Re: ranging opines about the range
[ I have rearranged Zar's note.] After this one,
Harold W Kerster [EMAIL PROTECTED] 10/29/01 04:31PM
If you define the range as max - min, you get zero, not one. What
definition are you using.
On 29 Oct 2001 16:11:15 -0800, [EMAIL PROTECTED] (Jerrold Zar)
wrote:
I was referring to the definition that others on the list had proposed:
max - min +1. It is NOT a definition with which I agree.
If {max - min + K} had been a formal proposal, it should have
stated that K will be 1 when the numbers are reported to
the nearest integer, but -- generally -- K should sensibly
reflect the precision of measurement-and-reporting.
I don't know who needs it in the real world most of the time,
but using K gives a better -- usually safer -- estimate when
you are using the range to estimate the standard deviation.
But.
Whenever {max-min} is small enough that K is a sizable
correction, someone needs to speak carefully about the 'range.'
To put it another way: If all the cases all are observed at
the same value, and it matters, then the audience really
does deserve to hear the details.
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
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Re: ranging opines about the range
If you define the range as max - min, you get zero, not one. What definition are you using. Harold W. Kerster, Professor Emeritus Environmental Studies Calif. State U., Sacramento Ph: 916-363-7837 FAX 916-278-7582 = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: ranging opines about the range
I was referring to the definition that others on the list had proposed: max - min +1. It is NOT a definition with which I agree. Jerrold H. Zar, Professor Department of Biological Sciences Northern Illinois University DeKalb, IL 60115 [EMAIL PROTECTED] Harold W Kerster [EMAIL PROTECTED] 10/29/01 04:31PM If you define the range as max - min, you get zero, not one. What definition are you using. Harold W. Kerster, Professor Emeritus Environmental Studies Calif. State U., Sacramento Ph: 916-363-7837 FAX 916-278-7582 = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: ranging opines about the range
The range is routinely considered a measure of dispersion or variability. Applying your definition to a sample of data in which every measurement is identical (for example, 100 body weights, with each body weight being 50 grams), then--even though there is no dispersion, no variability, among the data--the range would be expressed as 1 (in this case, 1 gram). Interesting. Jerrold H. Zar Associate Provost for Graduate Studies and Research and Dean of the Graduate School Northern Illinois University DeKalb, IL 60115-2864 815-753-1883 fax: 815-753-6366 [EMAIL PROTECTED] jeff rasmussen [EMAIL PROTECTED] 10/04/01 05:24PM 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; and irrespective of what the students' textbook and also SPSS said (when I ran some numbers through it) I thought that was the commonly accepted answer. I favor the plus one account as I feel that it balances out the minus one of degrees of freedom and thus puts the Tao correctly in balance. I asked a colleague who also came up with the same answer. Below in I and II are answers from internet sites that also agree. There are also however some sites that define it nakedly as the difference between the maximum minimum; my theory is that the Evil SPSS Empire bought them off as part of their plan for world domination snip = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: ranging opines about the range
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. On a lighter note - sorry - Brits can't use stones as however reluctantly we are now metricated. Selling things in pounds and stones is against the law - though I suppose that using the measure is not - yet! I just tell students I'm B.C. - Before Centimetres. The main thing measured in stones surely used to be people (as in my example) and selling people has been highly illegal for a long time now. -Robert = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: ranging opines about the range
William B. Ware [EMAIL PROTECTED] wrote: 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... I recall textbooks (in the late 1960s and 1970s) that defined both an exclusive range (= max - min) and an inclusive range (= max - min + 1), the latter invariably being illustrated with examples of data that came in integers. (In fact, the examples _may_ always have been of variables that were counts.) On Sat, 6 Oct 2001, Stan Brown replied: Perhaps a better argument is that if you count the numbers you get forty of them: 50, 51, 52, ..., 59 makes ten, and similarly for the 60s, 70s, and 80s. I see the argument, but I don't know as I'd call it better. Seems to be confusing apples with oranges. By the idea of range, does one want to mean the _distance_ between the largest and smallest values in the data, or the _number_of_different_values_ between those two extremes? (These are NOT equivalent concepts!) And if the latter is of interest, does one want the number of different values _in_this_data_set_, or the number of _possible_ different values that might have been observed (under what hypothetical conditions?)