Table 2.1 Modal observed categories (most probable categories)

(controlled by T2SELECT=, MRANGE=, MTICK=, CATREF=)

 

Table 2.1: shows the most probable response on the latent variable, relative to each of the other responses. The most probable response for an item (row) is the category number shown to the left of the desired location on the x-axis. The items are shown vertically by difficulty distribution. The person distribution is shown below the plot.

 

MOST PROBABLE RESPONSE: MODE  (BETWEEN "0" AND "1" IS "0", ETC.) (ILLUSTRATED BY AN OBSERVED CATEGORY)

-5   -4    -3    -2    -1     0     1     2     3     4     5

|-----+-----+-----+-----+-----+-----+-----+-----+-----+-----|  NUM   TAP

0                                                          11   15  1-3-2-4-1-3

0                                                          11   16  1-4-2-3-1-4

0                                                          11   17  1-4-3-1-2-4

|                                                           |

|                                                           |

0                                                 1         1   14  1-4-2-3-4-1

|                                                           |

0                                          1                1   12  1-3-2-4-3

0                                         1                 1   13  1-4-3-2-4

|                                                           |

0                                  1                        1   11  1-3-1-2-4

|                                                           |

|                                                           |

0                    1                                      1   10  2-4-3-1

|                                                           |

0               1                                           1    8  1-4-2-3

|                                                           |

0         1                                                 1    6  3-4-1

0         1                                                 1    9  1-3-2-4

0      1                                                    1    5  2-1-4

0      1                                                    1    7  1-4-3-2

0   1                                                       1    4  1-3-4

|-----+-----+-----+-----+-----+-----+-----+-----+-----+-----|  NUM   TAP

-5   -4    -3    -2    -1     0     1     2     3     4     5

 

                            1

1   1   2   2    2    3     2       5     4    1    2          KID

 T            S             M            S            T

0      10       20   30    60      80    90        99          PERCENTILE

 

Multiple-choice items

 

this example, for item "al07", "a" (or any other incorrect option) is most probable up to 3.2 logits, when "d", the correct response, becomes most probable according to the Rasch model.

 

TABLE 2.1: MOST PROBABLE RESPONSE: MODE  (BETWEEN "0" AND "1" IS "0", ETC.) (ILLUSTRATED BY AN OBSERVED CATEGORY)

-4    -3     -2     -1      0      1      2      3      4

|------+------+------+------+------+------+------+------|  NUM   TOPIC

a                                                  d    d   55  al07  newspaper

a                                                 c     c   64  sa01  magazine

......

b     a                                                 a   12  nm07  sign on wall

a     d                                                 d   10  nm05  public place

|------+------+------+------+------+------+------+------|  NUM   TOPIC

-4    -3     -2     -1      0      1      2      3      4

 

      1        11 1111 111 212 3 2 12   12 1     1      2  STUDENTS

      T            S           M           S            T

      0        10  20  30 40 50 60 70  80 90           99  PERCENTILE

 

M = Mean, the average of the person measures, S = One Standard Deviation from the mean, T = Two P.SDs. from the mean. Percentile is percentage below the specified position.

 

Table 2.11 is the same as Table 1, but the options are shown by their scored values, not by their codes in the data.

 

TABLE 2.11: MOST PROBABLE RESPONSE: MODE  (BETWEEN "0" AND "1" IS "0", ETC.) (BY CATEGORY SCORE)

-4    -3     -2     -1      0      1      2      3      4

|------+------+------+------+------+------+------+------|  NUM   TOPIC

0                                                  1    1   55  al07  newspaper

0                                                 1     1   64  sa01  magazine

 


 

Polytomous items

 

Tables 2.1, The "Most Probable Response" Table, selected with CURVES=001, answers the question "which category is a person of a particular measure most likely to choose?" This is the most likely category with which the persons of logit (or user-rescaled) measure shown below would respond to the item shown on the left. The area to the extreme left is all "0"; the area to the extreme right is at the top category. Each category number is shown to the left of its modal area. If a category is not shown, it is never a most likely response. An item with an extreme, perfect (maximum possible) or zero (minimum possible), score is not strictly estimable, and is omitted here. Blank lines are used to help approximate the placement of the items on the latent variable.

 

This table presents in one picture the results of this analysis in a form suitable for inference. We can predict for people of any particular measure what responses they would probably make. "M" depicts an "average" person. The left "T" a low performer. The right "T" a high performer. Look straight up from those letters to read off the expected response profiles.

 

Table 2.1 to 2.7 reports with observed categories, i.e., those in the CODES= statement.

Table 2.11 to 2.17 report with scored categories, i.e., after IVALUE=, RESCORE=, KEY1=, etc., if any.

 

 MOST PROBABLE RESPONSE: MODE  (BETWEEN "0" AND "1" IS "0", ETC.)              

 NUM  ITEM       -5    -4    -3    -2    -1     0     1     2     3     4     5

                  -------------------------------------------------------------                             

   5 FIND BOTTLES 0                                      1          2         2

  20 WATCH BUGS   0                                   1          2            2

   8 LOOK IN SIDE 0                                  1          2             2

   7 WATCH ANIMAL 0                              1          2                 2

  17 WATCH WHAT A 0                         1          2                      2

deliberate space  |                                                           |

  21 WATCH BIRD M 0                   1          2                            2

  10 LISTEN TO BI 0               1          2                                2

  12 GO TO MUSEUM 0            1          2                                   2

  18 GO ON PICNIC 0      1          2                                         2

                  -------------------------------------------------------------                             

                 -5    -4    -3    -2    -1     0     1     2     3     4     5

               

                  1                            

PERSON                                1 2 1121 174135336222232221 11 1  1    11

                                       T      S      M       S      T          

 


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