Greetings and Happy New Year,
One of the most useful outputs from the Rasch Winsteps
program is the Wright Map. The Wright
Map can be helpful for any organization that uses multiple choice examinations,
as it provides a picture of how well their exam is measuring.
Mary E. Lunz, Ph.D.
Using The Very Useful Wright Map|
The Wright Map provides a picture of a multiple
choice exam by placing the difficulty of the exam items on the same measurement
scale as the ability of the candidates.
This provides the user with a comparison of candidates and items, to better
understand how appropriately the test measured. A sample Wright Map is shown below.|
The Wright Map is organized as two vertical histograms. The left side shows candidates and the
right side shows items. The left side of the map shows the distribution of the
measured ability of the candidates from most able at the top to least able at
the bottom. The items on the right side
of the map are distributed from the most
difficult at the top to the least difficult
at the bottom.
On the left side, the Wright Map shows the mean
(M) and two standard deviation points (S = one SD and T = two SD) for measured candidate
ability. On the right side of the map,
the mean difficulty of the items (M) and two standard deviation points (S = one
SD and T = two SD) for the items are shown.
The sample map below shows that the mean (M) ability of the candidates
is approximately one standard deviation (S) above the mean (M) difficulty of
Each "x" represents a candidate on the left side or an item
on the right side of the map. The
candidates at the top of the map had the highest scores, while the items at the
top of the map are the most difficult. The candidates at the bottom of the map earned
the lowest scores, and the items at the bottom of the map are easiest. Theoretically,
when candidates and items are opposite each other on the map, the difficulty of
the item and the ability of the candidate are comparable, so the candidate has
approximately a 50% probability of answering the item correctly.
The items at the top of the map were probably answered
correctly by about 30% of the candidates who are the most able. The items at
the bottom of the map are the very easy items and were probably answered
correctly by over 90% of the candidates.
Those items are well below the ability of the least able candidate
indicating that all candidates have a greater
than 50% probability of answering the items correctly. However, tests discriminate best between
marginally acceptable and marginally unacceptable candidates when a large group
of items have difficulty estimates close to the pass point. The ability of the
candidates close to the pass point is the most essential differentiation to
make, and having a large number of items at this critical point gives the most
accurate information for those candidates.
The pass point is marked on the map. The map shows that over half of the items were
within plus or minus one standard deviation of the pass point. There were also many candidates aligned within
one standard deviation of the pass point.
Therefore, this sample exam includes a sufficient number of items in the
center of the item distribution, close to the pass point to differentiate
between candidates who should pass or fail as accurately as possible.
The Wright Map
MEASURE | MEASURE
<more> --------------------- PERSONS
-+- ITEMS ---------------------
3 + 3
More able candidates |
More difficult items
2 X + 2
X | X
XXX | X
XXXXXXX | XX
XXXXXXXXXXXXXXXX S| XXX
XXXXXXXXXXXXX | XX
1 XXXXXXXXXXXXXXXX +
XXXXXXXXXXXXXX | XXXX
XXXXXXXXXXXXXXXXXXXXX M|S XXXXX
Pass point XXXXXXXXXXXXXXX |
XXXXXXX S| XXXXXX
0 XXXXXXX +M
X T| XXXXX
Less able candidates X
-1 + XXX -1
-2 + -2
| Less difficult items
-3 + -3
<less> --------------------- PERSONS
-+- ITEMS ------------------<frequent>