 13 (N= 1) AND G 17 (N= 1). ERROR = 2.9148
52 GROUPS AFTER COMBINING G 16 (N= 2) AND G 19 (N= 1). ERROR = 2.9873
51 GROUPS AFTER COMBINING G 27 (N= 2) AND G 43 (N= 1). ERROR = 3.0071
50 GROUPS AFTER COMBINING G 11 (N= 1) AND G 18 (N= 1). ERROR = 3.3413
49 GROUPS AFTER COMBINING G 6 (N= 2) AND G 33 (N= 2). ERROR = 3.7436
48 GROUPS AFTER COMBINING G 87 (N= 1) AND G 89 (N= 1). ERROR = 3.8349
47 GROUPS AFTER COMBINING G 4 (N= 1) AND G 9 (N= 1). ERROR = 3.9014
46 GROUPS AFTER COMBINING G 88 (N= 1) AND G 90 (N= 1). ERROR = 3.9305
45 GROUPS AFTER COMBINING G 1 (N= 1) AND G 5 (N= 1). ERROR = 4.3061
44 GROUPS AFTER COMBINING G 34 (N= 1) AND G 45 (N= 1). ERROR = 4.4521
43 GROUPS AFTER COMBINING G 51 (N= 1) AND G 56 (N= 2). ERROR = 4.5931
42 GROUPS AFTER COMBINING G 83 (N= 2) AND G 85 (N= 1). ERROR = 4.6762
41 GROUPS AFTER COMBINING G 26 (N= 2) AND G 36 (N= 2). ERROR = 4.8473
40 GROUPS AFTER COMBINING G 14 (N= 1) AND G 24 (N= 1). ERROR = 4.9716
39 GROUPS AFTER COMBINING G 7 (N= 3) AND G 8 (N= 2). ERROR = 5.2206
38 GROUPS AFTER COMBINING G 65 (N= 1) AND G 72 (N= 1). ERROR = 5.2261
37 GROUPS AFTER COMBINING G 86 (N= 1) AND G 88 (N= 2). ERROR = 5.3701
36 GROUPS AFTER COMBINING G 25 (N= 1) AND G 27 (N= 3). ERROR = 5.4182
35 GROUPS AFTER COMBINING G 26 (N= 4) AND G 31 (N= 1). ERROR = 5.7392
34 GROUPS AFTER COMBINING G 13 (N= 2) AND G 20 (N= 1). ERROR = 6.3956
33 GROUPS AFTER COMBINING G 47 (N= 2) AND G 50 (N= 1). ERROR = 6.4252
32 GROUPS AFTER COMBINING G 63 (N= 2) AND G 66 (N= 2). ERROR = 7.3884
31 GROUPS AFTER COMBINING G 69 (N= 1) AND G 70 (N= 1). ERROR = 7.5707
30 GROUPS AFTER COMBINING G 10 (N= 2) AND G 11 (N= 2). ERROR = 9.0702
29 GROUPS AFTER COMBINING G 55 (N= 4) AND G 67 (N= 1). ERROR = 9.7529
28 GROUPS AFTER COMBINING G 28 (N= 9) AND G 48 (N= 2). ERROR = 9.8932
27 GROUPS AFTER COMBINING G 6 (N= 4) AND G 16 (N= 3). ERROR = 10.8787
26 GROUPS AFTER COMBINING G 73 (N= 1) AND G 87 (N= 2). ERROR = 10.9933
25 GROUPS AFTER COMBINING G 25 (N= 4) AND G 47 (N= 3). ERROR = 11.3449
24 GROUPS AFTER COMBINING G 74 (N= 6) AND G 75 (N= 3). ERROR = 11.9665
23 GROUPS AFTER COMBINING G 1 (N= 2) AND G 13 (N= 3). ERROR = 12.2107
22 GROUPS AFTER COMBINING G 4 (N= 2) AND G 41 (N= 1). ERROR = 12.2574
21 GROUPS AFTER COMBINING G 34 (N= 2) AND G 83 (N= 3). ERROR = 14.2278
20 GROUPS AFTER COMBINING G 51 (N= 3) AND G 55 (N= 5). ERROR = 14.4122
19 GROUPS AFTER COMBINING G 14 (N= 2) AND G 26 (N= 5). ERROR = 14.6862
18 GROUPS AFTER COMBINING G 25 (N= 7) AND G 28 (N= 11). ERROR = 17.8370
17 GROUPS AFTER COMBINING G 1 (N= 5) AND G 12 (N= 2). ERROR = 21.3998
16 GROUPS AFTER COMBINING G 63 (N= 4) AND G 65 (N= 2). ERROR = 21.4372
15 GROUPS AFTER COMBINING G 6 (N= 7) AND G 7 (N= 5). ERROR = 21.8961
14 GROUPS AFTER COMBINING G 34 (N= 5) AND G 86 (N= 3). ERROR = 23.6876
13 GROUPS AFTER COMBINING G 69 (N= 2) AND G 73 (N= 3). ERROR = 28.2190
12 GROUPS AFTER COMBINING G 14 (N= 7) AND G 51 (N= 8). ERROR = 33.5783
11 GROUPS AFTER COMBINING G 6 (N= 12) AND G 10 (N= 4). ERROR = 43.6128
10 GROUPS AFTER COMBINING G 2 (N= 2) AND G 4 (N= 3). ERROR = 45.0518
9 GROUPS AFTER COMBINING G 34 (N= 8) AND G 69 (N= 5). ERROR = 49.2468
G 1 (N= 7) ASTON PORSCH ROLLS MERCED ASTON JAGUAR JAGUAR
*******************************************************************************
G 2 (N= 5) FERRAR LAMBOR LOTUS FERRAR TOYOTA
