i think that the +1 is reasonable IF, we have a potentially continuous variable that, for convenience, we put tick marks at arbitrary points ... such as a 50 item test ... we let scores be 23, or 24, or 25, etc.
IF the assumption is that knowledge is continuous ... then i don't see anything amiss if we assume that the limits are set at 1/2 units below and above the arbitrary values we use ... since (as dividing points between 2 adjacent values), i don't see anything necessarily that would argue that our "observed" scores (23, or 24, etc.) would be biased one way or the other the difficulty in using the 1 for finding the range is primarily when we have scales that clearly are not in units of 1 ... either real or made so arbitrarily ... if the unit we use is not 1, then accumulating 1/2 of a unit size of 1 at the low end of the scale + 1/2 of a unit size of 1 at the high end of the scale ... makes no sense ... fundamentally, IF you are going to posit some extension of the lowest and highest scores ... on which to make the range calculation ... you at least have to consider the UNIT SIZE you are working with FIRST ... before taking half of it alan had mentioned that on a real continuous scale ... that the range really was between the lowest and highest value ... with nothing added to either end ... and, i would agree with this IF, our measuring tool could in reality take a measurement that translates to ANY value anywhere along that scale ... if not, then one might question a wee bit about whether the lowest and highest MEASURED numbers, are actually the lowest and highest possible values (of course, alan could counter that if they can only be measured as such ... they THEY are the only admissible values) of course, all of this is rather unimportant since, the range is not a very "helpful" statistic or value to calculate on a set of data ... that is, if you are using it for indexing dispersion and, in the illustration that alan gave for how the "public" view range ... the range of prices for an item is from $1.50 to $2.50 ... they would probably laugh at you if you said that the range is REALLY from $1.495 ... to $2.505 they would say ... huh? say what? At 10:58 AM 10/5/01 -0400, William B. Ware wrote: >Robert, > >I don't think I understand your argument... Are you saying that the >"descriptive statistic" should be invariant over scale? > >Anyway, more to the point... the "add one" is an old argument based on the >notion of "real limits." Suppose the range of scores is 50 to 89. It was >argued that 50 really goes down to 49.5 and 89 really goes up to >89.5. Thus the range was defined as 89.5 - 49.5... thus the additional >one unit... > >Personally, I don't subscribe to this position... It assumes that the low >score is always toward the low end of its value and that the upper value >is always toward the high end of its value... Sort of a maximum range... I >prefer not including the additional one unit... > >Bill > >__________________________________________________________________________ >William B. Ware, Professor and Chair Educational Psychology, >CB# 3500 Measurement, and Evaluation >University of North Carolina PHONE (919)-962-7848 >Chapel Hill, NC 27599-3500 FAX: (919)-962-1533 >http://www.unc.edu/~wbware/ EMAIL: [EMAIL PROTECTED] >__________________________________________________________________________ > > >On Fri, 5 Oct 2001, Robert J. MacG. Dawson wrote: > > > > > > > jeff rasmussen wrote: > > > > > > Dear statistically-enamored, > > > > > > There was a question in my undergrad class concerning how to > define the > > > range, where a student pointed out that contrary to my edict, the > range was > > > "the difference between the maximum & minimum". I'd always believed that > > > the correct answer was the "difference between the maximum & minimum plus > > > one" > > > > One what? Any statistic that depends on the units used seems rather > > arbitrary to me. If I compute the range of weights of a group of people > > (in kilograms) I ought to get the same actual *weight* as an American > > using pounds or a Brit using stones. > > > > Suppose I have three meter sticks - are you telling us that the range > > of their lengths is a little over one meter? > > > > I'm afraid I vote with your students. > > > > -Robert Dawson > > > > > > ================================================================= > > Instructions for joining and leaving this list and remarks about > > the problem of INAPPROPRIATE MESSAGES are available at > > http://jse.stat.ncsu.edu/ > > ================================================================= > > > > > >================================================================= >Instructions for joining and leaving this list and remarks about >the problem of INAPPROPRIATE MESSAGES are available at > http://jse.stat.ncsu.edu/ >================================================================= _________________________________________________________ dennis roberts, educational psychology, penn state university 208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED] http://roberts.ed.psu.edu/users/droberts/drober~1.htm ================================================================= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =================================================================
