Table 22 Sorted observed data matrix - Guttman scalogram

(controlled by LINELENGTH=).

 

Table 22.1 Sorted observed data matrix - Guttman scalogram

 

GUTTMAN SCALOGRAM OF RESPONSES:

KID |ACT                      

   |1111112 1 221  121    22  

   |8920311251427634569784035

   |-------------------------

 2 +2222222222222222222222222  M ROSSNER, LAWRENCE F.

41 +2222222222222222222222212  F FATALE, NATASHA

34 +2222222222222222222222211  F PASTER, RUTH

17 +2222222222222222222222210  F SCHATTNER, GAIL

50 +2222222222222222222122111  M DOEPPNER, TOM

45 +2222222222222222222221200  F MCLOUGHLIN, BILLY

 7 +2222222222222222220220220  M WRIGHT, BENJAMIN

16 +2222222222222222222111101  F BUFF, MARGE BABY

48 +2222222222222222212221100  M CHAZELLE, BERNIE

25 +2222222222222222212021101  F SEILER, KAREN

59 +2222222222222222212111020  F CLAPP, LB

18 +2222222222222222212102100  M ERNST, RICHARD MAX

The observations are printed in order of person and item measures as a Guttman Scalogram, with most able persons listed first, the easiest items printed on the left. This scalogram shows the extent to which a Guttman pattern is approximated. See also Guttman Coefficient of Reproducibility.

Table 22.2 Guttman scalogram of zoned responses

 

  GUTTMAN SCALOGRAM OF ZONED RES

KID |ACT                        

    |1111112 1 221  121    22  

    |8920311251427634569784035  

    |-------------------------  

  2 +2222222222222222222222222  M ROSSNER, LAWRENCE F.

 41 +22222222222222222222222A2  F FATALE, NATASHA  

 34 +22222222222222222222222AA  F PASTER, RUTH  

 17 +22222222222222222222222A@  F SCHATTNER, GAIL  

 50 +2222222222222222222A22A11  M DOEPPNER, TOM  

 45 +222222222222222222222AB@@  F MCLOUGHLIN, BILLY  

  7 +222222222222222222@2B@BB@  M WRIGHT, BENJAMIN  

 16 +2222222222222222222A111@1  F BUFF, MARGE BABY  

 48 +22222222222222222A22B11@@  M CHAZELLE, BERNIE  

 25 +22222222222222222A2@B11@1  F SEILER, KAREN  

 59 +22222222222222222A2A11@B@  F CLAPP, LB  

 18 +22222222222222222A21@B1@@  M ERNST, RICHARD MAX

The scalogram is that of Table 22.1, but with each observation marked as to whether it conforms with its expectation or not. Observations within 0.5 rating points of their expectation are deemed to be in their expected categories, and are reported with their category values, e.g., '1', '2', etc. These ratings support the overall inferential relationship between observations and measures. Observations more than 0.5 rating points away from their expectations, i.e., in a "wrong" category, are marked with a letter equivalent: 'A' = '0','B' = '1','C' = '2', etc. These contradict observation-to-measure inferences. The proportion of in- and out-of-category observations are reported by the COHERENCE statistics in Table 3.2.

Table 22.3 Guttman scalogram of original response codes

 

   GUTTMAN SCALOGRAM OF ORIGINAL RESPONSES:

 KID |ACT

     |1111112 1 221  121    22

     |8920311251427634569784035

     |-------------------------

   2 +2222222222222222222222222  M ROSSNER, LAWRENCE F.

  41 +2222222222222222222222212  F FATALE, NATASHA

  34 +2222222222222222222222211  F PASTER, RUTH

  17 +2222222222222222222222210  F SCHATTNER, GAIL

  50 +2222222222222222222122111  M DOEPPNER, TOM

  45 +2222222222222222222221200  F MCLOUGHLIN, BILLY

   7 +2222222222222222220220220  M WRIGHT, BENJAMIN

  16 +2222222222222222222111101  F BUFF, MARGE BABY

  48 +2222222222222222212221100  M CHAZELLE, BERNIE

  25 +2222222222222222212021101  F SEILER, KAREN

  59 +2222222222222222212111020  F CLAPP, LB

  18 +2222222222222222212102100  M ERNST, RICHARD MAX

The observations are printed in order of person and item measures, with most able persons listed first, the easiest items printed on the left. This scalogram shows the original codes in the data file.

 

 

Interpreting a Scalogram. Example of Table 22.1 for Example0.txt.  A scalogram orders the persons from high measure to low measure as rows, and the items from low measure (easy) to high measure (hard) as columns. The green boxes show the probabilistic advance from responses in high categories on the easy items to responses in low categories on the hard items.

 

Top left corner: where the “more able” (more liking) children respond to the “easier” (to like) items. So we expect to see responses of “Like” (2). We do! Unexpected responses in this area influence the Outfit statistics more strongly.

 

Top right corner: (blue box) where the “most liking” children and the “hardest to like items”  meet - you can see some ratings of 1.

 

Bottom right corner: where “less able” (less liking) children respond to the “harder” (to like) items. So we expect to see responses of “Dislike” (0). But do we?? Something has gone wrong! There are 1’s and 2’s where we expected all 0’s. Unexpected responses in this area influence the Outfit statistics more strongly.