*******************************************************************************
G 6 (N= 16) PORSCH MAZDA NISSAN CORVET LINCOL BMW 73 CADILL BMW 52 MASERA
TOYOTA MITSUB NISSAN FIREBI VOLVO MERKUR MERCED
*******************************************************************************
G 14 (N= 15) CADILL ACURA CHRYSL SHELBY FORD E DODGE BUICK CHEV. CHRYS.
HONDA DODGE MAZDA NISSAN SUBARU DODGE
*******************************************************************************
G 25 (N= 18) AUDI C HONDA ISUZU TOYOTA DODGE HONDA HYUNDI ISUZU MAZDA
MITSUB NISSAN SUBARU TOYOTA VW GOL YUGO G AUDI 5 TOYOTA TOYOTA
*******************************************************************************
G 34 (N= 13) CHEVRO FORD M NISSAN TOYOTA JEEP G S10 BL BRONCO JEEP C JEEP W
ISUZU MITSUB TOYOTA SUZUKI
*******************************************************************************
G 63 (N= 6) CHEV. DODGE FORD E CHEV A FORD A SUBURB
*******************************************************************************
G 71 (N= 1) VW VAN
*******************************************************************************
G 74 (N= 9) DODGE CHEV. ISUZU MAZDA MITSUB NISSAN TOYOTA DODGE JEEP C
*******************************************************************************
8 GROUPS AFTER COMBINING G 14 (N= 15) AND G 34 (N= 13). ERROR = 61.4199
G 1 (N= 7) ASTON PORSCH ROLLS MERCED ASTON JAGUAR JAGUAR
*******************************************************************************
G 2 (N= 5) FERRAR LAMBOR LOTUS FERRAR TOYOTA
*******************************************************************************
G 6 (N= 16) PORSCH MAZDA NISSAN CORVET LINCOL BMW 73 CADILL BMW 52 MASERA
TOYOTA MITSUB NISSAN FIREBI VOLVO MERKUR MERCED
*******************************************************************************
G 14 (N= 28) CADILL ACURA CHRYSL SHELBY CHEVRO FORD E FORD M DODGE BUICK
CHEV. CHRYS. HONDA DODGE MAZDA NISSAN SUBARU DODGE NISSAN
TOYOTA JEEP G S10 BL BRONCO JEEP C JEEP W ISUZU MITSUB TOYOTA
SUZUKI
*******************************************************************************
G 25 (N= 18) AUDI C HONDA ISUZU TOYOTA DODGE HONDA HYUNDI ISUZU MAZDA
MITSUB NISSAN SUBARU TOYOTA VW GOL YUGO G AUDI 5 TOYOTA TOYOTA
*******************************************************************************
G 63 (N= 6) CHEV. DODGE FORD E CHEV A FORD A SUBURB
*******************************************************************************
G 71 (N= 1) VW VAN
*******************************************************************************
G 74 (N= 9) DODGE CHEV. ISUZU MAZDA MITSUB NISSAN TOYOTA DODGE JEEP C
*******************************************************************************
7 GROUPS AFTER COMBINING G 1 (N= 7) AND G 2 (N= 5). ERROR = 76.0091
G 1 (N= 12) ASTON FERRAR LAMBOR LOTUS PORSCH FERRAR ROLLS MERCED ASTON
JAGUAR JAGUAR TOYOTA
*******************************************************************************
G 6 (N= 16) PORSCH MAZDA NISSAN CORVET LINCOL BMW 73 CADILL BMW 52 MASERA
TOYOTA MITSUB NISSAN FIREBI VOLVO MERKUR MERCED
*******************************************************************************
G 14 (N= 28) CADILL ACURA CHRYSL SHELBY CHEVRO FORD E FORD M DODGE BUICK
CHEV. CHRYS. HONDA DODGE MAZDA NISSAN SUBARU DODGE NISSAN
TOYOTA JEEP G S10 BL BRONCO JEEP C JEEP W ISUZU MITSUB TOYOTA
SUZUKI
