Rating scale conceptualization

(See Table 3.2, Table 12, Table 21, Graphs)

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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1. If you conceptualize the rating scale in terms of the probability of individual categories (Andrich's approach), then the "Structure or Step Calibrations" are of interest. The calibrations (Rasch-Andrich thresholds) are the points at which adjacent categories are equally probable.

CATEGORY PROBABILITIES MODES - Structure measures 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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| 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 "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.

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.