﻿ Rating scale conceptualization

# Rating scale conceptualization

There are several ways of conceptualizing a rating scale item. They all contain exactly the same measurement information, but communicated in different ways

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|CATEGORY   OBSERVED|OBSVD SAMPLE|INFIT OUTFIT|| ANDRICH |CATEGORY|

|LABEL SCORE COUNT %|AVRGE EXPECT|  MNSQ  MNSQ||THRESHOLD| MEASURE|

|-------------------+------------+------------++---------+--------          |

|  0   0     378  20|  -.87 -1.03|  1.08  1.19||  NONE   |( -2.07)| 0 Dislike

|  1   1     620  34|   .13   .33|   .85   .69||    -.86 |    .00 | 1 Neutral

|  2   2     852  46|  2.24  2.16|  1.00  1.47||     .86 |(  2.07)| 2 Like

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0. Distribution of frequencies of observation in each category. For a rating-scale for which inferences will be made at the category level, we like to see a uniform process at work. When applied to a sample, this would produce a smooth distribution of category frequencies. Unimodal without sharp peaks or troughs. No statistical test is intended, but merely Berkson's "inter-ocular traumatic test" (= what hits you between the eyes).

1. If you conceptualize the rating scale in terms of the probability of individual categories (Andrich's approach), then the  Andrich Thresholds are of interest. The Andrich thresholds are the points at which adjacent categories are equally probable.

CATEGORY PROBABILITIES MODES - Andrich Thresholds at intersections

P       -------------------------------------------------------------

R  1.0  00000000                                             22222222

O               0000000                               2222222

B   .8                 000                         222

A                         000                   222

B   .6                       00               22

I   .5                         00*111111111*22

L   .4                        111|00     22|111

I                          111   |  00 22  |   111

T   .2                 1111      |  22*00  |      1111

Y               1111111        22222     00000        1111111

.0  ********222222222222222  |         |  000000000000000********

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

PERSON [MINUS]  ITEM  MEASURE

2. If you conceptualize the rating scale in terms of average ratings on the model (predicted) item characteristic curve (ICC), then "Category measures" are of interest. The "Category Measures" are the points on the latent variable at which the expected score on the item equals the category number. The Rasch-half-point thresholds define the ends of each category interval.  These are shown in Table 12.5.

EXPECTED SCORE OGIVE MEANS

E       -------------------------------------------------------------

X    2                                                   222222222222

P                                                 2222222

E  1.5----------------------------------------2222*

C                                          111    *

T                                       111       *

E    1-------------------------------111          *

D                                 111 *           *

111    *           *

S   .5--------------------00000       *           *

C                   000000*           *           *

O    0  000000000000      *           *           *

R       ------------------------------------------------------------

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

PERSON [MINUS]  ITEM  MEASURE

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|CATEGORY    STRUCTURE   |  SCORE-TO-MEASURE   | 50% CUM.| COHERENCE|ESTIM|

| LABEL    MEASURE  S.E. | AT CAT. ----ZONE----|PROBABLTY| M->C C->M|DISCR|

|------------------------+---------------------+---------+----------+-----|

|   0      NONE          |( -2.07) -INF   -1.19|         |  62%  42%|     | 0 Dislike

|   1        -.86    .07 |    .00  -1.19   1.19|   -1.00 |  54%  71%|  .73| 1 Neutral

|   2         .86    .06 |(  2.07)  1.19  +INF |    1.00 |  85%  78%| 1.19| 2 Like

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3. If you conceptualize the rating scale in terms of the probability of accumulated categories (Thurstone's approach), then Rasch-Thurstone thresholds = "50% Cumulative Probabilities" are of interest. 50% Cum Probability is the point at which the probability of being observed in the categories below = the probability of being observed in this category or above.  These are shown in Table 12.6.

The Rasch-Thurstone thresholds also approximate the item difficulties when the rating scales are dichotomized between the categories below the target category and those at and above the  target category. This is useful when the probability of "success" on a polytomous item must be computed. www.rasch.org/rmt/rmt233e.htm

MEDIANS - Cumulative probabilities

P       -------------------------------------------------------------

R  1.0  ********222222222222222

O       0       1111111        22222

B   .8  0              111          222

A       0                 111          22

B   .6  0                    11          22

I   .5  0----------------------111---------222-----------------------

L   .4  0                       | 11        | 22

I       0                       |   11      |   222

T   .2  0                       |     111   |      222

Y       0                       |        11111        2222222

.0  0                       |           | 111111111111111********

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

PERSON [MINUS]  ITEM  MEASURE

The plots corresponding to these three approaches are shown in Table 21, and also on the Graphs screen.

Usually, one of these three alternatives will be most meaningful for your audience.

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