*******************************************************************************
G 25 (N= 18) AUDI C HONDA ISUZU TOYOTA DODGE HONDA HYUNDI ISUZU MAZDA
MITSUB NISSAN SUBARU TOYOTA VW GOL YUGO G AUDI 5 TOYOTA TOYOTA
*******************************************************************************
G 63 (N= 6) CHEV. DODGE FORD E CHEV A FORD A SUBURB
*******************************************************************************
G 71 (N= 1) VW VAN
*******************************************************************************
G 74 (N= 9) DODGE CHEV. ISUZU MAZDA MITSUB NISSAN TOYOTA DODGE JEEP C
*******************************************************************************
6 GROUPS AFTER COMBINING G 6 (N= 16) AND G 74 (N= 9). ERROR = 87.9826
G 1 (N= 12) ASTON FERRAR LAMBOR LOTUS PORSCH FERRAR ROLLS MERCED ASTON
JAGUAR JAGUAR TOYOTA
*******************************************************************************
G 6 (N= 25) PORSCH MAZDA NISSAN CORVET LINCOL BMW 73 CADILL BMW 52 MASERA
TOYOTA MITSUB NISSAN FIREBI VOLVO MERKUR MERCED DODGE CHEV.
ISUZU MAZDA MITSUB NISSAN TOYOTA DODGE JEEP C
*******************************************************************************
G 14 (N= 28) CADILL ACURA CHRYSL SHELBY CHEVRO FORD E FORD M DODGE BUICK
CHEV. CHRYS. HONDA DODGE MAZDA NISSAN SUBARU DODGE NISSAN
TOYOTA JEEP G S10 BL BRONCO JEEP C JEEP W ISUZU MITSUB TOYOTA
SUZUKI
*******************************************************************************
G 25 (N= 18) AUDI C HONDA ISUZU TOYOTA DODGE HONDA HYUNDI ISUZU MAZDA
MITSUB NISSAN SUBARU TOYOTA VW GOL YUGO G AUDI 5 TOYOTA TOYOTA
*******************************************************************************
G 63 (N= 6) CHEV. DODGE FORD E CHEV A FORD A SUBURB
*******************************************************************************
G 71 (N= 1) VW VAN
*******************************************************************************
5 GROUPS AFTER COMBINING G 14 (N= 28) AND G 25 (N= 18). ERROR = 100.3185
G 1 (N= 12) ASTON FERRAR LAMBOR LOTUS PORSCH FERRAR ROLLS MERCED ASTON
JAGUAR JAGUAR TOYOTA
*******************************************************************************
G 6 (N= 25) PORSCH MAZDA NISSAN CORVET LINCOL BMW 73 CADILL BMW 52 MASERA
TOYOTA MITSUB NISSAN FIREBI VOLVO MERKUR MERCED DODGE CHEV.
ISUZU MAZDA MITSUB NISSAN TOYOTA DODGE JEEP C
*******************************************************************************
G 14 (N= 46) CADILL ACURA AUDI C CHRYSL HONDA ISUZU SHELBY TOYOTA CHEVRO
DODGE FORD E HONDA HYUNDI ISUZU MAZDA MITSUB NISSAN FORD M
SUBARU TOYOTA VW GOL YUGO G AUDI 5 DODGE TOYOTA BUICK CHEV.
CHRYS. HONDA DODGE MAZDA NISSAN SUBARU TOYOTA DODGE NISSAN
TOYOTA JEEP G S10 BL BRONCO JEEP C JEEP W ISUZU MITSUB TOYOTA
SUZUKI
*******************************************************************************
G 63 (N= 6) CHEV. DODGE FORD E CHEV A FORD A SUBURB
*******************************************************************************
G 71 (N= 1) VW VAN
*******************************************************************************
4 GROUPS AFTER COMBINING G 63 (N= 6) AND G 71 (N= 1). ERROR = 104.5126
G 1 (N= 12) ASTON FERRAR LAMBOR LOTUS PORSCH FERRAR ROLLS MERCED ASTON
JAGUAR JAGUAR TOYOTA
*******************************************************************************
G 6 (N= 25) PORSCH MAZDA NISSAN CORVET LINCOL BMW 73 CADILL BMW 52 MASERA
TOYOTA MITSUB NISSAN FIREBI VOLVO MERKUR MERCED DODGE CHEV.
