﻿ Fair averages based on = Mean

# Fair averages based on = Mean

Fair average scores are reported in the output for each element. These are the scores that correspond to the logit measures as though each element of that facet encountered elements of similar difficulty in the other facets. Fair averages are intended for communicating the measures as adjusted ratings. This is useful when the audience have a strong conceptualization of the rating scale, but little interest in, or understanding of, the measurement system.

Fair average = Mean

This provides a norm-referenced average the measures for all elements (except this element) are set to the average values of the elements in their facets. It uses mean measure of the elements of each facet (except the current element) as the reference for computation. This is the default option. It is shown as Fair(M) in Table 7.

Fair average = Zero

This provides a criterion-referenced average the measures for all elements (except this element) are set to zero (logits or on user-scaling). It uses the origin of the measurement scale for each facet (except the current element) as the reference for computation. This was the default option in early version of Facets. It is shown as Fair(Z) in Table 7.

For the non-centered facet (typically persons), these two fair averages are usually the same. For a centered facet (e.g., items or raters) they are different. So for your non-centered rater facet, do you want the "fair-average" for a rater to be the rating given by this rater to a person with an "average" measure, or to a person with a "zero" measure? You may need to try both to identify which is actually what you want to report.

Look at your non-centered facet. Do you want the fair averages for all elements to be determined by a person at the Umean= value (Fair=zero)  or a person at the person-sample mean (Fair=mean).  If you are describing performances on this test then (fair=mean).

Example 1: An examination board wishes to use criterion-referenced fair scores for rater comparisons, because a "zero" logit person is at the pass-fail point:

Fair score = Zero

Example 2: An examination board wishes to use ratings based on an average task rated by an average rater:

Fair score = Mean

Example 3: I wanted to use a fair average (with Fair=zero) of 2

as a cutscore. No person has exactly this. How can I find the person measure?

One approach:

1. Analyze your data and output an Anchorfile=

2. look for person measures with Fair Average near 2

3. In the Anchorfile=, change the anchored person measures so they cover the range discovered in 2. No need to change the data.

4. Analyze the modified anchor file and see which person measure has a Fair Average near enough to 2.0

5. redo 2, 3, 4 if needed.

Another approach:

1. Analyze your data and output  the Scorefile= for the persons to Excel

2. Sort on the Fair Average column

3. Delete all values far from a Fair Average of 2.0

4. Plot  Measureagainst Fair Average

5. Tell Excel to draw the trend line and display the equation

6. Put value of 1.33 into the equation.

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