One question that arises is how do the people who take the test in your office differ from the people who were used for standardizing the state exam? Is there any reason that you would expect the same percent to fail your test as fail the state's test or to have the same distribution of scores? If the people who show up at your office are better qualified than the group taking the state test you certainly don't want to penalize them by failing the same percentage.

The real question is what is your goal? Do you want to spare candidates from taking the state exam, substituting your own in its place? If so you're probably going to have to administer your test to more people and perhaps different types of people. Do you just want to be as "tough" as the state and fail the same percentage? What are the consequences of incorrectly predicting a fail on the state test based on your test? Or incorrectly predicting a pass?

In a message dated 10/28/2009 10:40:09 A.M. Central Daylight Time, net@pmean.com writes:
Wilkening, Kurt wrote:

> We administer an employment test here in our office for Detention Deputy
> Trainee and want to adjust the test's cutoff score to match the cutoff
> score of a state exam. Below I have copied the raw scores of actual
> candidates who took both exams. D=Detention Deputy scores, whereas F
> Act=State exam scores. If the state's cutoff score is 77, what should be
> the cutoff score be for our D exam?

Interesting question. I don't think that regression will help here.
Instead, if you are comfortable with an assumption that the data is
normally distributed, then note that the mean and standard deviation of
F Act are 89.0 and 4.4. That means that a cutoff of 77 corresponds to a
z-score of -2.73 (= (77-89)/4.4).

In the D scores, the mean and standard deviation are 52.8 and 4.9. A
z-score of -2.73 would be equal to 39.4 (= 52.8-2.73*4.9) on this scale.

So 39.4 is a good cut-off, if the data is normally distributed, in the
sense that the same proportions are likely to pass using this cutoff. If
you are uncomfortable with the normality assumption, you could fit a
different distribution to account for the slight skewness in your data
and equate the percentiles of the distributions.

Everything is going to be an extrapolation beyond the range of your
data, but only slightly so.