﻿ Table 2 Multiple-choice distractor plot

# Table 2 Multiple-choice distractor plot

(controlled by T2SELECT=, MRANGE=)

The codes for the response options (distractors) are located according to the measures corresponding to them. Each subtable is presented two ways: with the response code itself (or one of them if several would be in the same place), e.g., Table 2.1, and with the score corresponding to the option, e.g. Table 2.11 (numbered 10 subtables higher).

Table 2 for polytomous items.

Table 2.1: shows the most probable response on the latent variable. In 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

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

Table 2.3 shows the Rasch-Thurstone thresholds = 50% cumulative probability points. The lower category ("a" and other wrong answers) has a greater than 50% probability of being observed up to 3.2 logits, when "d", the correct answer, has a higher than 50% probability.

TABLE 2.3 50% CUMULATIVE PROBABILITY (RASCH-THURSTONE THRESHOLD): MEDIAN (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

Table 2.13 is the same as Table 3, but the options are shown by their scored values, not by their codes in the data.

TABLE 2.13 50% CUMULATIVE PROBABILITY (RASCH-THURSTONE THRESHOLD): MEDIAN (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

Table 2.4 shows the item difficulties (or more generally the Rasch-Andrich thresholds) coded by the option of the higher category. For item "al07" this is "d", the correct option.

TABLE 2.4 STRUCTURE MEASURES (RASCH-ANDRICH THRESHOLDS: equal-adjacent-probability thresholds) (ILLUSTRATED BY AN OBSERVED CATEGORY)

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

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

|                                                  d    |   55  al07  newspaper

|                                                 c     |   64  sa01  magazine

Table 2.14 is the same as Table 4, the Rasch-Andrich thresholds, but the options are shown by their scored values, not by their codes in the data.

TABLE 2.14 STRUCTURE MEASURES (RASCH-ANDRICH THRESHOLDS: equal-adjacent-probability thresholds) (BY CATEGORY SCORE)

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

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

|                                                  1    |   55  al07  newspaper

|                                                 1     |   64  sa01  magazine

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

Table 2.6, shown first from the Diagnosis menu, shows the average measures from Table 14.3 of the persons choosing each distractor. "m" usually indicates the average measure of persons with missing data. Table 2.6 shows the average ability of the group of examinees who chose each option. Table 2.15 (above) shows the average ability of the people who got an item right and wrong. Table 2.5 (above again) has the right and wrong scoring illustrated with specific MCQ options. If there are more than one correct or incorrect option, only one of each is shown.

TABLE 2.6 OBSERVED AVERAGE MEASURES FOR STUDENTS (unscored) (BY OBSERVED CATEGORY)

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

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

|                         m    ab     c                 d   55  al07  newspaper

|                          m                d        c  |   64  sa01  magazine

Code for unidentified missing data: m

Table 2.16 is the same as Table 6, but the options are shown by their scored values, not by their codes in the data.

TABLE 2.16 OBSERVED AVERAGE MEASURES FOR STUDENTS (unscored) (BY CATEGORY SCORE)

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

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

|                         m    00     0                 1   55  al07  newspaper

|                          m                0        1  |   64  sa01  magazine

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.

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 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

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