Date:         Wed, 28 Oct 2009 10:36:26 -0500
Reply-To:     "Steve Simon, P.Mean Consulting" <net@pmean.com>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         "Steve Simon, P.Mean Consulting" <net@pmean.com>
Subject:      Re: Regression Analysis Questions
Comments: To: "Wilkening, Kurt" <WilkeningK@HillsboroughCounty.ORG>
In-Reply-To:  <68FDE32AE952BB4B82E80CB7DC13E390A24D7B5EF5@CMBS3CC.hcbocc.ad>
Content-Type: text/plain; charset=ISO-8859-1; format=flowed

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.

Could I use your data on my website? It's an interesting application of
z-scores.
--
Steve Simon, Standard Disclaimer
Second free statistics webinar, Wed, Nov 4, 11am-noon CST.
"The first three steps in data entry, with examples in PASW/SPSS"
Details at www.pmean.com/webinars

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