? The inclusive range rule supplies the latter (under the assumption that the possible values can only be integers, which is an interesting restriction in itself) -- but not for all imaginable variables. [Counterexample: What's the range of possible values of a hand in cribbage? The smallest possible value is 0, the largest is 29. The exclusive range (in a possibly artificial data set that includes all possible hands, or at least all possible values) is 29-0 = 29. The inclusive range is 30, which is the number of integers between 0 and 29 inclusive. The number of _actual_values_ that can possibly be observed is 29 (of the integers from 0 to 29, 19 is not a possible value for a cribbage hand).] Anyway: one justification for arguing about how to calculate the range lies in not having decided whether one wants to mean range in the sense of distance in the measured variable, or range in the sense of number of [possible?] different values of the measured variable, and indeed in not having perceived that there _is_ such a distinction to be made. As William Ware reminds us, in the idea of range as distance, there may still be a distinction to be made based on the size of the units of measurement to which the measured variable is reported, and on whether one wishes to include the (presumed) half-units at either end of the empirical distribution (or, for variables like age that are customarily truncated rather than rounded, the (presumed) whole unit at the right end). The inclusive argument seems essentially to require (i) that the latent variable being measured be continuous, (ii) that one knows the precision of measurement to which the measured variable is being reported, and (iii) that one wishes not so much to describe the (empirical) sample in hand as to make inferences to the population from which one conceives it to have been drawn, under a specific (but usually only IMplicit) model under which the observed values are thought to have been derived from the latent values. Hmph. Didn't intend to be quite so long-winded. -- DFB. Donald F. Burrill [EMAIL PROTECTED] 184 Nashua Road, Bedford, NH 03110 603-471-7128 = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: ranging opines about the range
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/ =
Re: ranging opines about the range
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/ =
Re: ranging opines about the range
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/
Re: ranging opines about the range
William B. Ware said on 10/5/01 8:58 AM: 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... Another problem with the add one notion based on real limits is that it does not necessarily apply to many real limits situations. The way I introduce real limits to a class is to pass around a piece of paper asking each student to write down their weight. The paper comes to the front of the room while I go through the announcements, review questions, etc. I then write all the numbers on the board and point out that nearly all the students wrote down their weight to the nearest 5th pound. A few went to the nearest single pound. We then discuss in the context of real limits how a weight of 125 pounds represents weights from 122.5 to 127.5, etc. Then we can discuss how all measurements are necessarily representing ranges of values which are beyond the precision of the measuring system. Note, if the idea of real limits necessitating the adding one to the calculation of the range were valid, then in the case of figuring the range of weights for a class, I would do well to add 5. In all cases the amount added to the range calculation depends on the precision of measurement, which becomes a problematic notion, IMO. Paul = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: ranging opines about the range
In article [EMAIL PROTECTED], Robert J. MacG. Dawson [EMAIL PROTECTED] writes 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. On a lighter note - sorry - Brits can't use stones as however reluctantly we are now metricated. Selling things in pounds and stones is against the law - though I suppose that using the measure is not - yet! I just tell students I'm B.C. - Before Centimetres. - Jonathan Robbins 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/ =
Re: ranging opines about the range
William B. Ware [EMAIL PROTECTED] wrote in sci.stat.edu: 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... Perhaps a better argument is that if you count the numbers you get forty of them: 50, 51, 52, ..., 59 makes ten, and similarly for the 60s, 70s, and 80s. -- Stan Brown, Oak Road Systems, Cortland County, New York, USA http://oakroadsystems.com My reply address is correct as is. The courtesy of providing a correct reply address is more important to me than time spent deleting spam. = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
ranging opines about the range
