SUBTITLE A: EDUCATION
CHAPTER I: STATE BOARD OF EDUCATION
SUBCHAPTER b: PERSONNEL
PART 25 EDUCATOR LICENSURE
SECTION 25.APPENDIX A STATISTICAL TEST EQUATING – LICENSURE TESTING SYSTEM
Section 25.APPENDIX A Statistical Test Equating – Licensure Testing System
The Z-score formula set forth below will be used in all cases except where none of the scorable items on a test form has appeared on any previous test form. In such cases, the linear equating formula will be used.
Z-Score Formula
The following formula is used for z-score equating.
1. Define:
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the mean raw score achieved on the new test form's scorable items |
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sx |
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the standard deviation of X |
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the mean raw score achieved on the previous test form's scorable items |
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the standard deviation of Y |
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a given raw score on the new test form |
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the raw score equivalent to Xi expressed in the raw score metric of form Y |
2. Set zx = zy
3. In order to find the equivalent passing score on the new form, solve for Xi, where Yi = the passing score on the previous form rounded to one decimal place.
The linear equating formula is as follows.
1. Define:
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mean total test score on a new test form |
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s |
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variance of total test scores on the new form |
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mean of common items on the new form |
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variance of common item scores on the new form |
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covariance of total test and common item set for the new form |
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number of candidates taking the new form |
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, 
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and 
are corresponding statistics
for the previous test form
2. Compute estimated descriptive statistics for the total group (i.e., candidates from new and previous test form administrations).
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where n |
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the smaller of nx or ny |
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3. In order to find the equivalent passing score on the new form, solve for Xi, where Yi = the passing score on the previous form rounded to one decimal place.
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(Source: Amended at 37 Ill. Reg. 8379, effective June 12, 2013)