## Thursday, February 10, 2011

### Simple Virtual Equating

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Another simple method of equating involves printing out Ministep Table 1.0 for each test and then sliding one along side the other until they are in reasonable agreement. This post also introduces six equally spaced common items in preparation for common item equating. The 24 by 24 student/item nursing school test was divided into two sets of nine items and one set of six common items. This produced two 15-student by 24 item tests (A9C6 and B9C6).

The average measure for the six items selected as common items was zero, that is, they were indeed uniformly distributed on the linear logit scale.

Winsteps Table 1.0 printed out with 12 divisions between each measure for both Test A and Test B. The spacing was identical for the two tests between -2 and +3 logits. The six common items can be identified by their answer sheet code, x2x, plus the item number: x2x 4. Winsteps Table 1.0 is a uniform linear playing field.

Without using the six common items, you must slide Test B vertically past Test A until “the overall hierarchy makes the most sense”. With the common items, you slide until the common items are in a best registration location. “The relative placement of the local origins (zero points) of the two maps is the equating constant.”  (The student ability zero points on the two tests also come together. This makes sense as equivalent student ability and item difficulty have been plotted at the same points on this linear logit scale.)

In my judgment, the distance between the Test A and Test B item zero points is about 4 divisions x 1/12 logits or -0.33 logits.

Test A was more difficult than Test B. The constant -0.33 can now be added to Table 13.1 measures in Test B. Test B 2.10 + (-0.33) = Test A 1.77. Equating reduces Test B student ability and item difficulty measures when placed within the Test A frame of reference.

This post presents a visual view of what equating involves. A single constant can be added to all measures, to equate two tests, as the measures are now on a linear logit scale. This constant is calculated when using [common item equating] rather than judging the value as above.[link next]