ISUZU MAZDA MITSUB NISSAN TOYOTA DODGE JEEP C
*******************************************************************************
G 14 (N= 46) CADILL ACURA AUDI C CHRYSL HONDA ISUZU SHELBY TOYOTA CHEVRO
DODGE FORD E HONDA HYUNDI ISUZU MAZDA MITSUB NISSAN FORD M
SUBARU TOYOTA VW GOL YUGO G AUDI 5 DODGE TOYOTA BUICK CHEV.
CHRYS. HONDA DODGE MAZDA NISSAN SUBARU TOYOTA DODGE NISSAN
TOYOTA JEEP G S10 BL BRONCO JEEP C JEEP W ISUZU MITSUB TOYOTA
SUZUKI
*******************************************************************************
G 63 (N= 7) CHEV. DODGE FORD E CHEV A FORD A VW VAN SUBURB
*******************************************************************************
3 GROUPS AFTER COMBINING G 1 (N= 12) AND G 6 (N= 25). ERROR = 181.3109
G 1 (N= 37) ASTON FERRAR LAMBOR LOTUS PORSCH PORSCH MAZDA NISSAN FERRAR
CORVET LINCOL ROLLS MERCED ASTON BMW 73 JAGUAR CADILL BMW 52
JAGUAR MASERA TOYOTA MITSUB NISSAN FIREBI VOLVO TOYOTA MERKUR
MERCED DODGE CHEV. ISUZU MAZDA MITSUB NISSAN TOYOTA DODGE
JEEP C
*******************************************************************************
G 14 (N= 46) CADILL ACURA AUDI C CHRYSL HONDA ISUZU SHELBY TOYOTA CHEVRO
DODGE FORD E HONDA HYUNDI ISUZU MAZDA MITSUB NISSAN FORD M
SUBARU TOYOTA VW GOL YUGO G AUDI 5 DODGE TOYOTA BUICK CHEV.
CHRYS. HONDA DODGE MAZDA NISSAN SUBARU TOYOTA DODGE NISSAN
TOYOTA JEEP G S10 BL BRONCO JEEP C JEEP W ISUZU MITSUB TOYOTA
SUZUKI
*******************************************************************************
G 63 (N= 7) CHEV. DODGE FORD E CHEV A FORD A VW VAN SUBURB
*******************************************************************************
2 GROUPS AFTER COMBINING G 1 (N= 37) AND G 63 (N= 7). ERROR = 228.0302
G 1 (N= 44) ASTON FERRAR LAMBOR LOTUS PORSCH PORSCH MAZDA NISSAN FERRAR
CORVET LINCOL ROLLS MERCED ASTON BMW 73 JAGUAR CADILL BMW 52
JAGUAR MASERA TOYOTA MITSUB NISSAN FIREBI VOLVO TOYOTA MERKUR
MERCED CHEV. DODGE FORD E CHEV A FORD A VW VAN SUBURB DODGE
CHEV. ISUZU MAZDA MITSUB NISSAN TOYOTA DODGE JEEP C
*******************************************************************************
G 14 (N= 46) CADILL ACURA AUDI C CHRYSL HONDA ISUZU SHELBY TOYOTA CHEVRO
DODGE FORD E HONDA HYUNDI ISUZU MAZDA MITSUB NISSAN FORD M
SUBARU TOYOTA VW GOL YUGO G AUDI 5 DODGE TOYOTA BUICK CHEV.
CHRYS. HONDA DODGE MAZDA NISSAN SUBARU TOYOTA DODGE NISSAN
TOYOTA JEEP G S10 BL BRONCO JEEP C JEEP W ISUZU MITSUB TOYOTA
SUZUKI
*******************************************************************************
MATRIX OF GROUP MEMBERSHIP: LAST 10 GROUPS
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 2 2 2
1 1 1 1 1 1 1 2 2 2
1 1 1 1 1 1 1 2 2 2
1 1 1 1 1 1 1 1 1 1
1 1 1 2 2 2 2 3 3 3
1 1 1 2 2 2 2 3 3 3
1 1 1 2 2 2 2 3 3 3
....
....
.... REMAINING OBSERVATION GROUP
.... IDENTIFICATION INFORMATION
....
....
1 1 1 2 2 2 7 8 9 10
1 1 1 2 2 2 7 8 9 10
1 1 1 2 2 2 7 8 9 10
1 2 2 3 3 3 3 4 6 6
1 2 2 3 3 3 3 4 6 6
1 2 2 3 3 3 3 4 6 6
1 2 2 3 3 3 3 4 6 6
1 2 2 3 3 3 3 4 6 8
1 2 2 3 3 3 3 4 6 6
1 2 2 3 3 3 3 4 6 8
1 2 2 3 3 3 3 4 6 6
************** SUCCESSFUL COMPLETION OF CLUSTER ANALYSIS **************