 

Diagonal transition zone: Between the red diagonals lies the transition zone where we expect 1’s. In this zone Infit is more sensitive to unexpected patterns of responses. More categories in the rating scale means a wider transition zone. Then the transition zone can be wider than the observed responses.

 

Example of Table 22.2. Five categories: 0,1,2,3,4. Categories in the wrong scores bands are shown as @ (=0), A (=1), B (=2), C (=3), D (=4). The 5 score bands have different colors here. Band 0 is yellow. Band 1 is green. Band 2 is blue. Band 3 is white. Band 4 is mauve.

 

 

Example of Table 22.3. Here is the Scalogram for Example 5, a computer-adaptive, multiple-choice test. The original responses are shown.

 

GUTTMAN SCALOGRAM OF ORIGINAL RESPONSES:

STUDENT |TOPIC

        |  11  3  11 1 3212232212132425654421434145625 36555366356465464633654

        |640215038189677748390992315641640517264579268221076889430372139553458

        |---------------------------------------------------------------------

      3 +                                     d   b     c    db   d   c b  cd   S   STA

      6 +                              c          b     c    d     d  c    cd   S   CHU

     27 +                           c  c  c             c   cbb  a dd c b  dd   S   ERI

      4 +                              c     b     a d  cb c dd    d  b d  dc   S   CHE

      9 +              d    c      a a cbc     c  ba b dca c db   dc bbdbb   c  S   MEL

     25 +              c  b       d c   bc   a     a d  a  c dba  d   cbccbd c  S   DAN

     24 +          a          d      ac      b     c d      c  b a    a         AP  SAR

     12 +              c  b         c    c   b b     b   b a    cb  cc c        A   ALL

     28 +                   c       c a bcc  b c acc d   b bc   b c bdcb     d  IH  GRE

     21 + b       c b a     c  b     a  bc  bb  ab a db bbd      cc   b     b   AP  MIL

     11 +   a  d  c b  cc  cbad  d  ca c   d   ca ba b ac    bac   bc  d c cc   S   CHR

     17 +      d     d c    c      acac cac  b c a     a  b    c  c bc b ac ac  IH  FRA

      7 +      d  c  d ccaaac d bcd ca    b cb c b  a  a a  a  ab   b    bb ac  IH  JAN

      1 +              c    c      ab    ca   dc b       a  a     c    a     c  IM  CAT

     20 +     bd    b   c b cad  cd  a        bac      b    a  b     c    b     IL  JAM

     22 +  d       a d c  b   d  cdabcc bbc cbdb a     a dbac     c dc   d  a   IM  BAR

     30 +      d   a  a cab cdd   d  d      da      c       d  c     c   db     IL  HOL

     14 + b    d  c  db caa caa   da c   dcd  b c   a cd    d     c  c   d  b   IL  TAK

     23 +      d  cab  dcaa cadbbbba a   c a db     c  b    a     c  c   ab  c  IL  MEI

     26 +      d   a   cc b  ac  cdd b   a  d db a  d       b  d     d   cb  c  IL  MIT

     15 +  d   d   a  a caba  dcbddc c      d b     b  a       c         bb     NH  MAR

     13 +  d   d     d  c bac dc  bd      d dcd     d  a    d  d  c  b    b     NH  KEL

     29 +b dbd  bdcabd  baaacbd  c d c     ab   a     dd          d    c  b  c  NH  RIC

      8 +bbdadbd abaa acbcbccacbcadab   c   d cdab  a  d    a  a  c  c   cb     IL  ROB

     16 +b da b bdccbbbcccbadaabba ccd   c ac bd a  a           b               NM  HEL

     18 +b  a  a d  bca bc a   cccc  a     db   c   a  a       d         d      NH  JOE

     10 +b badbdbcccadacbababcda cba a   a acd  a   d       a             b     NM  JON

     19 +bbdad   dacbdb cabdbc  c ad     d ab b     c  a    b                   NM  THE

      2 +bbda  a d aaaa  c c a   cbd       ab   a   d                    c      NM  KAT

      5 +    aad a            ab           a  b       a                         NL  SMI

        |---------------------------------------------------------------------

        |  11  3  11 1 3212232212132425654421434145625 36555366356465464633654

        |640215038189677748390992315641640517264579268221076889430372139553458

 

Example: To display Scalogram response strings on the person Tables 6, 17, 18,19.

1. Perform your standard Winsteps analysis.

2. Output Table 22, with a LINELENGTH= big enough for all observations to be on one line.

3. Save Table 22 to your Desktop (or wherever).

4. Open the Table 22 file in software that can do a rectangular copy (NotePad++, TextPad, Word, etc.)

5. Open your Winsteps data file using the same rectangular-copy software.

6. Rectangular copy the Scalogram immediately adjacent to the person labels.

7. Adjust Winsteps control NAMELENGTH= etc for the new data file format.

8. Save the control and data file(s)

9. Perform your revised Winsteps analysis.

10. Table 6 should now display the Scalogram as part of the person label.


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