﻿ Table 2.17 Expected average measures of persons

# Table 2.17 Expected average measures of persons

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

EXPECTED AVERAGE MEASURES FOR KID (scored) (BY CATEGORY SCORE)

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

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

|                          0                  1             |   15  1-3-2-4-1-3

|                          0                  1             |   16  1-4-2-3-1-4

|                          0                  1             |   17  1-4-3-1-2-4

|                                                           |

|                                                           |

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

|                                                           |

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

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

|                                                           |

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

|                                                           |

|                                                           |

|               0                1                          |   10  2-4-3-1

|                                                           |

|            0                  1                           |    8  1-4-2-3

|                                                           |

|        0                     1                            |    6  3-4-1

|        0                     1                            |    9  1-3-2-4

|       0                     1                             |    5  2-1-4

|       0                     1                             |    7  1-4-3-2

|    0                        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 2.17 is used for description, but can be 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 2.7 shows the measures that would be predicted to be observed for incorrect and correct responses if the persons responded exactly as the Rasch model predicts. "a" (an incorrect distractor) shows the average measure for persons in the sample who would be predicted to fail the item, and "d" (a correct distractor) shows the average measure for persons in the sample who would be predicted to succeed on the item. Compare this with Tables 2.5 and 2.6 for the empirical locations, and Table 2.2 for the sample-free locations.

TABLE 2.7 EXPECTED AVERAGE MEASURES FOR STUDENTS (scored) (ILLUSTRATED BY AN OBSERVED CATEGORY)

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

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

|                                  a                   d|   55  al07  newspaper

|                                         a             c   64  sa01  magazine

Table 2.17 is the same as Table 2.7, but the options are shown by their scored values, not by their codes in the data.

TABLE 2.17 EXPECTED AVERAGE MEASURES FOR STUDENTS (scored) (BY CATEGORY SCORE)

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

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

|                                  0                   1|   55  al07  newspaper

|                                         0             1   64  sa01  magazine

Polytomous items

Tables 2.7 & 2.17 plot the expected average person measures for each category score. It reflects how this sample were expected to use these categories. The plotted values cannot fall outside the range of the sample. Compare this with Tables 2.5 and 2.6 for the empirical locations, and Table 2.2 for the sample-free locations.

EXPECTED AVERAGE MEASURES FOR KID (scored) (BY CATEGORY SCORE)

-6       -4        -2         0         2         4         6

|---------+---------+---------+---------+---------+---------|  NUM   ACT

|                               0    1        2             |    5  FIND BOTTLES AND CANS

|                                                           |

|                               0   1        2              |   23  WATCH A RAT

|                                                           |

|                              0    1       2               |   20  WATCH BUGS

|                              0    1      2                |    4  WATCH GRASS CHANGE

|                              0   1       2                |    8  LOOK IN SIDEWALK CRACKS

|---------+---------+---------+---------+---------+---------|  NUM   ACT

-6       -4        -2         0         2         4         6

1

12 2 2117083563422342 111 1 1   1     1  KID

T      S      M      S     T

0    10 30 50 70 80 90               99  PERCENTILE

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