That was the context I was in when I Windsorized data, pigeon choice latency. I was proud of the study because we started collecting data without latency (as usually done), and after a few hours watching pigeons make choices I noticed some interesting patterns that strongly support my advisor's theory, so we added latency in the next study. It was my introduction to serendipity.
Back to the original question about central tendency and grades, I find that a simple stem-plot works wonders for grade feedback, and I use them myself when I look at how well a class is doing, since I find the skew/outliers informative. ========================== John W. Kulig Professor of Psychology Plymouth State University Plymouth NH 03264 ==================================================================== GALILEO GALILEI: I do not feel obligated to believe that the same God who has endowed us with sense, reasons, and intellect has intended us to forgo their use. ==================================================================== ----- Original Message ----- From: "Patrick Dolan" <[email protected]> To: "Teaching in the Psychological Sciences (TIPS)" <[email protected]> Sent: Friday, April 23, 2010 9:12:21 AM Subject: RE: [tips] mean,median,mode I'm sure this varies a lot between different labs, traditions, and area of study, but trimming RT data as described by Jim Clark is fairly standard in the LDT & word reading literature, and increasingly more commonly in the episodic recognition. Patrick Patrick O. Dolan, Ph.D. Associate Professor and Chair of Psychology Drew University Madison, NJ 07940 973-408-3558 [email protected] >>> Annette Taylor <[email protected]> 4/22/2010 11:04 PM >>> I'm in Mexico at WPA and have horrible email service here so maybe I've missed some part of this conversation but in my training in cog psych in grad school and beyond I've always used medians for RT data for both rapid responses (premature firing of motor program prior to completing cognitive task) or elevated RTs for various inattentive reasons. Annette Annette Kujawski Taylor, Ph. D. Professor, Psychological Sciences University of San Diego 5998 Alcala Park San Diego, CA 92110 [email protected] ________________________________________ From: Jim Clark [[email protected]] Sent: Thursday, April 22, 2010 8:52 AM To: Teaching in the Psychological Sciences (TIPS) Subject: Re: [tips] mean,median,mode Hi Although John's terms are not generally used (i.e., trimmed mean, Windsorized), many studies in cognitive psychology (and perhaps other areas I'm less familiar with) in fact adopt practices like this for RTs and sometimes other scores. Specifically, it is common to drop or truncate scores that are so many SDs away from the mean or that are clearly too small or too large (RT = 50 ms and RT = 10,000 ms for lex decision are both unrealistic values), suggesting some other process was operating (i.e., anticipatory response, nonattentive to task, ...). Jim James M. Clark Professor of Psychology 204-786-9757 204-774-4134 Fax [email protected] Department of Psychology University of Winnipeg Winnipeg, Manitoba R3B 2E9 CANADA >>> John Kulig <[email protected]> 22-Apr-10 9:46 AM >>> Since I haven't posted in a while let me put in my plug for the classic compromise between the median and mean: the trimmed mean. The mean has the useful property of using the value of every score, though you do NOT want the outliers/skew to drag the mean all over the place, so a trimmed mean lops off a certain % of scores at both ends, and the mean is calculated on those remaining. You can think of the regular mean as a 0% trim, and the median as a 50% trim, with the term "trimmed mean" being trims between 0 and 50% (10 and 20% trims are usually given as examples). So you use alot of the data in the middle but ignore the most extreme scores. I don't see these used too often, it's probably overkill to use them to report grades where most students are content with a letter grade (here, anyway). I usually don't report either one in small classes, usually I just scratch out the stem-plot on the board if they want to see how they compared to others. But if you really want overkill, there is the "Windsorized" mean, which is leaving N intact, but replacing (say) the bottom 3 scores with values of the 4th lowest, and the top 3 with the value of the 4th highest - often under the assumption that even if the extreme scores are not mistakes, knowing how far they are out in the tail does not contribute to an understanding of whatever you are studying. I used that ONCE in my life when I had some extreme pigeon latency scores to deal with. I almost never see these anymore (maybe cause I don't look at pigeon latency scores anymore!). Both procedures are helpful to eliminate data errors, though skew is not always handled perfectly with them, which was the main point of the grading issue .... ========================== John W. Kulig Professor of Psychology Plymouth State University Plymouth NH 03264 ==================================================================== GALILEO GALILEI: I do not feel obligated to believe that the same God who has endowed us with sense, reasons, and intellect has intended us to forgo their use. ==================================================================== ----- Original Message ----- From: "Christopher D. Green" <[email protected]> To: "Teaching in the Psychological Sciences (TIPS)" <[email protected]> Sent: Thursday, April 22, 2010 9:57:54 AM Subject: Re: [tips] mean,median,mode michael sylvester wrote: I can not remember ever being asked to describe an exam results in terms of the median or mode but it seems that everyone is interested in the mean (average) performance of the class. Why isn't knowing the mode and the median just as important? One is more likely to come across "median income" than "median class performance" or "modal class performance". I regularly use the median in describing my grade distribution, and I do it for exactly the same reason one should look at median (rather than mean) income: the distribution is typically highly skewed. A reasonable grade distribution looks much worse (for the students) than it really is if a couple of 8s and 13s drag the mean down. There is no reason that these students' grades should have any more impact on the average than those of students who got 38 or 43. So I usually use the median, to show students where the middle of the grade distribution was. Grade inflation of recent years has made the skew worse even worse. Average grades "should" be at 50. But, alas, we are stuck with what we are stuck with, so we have to use the best statistics we can find. And the best for central tendency in grade distributions is the median. Chris Green York U. Toronto ============ --- You are currently subscribed to tips as: [email protected] . To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13338.f659d005276678c0696b7f6beda66454&n=T&l=tips&o=2161 (It may be necessary to cut and paste the above URL if the line is broken) or send a blank email to leave-2161-13338.f659d005276678c0696b7f6beda66...@fsulist.frostburg.edu --- You are currently subscribed to tips as: [email protected]. 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