HOW TO USE WARD


Ward's method for cluster analysis takes as input, a subject by variable matrix of maximum size (300 x 300). Ward's method is a hierarchical method designed to optimize the minimum variance within clusters.

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

Ward's method creates clusters of near equal size, having hyperspherical shapes.


PROGRAM INPUT

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.


Input Data Format

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


WARD SAMPLE DATA

(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    **************