﻿ Table 2.15 Observed average measures for categories

# Table 2.15 Observed average measures of persons for scored categories (empirical averages)

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

OBSERVED 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 2.155 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.

To plot Table 2.5 in Excel:

The numbers for the Y-axis are in IFILE= (MEASURE)
The number for the X-axis are in DISFILE= (AVGE MEAS)

Multiple-choice items

Table 2.5 shows the average measures of persons choosing wrong distractors (illustrated by one of the wrong distractors, "a") and the average measures or persons choosing a correct distractor (illustrated by one of the correct distractors, "d").

TABLE 2.5 OBSERVED 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 2.15 is the same as Table 5, but the options are shown by their scored values, not by their codes in the data.

TABLE 2.15 OBSERVED 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 2.5 & 2.15 plot the observed average person measures for each scored category. It reflects how this sample used these categories. The plotted values cannot fall outside the range of the sample.

The rating-scale categories, such as 0, 1 and 2, are plotted for each item (y-axis) at the average measure of the persons who responded in that category (x-axis).

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

-2     -1       0       1       2       3       4       5

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

|                       000102                          |    5  FIND BOTTLES AND CANS

|                                                       |

|                       000102                          |   23  WATCH A RAT

|                                                       |

|                   00  01         02                   |   20  WATCH BUGS

|                 00    01               02             |    4  WATCH GRASS CHANGE

|                   0001                02              |    8  LOOK IN SIDEWALK CRACKS

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

-2     -1       0       1       2       3       4       5

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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