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X
Formula for Equating
Define:
X
= the mean raw score achieved on the new test form's scorable items based on response data from the parent form (Y)
s
x
= the standard deviation of the scorable items on X based on response data from the parent form (Y)
Y
= the mean raw score achieved on the parent test form's scorable items
s
y
= the standard deviation of the scorable items on Y
X
i
= a given raw score on the new test form
Y
i
= the raw score equivalent to X
i
expressed in the raw score metric of form Y
Set z
x
= z
y
In order to find the equivalent raw cutscore on the new form, solve for X
i
, where Y
i
= the raw cutscore on the parent form rounded to one decimal place.
X
i
=
X
+ (s
x
/s
y
)(Y
i
−
Y
)