Dr. Richard L. Froman
Psychology Department
John Brown
University
Siloam Springs, AR 72761
e-mail: [EMAIL PROTECTED]
phone and
voice mail: (479)524-7295
http://www.jbu.edu/sbs/rfroman.html
--------Original Message-----
From: John W. Kulig [mailto:[EMAIL PROTECTED]]
Sent: Tuesday, February 12, 2002 10:35 AM
To: Teaching in the Psychological Sciences
Subject: Re: embarrassing statistical question
Miguel. Just a random or two.(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
nwWhere L represents the lower real limit of the category containing the percentile of interest.
N is the total number of scores in the distribution
nl is the number of individuals with scores less than L
nw is the number of individuals with scores within the category containing the percentile of interest
i represents the interval of the category that contains 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>
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John W. Kulig [EMAIL PROTECTED]
Department of Psychology http://oz.plymouth.edu/~kulig
Plymouth State College tel: (603) 535-2468
Plymouth NH USA 03264 fax: (603) 535-2412
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