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; and irrespective of what the students' textbook and also SPSS said (when I ran some numbers through it) I thought that was the commonly accepted answer. I favor the plus one account as I feel that it balances out the minus one of degrees of freedom and thus puts the Tao correctly in balance. I asked a colleague who also came up with the same answer. Below in I and II are answers from internet sites that also agree. There are also however some sites that define it nakedly as the difference between the maximum minimum; my theory is that the Evil SPSS Empire bought them off as part of their plan for world domination Finally, we have a waffler's answer in III below... Curious to hear what you think about this defining issue for our times. best, JR from http://www.cuny.edu/tony/edstat22.html I. Measures of Dispersion or Spread Range - is the difference between the highest and lowest values in a group of values plus one. For example, the range of the following group of values 60,70,80,90,100 is 41 and is calculated by subtracting the lowest value (60) from the highest value (100) = 40 plus 1 = 41. from http://www.uwsp.edu/psych/stat/5/CT-Var.htm#II1 II. Range As we noted when discussing the rules for creation of a grouped frequency distribution, the range is given by the highest score in the distribution minus the lowest score plus one. R = XH - XL + 1 from http://luna.cas.usf.edu/~rasch/stat.html III. Measures of Dispersion Range: The Inclusive Range is the highest score minus the lowest score in a distribution plus 1. If the highest score on an examination is 97 and the lowest score 65, the range is 33. The plus 1 correction captures the values from 97.49 to 64.50. The Exclusive Range is just the highest score minus the lowest score. In the above example 32. Jeff Rasmussen http://www.symynet.com website graphic design quantitative software spirit of tao te ching paperback taoism = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: ranging opines about the range
This is news to me - I have only ever heard the range defined as 'maximum - minimum' (and then usually wiped out as a mostly useless statistic..) I usually point out to students that in everyday language the word 'range' is used for the interval - as in 'prices for cabbages ranged from $1 to $2.50', so the statistical usage is (another) one of these words with a different meaning in the field. For a continuous (numeric) variable, the range only makes sense using the max - min definition. If the min is 27.324 and the max is 33.654, the range is 6.333. For a discrete (numeric) variable, you can argue that the concept of 'range' requires continuity, so that we have to assume the values are rounded. So for exam marks, recorded to the nearest per cent, a max of 97 is assumed to be rounded from somewhere in the interval 96.5 to 97.5; a min of 35 is likewise considered to be rounded from 34.5 to 35.5. With this model, the max value may have been as high as 97.5 and the min as low as 34.5, so the range is calculated as 97.5 - 34.5. This gives you your +1 calculation - that is, it is a correction for continuity. Regards, Alan 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; and irrespective of what the students' textbook and also SPSS said (when I ran some numbers through it) I thought that was the commonly accepted answer. I favor the plus one account as I feel that it balances out the minus one of degrees of freedom and thus puts the Tao correctly in balance. I asked a colleague who also came up with the same answer. Below in I and II are answers from internet sites that also agree. There are also however some sites that define it nakedly as the difference between the maximum minimum; my theory is that the Evil SPSS Empire bought them off as part of their plan for world domination Finally, we have a waffler's answer in III below... Curious to hear what you think about this defining issue for our times. best, JR from http://www.cuny.edu/tony/edstat22.html I. Measures of Dispersion or Spread Range - is the difference between the highest and lowest values in a group of values plus one. For example, the range of the following group of values 60,70,80,90,100 is 41 and is calculated by subtracting the lowest value (60) from the highest value (100) = 40 plus 1 = 41. from http://www.uwsp.edu/psych/stat/5/CT-Var.htm#II1 II. Range As we noted when discussing the rules for creation of a grouped frequency distribution, the range is given by the highest score in the distribution minus the lowest score plus one. R = XH - XL + 1 from http://luna.cas.usf.edu/~rasch/stat.html III. Measures of Dispersion Range: The Inclusive Range is the highest score minus the lowest score in a distribution plus 1. If the highest score on an examination is 97 and the lowest score 65, the range is 33. The plus 1 correction captures the values from 97.49 to 64.50. The Exclusive Range is just the highest score minus the lowest score. In the above example 32. Jeff Rasmussen http://www.symynet.com website graphic design quantitative software spirit of tao te ching paperback taoism = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ = -- Alan McLean ([EMAIL PROTECTED]) Department of Econometrics and Business Statistics Monash University, Caulfield Campus, Melbourne Tel: +61 03 9903 2102Fax: +61 03 9903 2007 = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
