The person sample used for test construction and validation does
not have the same distribution as the people to whom you plan to
administer the test. The sample may be spread out - giving a high
separation, or shrunk together - giving a low one. What will be
the person separation (and reliability) for you? The "Central
Range" nomograph (overleaf) can be helpful. Think about your
target group. What logit range would encompass the central 50% of
their distribution? Or 67%? Or 90%? For example, you may think
that a range of 3 logits would include the central 50% of your
group. On the left side of the nomograph, locate this central
range on the x-axis, 3 logits. Go up until you meet the diagonal
line corresponding to the % of the group, 50%. The left-hand y-axis
shows that this is the same as specifying that the S.D. of
your group is 2.2 logits. Then proceed to the right-hand side of
the nomograph. On the x-axis, locate the average S.E. of person
measures from the sample data, e.g., .31 logits. This is usually
good enough for your group. Go up from the S.E. until you meet the
horizontal line drawn from the left-side. Proceed up the nearest
diagonal to the expected separation (and reliability). Here an
encouraging 7 (and .98).
J. Linacre
Linacre J.M. (1998) Central Range Nomograph. Rasch Measurement Transactions 11:4 p. 603-4.
Central Range Nomograph. Linacre J.M. … Rasch Measurement Transactions, 1998, 11:4 p. 603-4.
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