I would go further and hypothesize that the exam writer (and
instructor?) does not understand the interpretation of a p-value.
Both questions are misleading and impossible to answer without
rejecting the premise of the question itself. I would simply drop
them and use only the valid questions to determine a grade. The
danger is that the students have been taught this incorrect (but
common) interpretation throughout the course, and there may be
nothing that you can do to rectify that.
Ian
On Jul 13, 2010, at 11:52 AM, Greg Snow wrote:
Well the correct answer from a frequentist perspective is that the
probability is either 0 or 1, but there is not enough information
to tell which one (actually for question 2 it is possible that the
answer is both 0 and 1 (but not anything in between)). So any
student who expresses the idea of "I don't know" coherently should
get full credit. If we interpret mean or average to be sample
rather than population, then the answer is still 0 or 1, but they
can compute it. Whether students who give the p-value for the t
test should get full, partial, or no credit depends on what you (or
other teachers) have stressed. If you have stressed that p-values
are definitely not probabilities on the population parameters, then
the p-value is not the answer and should not get credit. If the
book and lecture were sufficiently vague on the point then they
could get some credit.
Either way both questions are clearly poorly worded (from a
Bayesian perspective as well).
--
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
[email protected]
801.408.8111
-----Original Message-----
From: [email protected] [mailto:r-sig-teaching-
[email protected]] On Behalf Of jose romero
Sent: Tuesday, July 13, 2010 7:22 AM
To: [email protected]
Subject: [R-sig-teaching] a statistic-teaching question
Dear R-teaching list:
I would like to put forward for your consideration an issue which is
not R related, but statistics-teaching related. Although i know full
well that this list is intended for discussion of the use of R in
teaching statistics, I also know that most (if not all) of you out
there are highly qualified statistics teachers, and as such, I'd like
to know your opinion on this issue:
As a statistics instructor in a open university (distance education),
part of my job functions consist in grading exams written at the
central level in my institution and presented by students nationwide.
Recently, i had to grade an exam of which the first two questions ran
like this (again, i did not write this exam):
1) The following is a sample of the duration (in minutes) of time
intervals between queries to a data base:
91 86 71 79 51 51 67 60 79 85
68 86 53 45 86 71 82 88 72 67
51 51 75 81 76 80 75 76 82 49
66 83 84 82 84 76 53 75 70 55
What is the probability that the mean time between queries is more
than
72.5 minutes?
2) For a certain region of the country, the rainfall measurements (in
mm) during the last 15 years are the following:
580 575 400 750 428 636 825 360
850 590 875 735 920 950 550
What is the probability that the average rainfall during the last 15
years is less than 625 mm?
Considering that these are exam questions for an introductory
statistical inference course (non bayesian), what are your
objections,
as a teacher, to the way these questions are posed? If you had to
grade exams with such questions, and it is not in your power to
cancel
this exam and re-schedule for another one, how would you grade your
pupils?
Once again, please excuse me for posting these non-R related and very
absurd questions for your consideration. However, i'd really like to
know the experts' opinion on this.
Thanks in advance,
josé romero
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