Rod, Maybe an example closer to home would help. Give him as an example his score on two hypothetical exams in the same class. Set it up so his numerical score on the first exam is lower than his numerical score on the second exam, but on the first exam is above the mean of the class and below it on the second exam. Ask him which exam he did better on. Obviously he did higher on the second, but relatively (and on the grading curve) he did poorer on the second exam. Maybe that will get him thinking a little outside his box. Dave
-----Original Message-----
From: Hetzel, Rod [mailto:[EMAIL PROTECTED]
Sent: Mon 2/24/2003 5:08 PM
To: Teaching in the Psychological Sciences
Cc:
Subject: z-score woes
Hi everyone:
I need your help with something. I have a student who just does not
understand z-scores. I have met with him for at least two hours outside
of class and he still doesn't understand the concept. In particular, he
doesn't seem to understand why you need to include standard deviation in
the calculation of z-scores. "Why can't you just compare the raw
scores?" is his frequent question. I explained to him in various ways
that the z-score is a transformed score that can take scores from two
different distributions and put them on a common metric, that it gives
you a summary statistic that tells you an individual's score in relation
to the mean and standard deviation, that it provides a way to compare
scores from two different distributions, etc.
Here is the example that my student keeps coming back to: "Jack and
Jill are intense competitors, but they never competed against each
other. Jack specialized in long-distance running and Jill was an
excellent sprint swimmer. As you can see from the distributions in each
table, each was best in their event. Take the analysis one step farther
and use z-scores to determine who is the more outstanding competitor."
LONG-DISTANCE RUNNING
Jack: 37 min
Bob: 39 min
Joe: 40 min
Ron: 42 min
SPRING SWIMMING
Jill: 24 sec
Sue: 26 sec
Peg: 27 sec
Ann: 28 sec
Here are the relevant statistics:
RUNNING MEAN: 39.5
RUNNING SD: 1.803
JACK'S ZSCORE: -1.39
SWIMMING MEAN: 26.25
SWIMMING SD: 1.479
JILL'S ZSCORE: -1.52
When I have met with the student, he has not understood how Jill is the
more outstanding competitor. He makes the comment that Jack is
obviously the better competitor because Jack scored an entire 3 minutes
faster than the next finisher whereas Jill scored only 2 seconds faster
than her runner-up. "Why do you have to even look at the other scores
in the distribution to tell that Jack is the better competitor? He
finished a full three minutes ahead of his competitors and Jill just
barely finished ahead of her competitors." I have drawn some diagrams
of normal distributions to show how Jill's score on the distribution is
further away from the mean and closer to the tail, but my student thinks
that I am somehow changing the scores and cheating the system when I
transform the raw scores to z-scores. Even after I show him how the
position of the score remains unchanged, he cannot grasp in this case
how Jill is the more outstanding competitor. I've tried switching
examples with him (e.g., distributions of test scores, changing C
temperature to F temperature, etc.), but nothing seems to be sinking in.
He has a fairly high level of anxiety about statistics but tends to
cover it up with humor and sarcasm. He took statistics with another
professor last semester and told me that all statistics is a bunch of
bull**** that serves no useful purpose other than obscuring the
painfully-obvious truth.
So, I have two questions for all of you out there in TIPS land...
1. Given what I've told you about the student's struggles with
z-scores, does anyone have any specific ideas on how to present this
information to him? I think I'm in a rut with him and need a fresh way
to explain this.
2. Would anyone be willing to share with me any z-score examples that
you use for your own assignments and exams? I am running out of new
examples to use with this student and was hoping that perhaps you would
be willing to share some of your own examples. This would give my
student some more opportunities to calculate z-scores
3. How do you work with students who just don't seem to get statistics?
Everyone else in the class seems to understand z-scores well, but I'm
struggling a bit in trying to reach this student. I find that I am
hardly ever at a loss for words when teaching clinical courses, but I'm
reaching my limit with this student. This is certainly not my area of
expertise, so I'm hoping that some of you stats-people can help out with
this!
Thanks for your assistance with this problem!
Rod
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