Why Do I Get A "Range" When Converting Raw Score to Scaled Score in Princeton Review?

[BigIs]

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@silverturtle

And so could someone score 450 one day and 800 the next; would that render the scores the same? Again, you have to apply some arbitrary standard. Your standard could be large enough that 450 and 800 are “not statistically different,” but you wouldn’t have many supporters.

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<p>The standard is not arbitrary, it is derived statistically by psychometricians, based on the testing population data (mean, population size, reliability, standard deviation). The standard error on any given administration is determined after the raw score data is available. The standard error of measurement runs around 30 points – see <a href=“http://professionals.collegeboard.com/profdownload/2009-Test-Characteristics-of-the-SAT.pdf[/url]”>Higher Education Professionals | College Board;

<p>Though this error will vary slightly on each administration, it is pretty much consistent.</p>

<p>Reliability on each section of the test runs around .9, meaning any changes in score beyond the standard error represents a real difference in performance.</p>

<p>Some definitions that the College Board Uses:</p>

<p>Standard Error of the Difference—SED
The SED is a tool for assessing how much two test scores must differ before they indicate ability differences. To be confident that two scores indicate a true difference in ability, the scores must differ by at least the SED times 1.5. For example, SAT verbal and math scores must differ by 60 points (40 x 1.5) in order to indicate true differences of ability.</p>

<p>Standard Error of Measurement—SEM
The SEM is an index of the extent to which students’ obtained scores tend to vary from their true scores. It is expressed in score units of the test. Intervals extending one standard error above and below the true score (see below) for a test taker will include 68 percent of that test taker’s obtained scores. Similarly, intervals extending two standard errors above and below the true score will include 95 percent of the test taker’s obtained scores.</p>

<p>True Score (See Standard Error of Measurement)
*True score is a hypothetical concept indicating what an individual’s score on a test would be if there were no error introduced by the measuring process. It is thought of as the hypothetical average of an infinite number of obtained scores for a test taker with the effect of practice removed. *</p>

<p>The calculation of score, SEM, SED, and the supporting statistical characteristics are reviewed by colleges who would not use the scores if they felt the SEM and SED were arbitrary, rather than statistical. Because the population size is so large, the numbers usually vary little from administration to administration.</p>

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@silverturtle

however someone with 2300 will usually get 2220-2380

No, I don’t think so; your range is too large. The people I know who score 2380+ almost never went below 2350 on practice tests, and the people who score ~2200 almost never hit 2300.

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<p>The ranges can’t be used to compare practice tests to actual tests. They only compare scaled scores earned on a given administration. It is always dangerous to generalize anecdotal data, though that seems to be one of the major reasons to post on CC.</p>