## Person-free and Item-free measurement |

A strength of Rasch methodology is that the estimates of Rasch measures ("Rasch scores", thetas and deltas) are person-free and item-free.

Person-free: as much as is statistically possible, the item-difficulty estimates are independent of the particularly sample of persons from a homogeneous population that are used in the estimation. The actual distribution of the items and persons is irrelevant.

Item-free: as much as is statistically possible, the person-ability estimates are independent of the particularly sample of items from a homogeneous population that are used in the estimation. The actual distribution of the items and persons is irrelevant.

Since each analysis has its own zero-point (frame-of-reference), we need to equate or link the tests to put all the analyses in the same frame-of-reference.

Ben Wright's (1967) demonstration of person-free and item-free estimation:

Item-free person-ability estimates:

1. Analyze a large dataset.

2. Split the items into easy items (low difficulties) and hard items (high difficulties)

3. Analyze each set of items separately.

4. Identify items and persons with extreme (zero, perfect) scores and remove from the analyses. Remove persons with extreme scores in one analysis also from the other analysis.

5. Reanalyze both sets of items.

6. Cross-plot the person estimates. They should form a fuzzy diagonal line. The Winsteps scatterplot includes confidence bands to show the statistical similarity of the two sets of person ability estimates.

Person-free item-difficulty estimates:

1. Analyze a large dataset.

2. Split the persons into high-ability persons and low-ability persons.

3. Analyze each set of persons separately.

4. Identify items and persons with extreme (zero, perfect) scores and remove from the analyses. Remove items with extreme scores in one analysis also from the other analysis.

5. Reanalyze both sets of persons.

6. Cross-plot the item estimates. They should form a fuzzy diagonal line. The Winsteps scatterplot includes confidence bands to show the statistical similarity of the two sets of item difficulty estimates.

Wright, B. D. (1967). Sample-Free Test Calibration and Person Measurement. In

B. S. Bloom (Chair), Invitational Conference on Testing Problems (pp.

84-101). Princeton, NJ: Educational Testing Service. Available at

Help for Winsteps Rasch Measurement Software: www.winsteps.com. *Author: John Michael Linacre*