Central Range Nomograph

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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