David Winsemius wrote
>Here are the three stated competencies that the test is supposed to measure:
>http://www.doe.mass.edu/mcas/01release/
>1) Select, create, and interpret an appropriate graphical representation
>(e.g.,
>scatterplot, table, stem-and-leaf plots, box-and-whisker plots, circle
>graph, line
>graph, and line plot) for a set of data and use appropriate statistics
>(e.g., mean,
>median, range, and mode) to communicate information about the data. Use
>these
>notions to compare different sets of data.
>
>2) Approximate a line of best fit (trend line) given a set of data (e.g.,
>scatterplot).
I don't know what the MA DOE curriculum guide means by a "trend line"
>3) Describe and explain how the relative sizes of a sample and the
>population affect
>the validity of predictions from a set of data.
>
>I think it is fair to say that the only "statistical" question that
>concerns competency(1) is Q39 and that it does a fairly poor job of
>assessing that competency.
Agreed
>A question that asked which of 4 box-and-whisker plots was summarizing a
>particular datset might be appropriate and fairly simple, or,
>
>A question that asked the student to compare two datasets wherein one had
>more outliers or outliers that were more extreme and aksed how the means and
>medians were affected, or,
<Snip>
Check out Question 39. The upper whisker is plotted improperly if it IS
supposed to be a Tukey boxplot. The whisker should only extend to the adjacent
point within 1.5 IQRs of the upper quartile. The IQR appears to be 6 (from 23
to 29), so the whisker should extend to the adjacent data point that is less
than 37. The plot shows the whisker extending to 41. The plot is wrong.
>Simply ask then to construct a box plot for a set of unordered data.
If the MCAS testers themselves plot the data improperly and the many reviewers
of this vital test missed the problem of plotting the upper adjacent values, do
you think it fair to require every 10th grader to know the defintions of IQR
and adjacent values in a Tukey boxplot in order to receive their high school
diploma? I don't think anybody would regard this as fair.
>On another point regarding q40, can anyone tell me how one would get a more
>"representative" sample of 25 students than by collecting 25 different
>estimates? I must have really missed the point here.
Good comment. Question 40 is also a poor question. The point that I think the
testers were going after, but doing it horribly, is to assess the need for
random sampling in a survey. However, the question misses the key part of the
problem that lies at the heart of probability and statistics: WHAT IS THE
SAMPLE SPACE or what is the population that is being surveyed?
In question 40, there are 25 students in the class and there are 25 estimates
in the sample. The question asks how much time the average student spends on
homework. But what is the population? Is it the students in the class, the
school, the grade, the town, the state or the country? The question is
miserable, because the sample size is 25 and there are 25 students in the
class, so by implication, the sample is the class. But 25 estimates of 25
students isn't a sample, it is a complete census.
So, any student taking last spring's MCAS test will have to sit there wondering
if the sample is the class or some larger unspecified population. Can you go
to the phone book and choose phone numbers at random and then choose students
of K-12 age and ask how many hours they spend on homework? Do you flag
students at random from a random selection of rooms in your school's classroom?
I agree with you, this question 40 may be worse than Question 39 since it is
not a multiple choice question. Students must write essays about what sampling
procedure they would use. Since virtually no student could get this question
correct, without writing that it is a bad question (how would that go over with
the MCAS grader being paid $9 per hour - would they reward that student or
flunk him or her? What if the essay were full of grammatical errors? Would
that be a pass? I suspect that anything that mentioned random sampling would
get a pass on the scoring exam, but if the sample size is 25 and the sample is
all 25 students in the class, then random sampling is NOT the correct answer)
As I've mentioned in other posts, this 10th grade MCAS test is a make-or-break
high stakes test. A straight-A average won't get you a diploma if you fail
this test, and the majority of 10th graders in MA fail this test, as it is now
being scored. 80% of hispanic students, 76% of black students, and 36% of
white students in MA failed the 2000 10th grade math test. This despite the
fact that MA has among the highest NAEP math scores in the nation.
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