Table 2.3 Median observed categories (cumulative category probabilities: Rasch-Thurstone thresholds)

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

 

Multiple-choice items

 

Table 2.3 shows the 50% cumulative probability points, the Rasch-Thurstone thresholds. 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) (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) (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 2.3 & 2.13: The "Cumulative Probability" Table: Rasch-Thurstone thresholds, selected with CURVES=001, answers the question "whereabouts in the category ordering is a person of a particular measure located?" This information is expressed in terms of median cumulative probabilities (the point at which the probability of scoring in or above the category is .5).

 

50% CUMULATIVE PROBABILITY: MEDIAN (equal-cumulative-probability Rasch-Thurstone thresholds) (ILLUSTRATED BY AN OBSERVED CATEGORY)

-6       -4        -2         0         2         4         6

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

0                                    1         2            2    5  FIND BOTTLES AND CANS

|                                                           |

0                                   1         2             2   23  WATCH A RAT

|                                                           |

0                                 1         2               2   20  WATCH BUGS

0                                 1         2               2    4  WATCH GRASS CHANGE

0                                1         2                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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Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
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