﻿ Table 2.2 Mean categories (average or expected)

# Table 2.2 Mean observed categories (average or expected categories: Rasch-half-point thresholds )

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

EXPECTED SCORE: MEAN  (Rasch-score-point threshold, ":" indicates Rasch-half-point threshold) (ILLUSTRATED BY AN OBSERVED CATEGORY)

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

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

0                                                   0      :1   15  1-3-2-4-1-3

0                                                   0      :1   16  1-4-2-3-1-4

0                                                   0      :1   17  1-4-3-1-2-4

|                                                           |

|                                                           |

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

|                                                           |

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

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

|                                                           |

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

|                                                           |

|                                                           |

0             0      :     1                                1   10  2-4-3-1

|                                                           |

0        0      :     1                                     1    8  1-4-2-3

|                                                           |

0  0      :     1                                           1    6  3-4-1

0  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

Table 2.2 is used for inference:

Past-sample-dependent inference: If you expect the future person to be from a person sample exactly like the past sample (distribution, ability level, misfit, etc.) , then base your decisions on Table 2.7.

Past-sample-distribution-dependent inference: If you expect the future person to be from a person sample similar to the past sample (distribution, ability level, but not misfit) , then base your decisions on Table 2.5.

Past-sample-independent-as-possible: If you have no information about the future person, except that the latent variable will be the same as for the past sample, then base your decisions on Table 2.2.

Does the future repeat the past? Or is the future something entirely new? The truth is usually somewhere between these extremes.

Multiple-choice items

Table 2.2: shows the predicted average response on the latent variable. In this example, for item "al07", "a" (or any other incorrect option) is the predicted average response up to 3.2 logits, then "d", the correct response, becomes the average predictions. The ":" is at the transition from an average expected wrong response to an average expected "right" response, i.e., where the predicted average score on the item is 0.5, the Rasch-half-point thresholds. The "a" below "2" is positions where the expected average score on the item is 0.25. Similarly "d" would be repeated where the expected average score on the item is 0.75, according to the Rasch model.

TABLE 2.2 EXPECTED SCORE: MEAN  (":" INDICATES HALF-POINT THRESHOLD) (ILLUSTRATED BY AN OBSERVED CATEGORY)

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

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

a                                          a       :    d   55  al07  newspaper

a                                         a       :     c   64  sa01  magazine

Table 2.12 is the same as Table 2, but the options are shown by their scored values, not by their codes in the data.

TABLE 2.12 EXPECTED SCORE: MEAN  (":" INDICATES HALF-POINT THRESHOLD) (BY CATEGORY SCORE)

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

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

0                                          0       :    1   55  al07  newspaper

0                                         0       :     1   64  sa01  magazine

Polytomous items

Tables 2.2 & 2.12: In the "Expected Score" Table, the standard output (or selected with CURVES=010) answers the question "what is the average rating that we expect to observer for persons of a particular measure?" This rating information is expressed in terms of expected scores (with ":" at the half-point thresholds). Extreme scores are located at expected scores .25 score points away from the extremes. This plot also indicates the operational range of each item.

In this example of a 5 category rating scale, the operation range of the top item is indicated in red.

-5       -3        -1         1         3         5         7

|---------+---------+---------+---------+---------+---------|  NUM   ITEM

1                        1  :   2  : 3 :  4    :   5        5   13  M. STAIRS

Operational range: ^-------------------------^

|---------+---------+---------+---------+---------+---------|  NUM   ITEM

-5       -3        -1         1         3         5         7

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