|
Please describe the nature of the
true scores for which the putatively interval data are a positive linear
function. I'm not familiar with
the metrics of judging skating performances. -----Original
Message----- To those of you on the
list who have ridiculed the importance of making a distinction between scales
of measurement (I say, unwisely kicking the drowsy canine), the recent
unpleasantness in the pairs skating at the Olympics might make you reconsider.
The Canadian pair lost because the scoring system calls for Ordinal data to
supercede Interval data. Sometimes millions of dollars in endorsements may
actually be riding on which scale of measurement you choose. Rick Dr. Richard L. Froman -----Original Message----- (1) i should be 1 for ungrouped (if the
numbers are integers) but i = interval width if grouped. So if you group into
categories 4 to 6, 7 to 9, 10 to 12, i = 3 (but I'm sure you already know
that). (2) IF ungrouped, but your interval
contains a bunch of identical scores (e.g. 6,6,6,6,6) we assume the
"true" scores lie between 5.5 and 6.4999.... therefore the formula
might give us the funky answer 5.25 if that particular percentile point is1/4
of the way through the interval. But if grouped, and an interval contains
all numbers between 4 and 6 inclusive (as example, 4,6,6,6,6,6,6,) the formula
might give us 5.25 if it's looking for the score 1/4 of the way through the
interval (under the assumption that all the "true" scores in the
interval are equally distribution throughout the range 3.5 to 6.5. This would
be the case in the long run, but not with this particular data set). But if the
same data was ungrouped, you'd get a number between 5.5 and 6.5 because your
point would be into the 6s in the data set 4,6,6,6,6,6,6. That's the best I can
do at the moment! To be honest, I hate those formulas,
mostly because getting percentiles and percentile points is useful with big
data sets, never small data sets, and with big data sets you don't usually have
to mess with interval widths and tied scores to get a _useful_ answer. The most
useful way I have taught this (following Richard Lehman's undergradaute text)
is to have students plot cumulative proportion on Y, data on X. Do a straight
edge line from Y from the percentile you want, hit the line, and then drop
straight down. If you plot carefully and use a straightedge, you get as much
accuracy as one needs (this sounds like a Tukey (1977) method - I'll check
later if I have time). This method also allows you to go in reverse, from a
particular X up to the line, then left to the percentile rank. Miguel Roig wrote: I think I'm going senile. The
other day I could not get sound out of my computer (I rarely use the speakers)
and spent a couple of hours connecting and reconnecting them, reinstalling the
Sound Blaster software, etc. I was in the process of opening up my
computer to check the sound card when a friend dropped by. As I was about
to open the computer to check out the card, my buddy asked: Did you try turning
up the volume? DOH!!! Now, I'm
having what I think is an analogous situation with a statistics homework
assignment. I had given students a set of scores for them to organize
into a frequency distribution and to calculate various statistics, including
percentiles. Yesterday when I received their homeworks and began to check
them I found that most students organized their data into ungrouped frequency
distributions as shown in the textbook. A couple of students decided to
organize them into grouped frequency distributions with intervals of 50.
Hey, no problem there. However, when I looked at their answers for
percentiles. Each group was coming up with different answers. Last
night I spent over two hours going over their calculations and they appeared to
have followed the formula correctly. I woke up this morning thinking that
perhaps I had activated a sufficient number of subconscious problem-solving
structures that would allow me to discover the answer to this problem, but
after nearly an hour at this I think I am ready for someone to point out to me
the equivalent of not having turned up the volume. Here is the
formula that we are working with: L + [ (N)
(P) - nl ] i Where L
represents the lower real limit of the category containing the percentile of interest.
Given the i
portion of the formula, shouldn't that formula yield the same percentile
regardless of whether the scores have been grouped or not? I've consulted
several undergraduate statistics books that I have laying around, but these
offer either examples of grouped data or examples of ungrouped data using what
appears to me to be the same formula. Am I missing something here?
This problem has not come up before though I admit that I've been only teaching
statistics for the past two years. Frankly, I'm a bit embarrassed to
bring it up to the entire group because I am pretty sure that either I am
making a simple mistake somewhere or I am overlooking something that is overly
obvious. I'm returning
these homeworks tomorrow and I'd love to have a good answer for them. One other
quick "I should have known-type" question. Do cranial nerves
have the same extent of contralateral control of the face and head as the
primary motor cortex does for the rest of the body? As always,
your answers would be greatly appreciated. Miguel <snip> -- --- You are currently subscribed to tips as: [EMAIL PROTECTED] To unsubscribe send a blank email to [EMAIL PROTECTED] |
- Importance of Scales of Measurement Rick Froman
- Re: Importance of Scales of Measurement Paul Brandon
- RE: Importance of Scales of Measurement Rick Froman
- Re: Importance of Scales of Measurement Stephen Black
- RE: Importance of Scales of Measurement Wuensch, Karl L
- RE: Importance of Scales of Measurement Joel S Freund
