Theory on test equating and linking
 

I am not a statistician but I have a question about test equating and
linking.
Currently I am using a linear equation formula that someone helped me
with(MartinW) to equate the test scores. We use a Mastery Test that
has different raw scores for each grade level; 106 for grade 3, 120
for grade 4, 140 for grade 5, 121 for grade 6, 124 for grade 7 and 148
for grade 8. For further information we use 70 percent as a passing
point, if that helps. For grade 3 a passing point would be 106 - 75
answers correct. This is how I am approaching it but, I do not have
enough experience in this area. Does anyone have any suggestions for
me? Is linear scaling a good approach? Need your expertise on this
one!

Thanks in advance PJ

This is an example of 2 different tests and is the formula approach
that I use.

Test 1: has as passing point of 70 and a max of 100
Test 2: has a passing point of 50 and a max of 70
To do a linear transformation
Call test1 y, and test2 x
Substitute into y = ax+b
At the passing score we get: 70 = a50+b
At maximum score we get: 100 = a70+b
Solve we a = 1.5 and b = -5
To convert test2 scores to a scale somewhat equivalent to test1 using
the formula : 1.5x-5
So a score of 60 on test 2 will transform to a score of 85
y=(1.5) 60 - 5 = 90- 5= 85.

Formula constructed by MartinW
=SLOPE($E$1:$F$1,$E$2:$F$2)*B1+INTERCEPT($E$1:$F$1 ,$E$2:$F$2)

With 70 in E1 and 100 in F1
With 50 in E2 and 70 in F2