Maxwell Gwynn wrote: > I'm not sure about your "beaten lengths" as an interval scale. Why is it > not at thr level of ratio scales (0=no lengths (Tied for first), and > beaten by 4 lengths is half as much as beaten by 8 lengths, etc).
-- Try to get away from the measurement itself, and think of what is being measured. Beaten lengths is not what is being measured. Instead, it is a measure of the horses' athletic abilities. Zero beaten lengths does not mean an absence of ability (quite the contrary!). However, it could be argued that the difference between horses assigned zero beaten lengths (the winner) and two beaten lengths, reflects the same difference in ability as the difference between 6 beaten lengths and 8 beaten lengths (regardless of the finish positions of the horses). Of course, this assumes that the horses ran the same distance. In watching a race, it is clear that some are fortunate to run near the rail, whereas others take "la grande promenade." This fact provides another teaching opportunity--levels of measurement are not as cut-and-dried as many methods text would suggest. Beaten lengths (like IQ?) is somewhere between ordinal and interval, but probably closer to interval. The actual distance problem produces even greater problems for supposedly ratio scales, like velocity (ft/sec) measures. Application of any metric to horse (or other) racing measures is further complicated by the fact that there are sprinters and routers. Sometimes the measures are obtained in less-than-ideal situations. Win pools, as a measure of the crowd's confidence in a horse, may provide an example of a ratio scale. (Ten times as much was bet on Secretariat than on Limp Pony.) This is even complicated by the track's take, breakage, and taxes. Horse racing also provides a good example of regression to the mean. Smart handicappers refer to "bounce", or the tendency of horses, after an exceptionally good race, to perform less-than-exceptionally in their next race. The crowd will overbet the horse, based on its last spectacular performance, only to be disappointed when a long-shot crosses the finish line first. Don't take this post as an indication that I know very much about horse racing. My bank account says otherwise. -- ***************************************************************** * Mike Scoles * [EMAIL PROTECTED] * * Department of Psychology * voice: (501) 450-5418 * * University of Central Arkansas * fax: (501) 450-5424 * * Conway, AR 72035-0001 * * ********* http://www.coe.uca.edu/psych/scoles/index.html ******** --- You are currently subscribed to tips as: [EMAIL PROTECTED] To unsubscribe send a blank email to [EMAIL PROTECTED]
