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One of the sections {2,3,4,5,6,7} will be for research purposes only and
will not be given a score. The section used for research purposes is
called the "variable" section.
Consider the non-variable sections that must appear in the set of sections
{2,3,4,5,6,7}:
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division questions total by division
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Math (M) 20 38
Math (M) 18
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Critical Reading (CR) 24 (+\-1) 48
Critical Reading (CR) 24 (+\-1)
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Writing (W) 35 35
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Therefore, the division with the variable section well be known as soon as one
encounters:
(1) a third section in the Math (M) division;
(2) a third section in the Critical Reading (CR) division;
or, (3) a second section in the Writing (W) division.
This will happen while taking the SAT, and thus, one will know,
before starting work on a section that matches one of the three cases, that
there is a (1/3) chance (cases 1 and 2) or a (1/2) chance (case 3) that
the current section is the variable section and will not be given a score.
Regardless of the sequence of sections, when a test taker encounters a section
that proves which division has the variable section, the test taker has a (1/3)
chance (cases 1 and 2) or a (1/2) chance (case 3) that the
current section is the variable section. Before gaining this information, the
probability was only (1/6). Also, the probability for all subsequent sections
becomes zero.
Furthermore, if a math section with 20 questions has been encountered, and then
another math section with 20 questions is encountered, then one knows, before
starting work on the second math section with 20 questions, that the variable
section is in the math division, and also that there is a (1/2) chance that the
current section is the variable section and will not be given a score.
Similarly, encountering a math section with 18 questions, and later encountering
another math section with 18 questions, leads to the same conclusions. The
probability of any subsequent section being the variable section becomes zero.
Okay, now consider this information leak from the perspective of the authors of
the SAT. The goal of the authors of the SAT is to have test takers work on the
variable section with the same concern and effort given to all other sections
of the SAT, giving the authors of the SAT a method of linking performance on
the particular version of the SAT to performances on versions administered
throughout the long history of the SAT. Therefore, the authors of the SAT want
to minimize the chance that a person taking the test will determine that a
particular section is the variable section.
For example, the authors of the SAT would probably avoid having sections #2
and #3 be math sections with exactly 20 questions each, because the test taker
would know, at the very beginning of section #3, that either section #2 or
section #3 must be the variable section. Also, the test taker would know that
all subsequent sections will be scored. In this hypothetical situation, the
test taker gets information about the variable section at the earliest
possible time in the sequence of sections in the SAT. The test taker can use
this information in a few ways. If the test taker is consciously or tacitly
"taking advantage" of the general (1/6) chance that each section, of the sections
{2,3,4,5,6,7}, is the variable section, putting in only (5/6) of maximum
personal effort to avoid wasting a full effort on the variable section, then
the test taker would change this conservative strategy after learning that the
sections {4,5,6,7} will be graded, investing full effort in to those sections.
The test taker might also take advantage of the (1/2) chance that section #3 is
the variable section, putting in less effort, or skipping the section entirely
and instead resting or doing work on another section (against SAT rules; don't
cheat!).
It is my guess that the authors of the SAT delay conclusive evidence of the
division containing the variable section until section #7. This minimizes
any advantage to the test taker. Section #7 itself need not be the variable
section, but I believe that delaying conclusive evidence of the division
having the variable section until section #7 is best for the test authors.
(NOTE: On the 2005 March 12th administration of the SAT, and form code BWBA,
section #7 itself happened to be variable section.)
In conclusion, there is a way to be certain which *division* has
the variable section while taking the SAT -- and this information might,
at the very least, offer some psychological relief (closure, or SATisfaction
of morbid curiosity) for a person taking the SAT.
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