Re: Statistical Distributions
In article [EMAIL PROTECTED], Dennis Roberts [EMAIL PROTECTED] wrote: not to disagree with alan but, my goal was to parallel what glass and stanley did and that is all ...seems like there are all kinds of distributions one might discuss AND, there may be more than one order that is acceptable most books of recent vintage (and g and s was 1970) don't even discuss what g and s did but, just for clarity sake ... are you saying that the nd is a logical SECOND step TO the binomial or, that if you look at the binomial, one could (in many circumstances of n and p) say that the binomial is essentially a nd (very good approximation).. ? the order i had for the nd, chis square, F and t seemed to make sense but, i don't necessarily buy that one NEED to START with the binominal certainly, however, if one talks about the binomial, then the link to the nd is a must I do not see this. The binomial distribution is a natural one; the normal distribution, while it has lots of mathematical properties, is not. As Alan McLean wrote, the normal occurs naturally as an approximation to the binomial, and it was only decades later that it became an important distribution. Gauss attempted to justify it as a distribution of errors on theoretical grounds, but there are flaws with the underlying assumptions, not with the mathematics. The normal distribution is an approximation to much more, and also methods based on the normal distribution are often robust, in the sense that they do well for other distributions. But converting observations or scales so the results will be normal, or even approximately so, should be considered a major error anywhere. Quetelet's naming of it as the distribution of a normal man is just plain wrong. At 06:36 PM 2/17/02 -0500, Timothy W. Victor wrote: I also think Alan's idea is sound. I start my students off with some binomial expansion theory. Alan McLean wrote: This is a good idea, Dennis. I would like to see the sequence start with the binomial - in a very real way, the normal occurs naturally as an 'approximation' to the binomial. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399 [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 = Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at http://jse.stat.ncsu.edu/ =
Re: Statistical Distributions
In article [EMAIL PROTECTED], Dennis Roberts [EMAIL PROTECTED] wrote: addendum if one manipulates n and p in a binomial and, gets to a point where a person would say (or we would say as the instructor) that what you see is very similar to ... and might even be approximated well by ... the nd ... this MEANS that the nd came first in the sense that one would have to be familiar with that before you could draw the parallel This is hardly the case, as the normal distribution seems to have been unknown before De Moivre came up with the approximation. What one does have to know is that a sum can be approximated by an integral; this reverse of this relation between sums and integrals, which is the way that integration should be taught, was known to those with enough mathematical education to be able to understand integration long before differential calculus was discovered. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399 [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 = Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at http://jse.stat.ncsu.edu/ =
Re: Statistical Distributions
At 07:34 AM 2/19/02 -0500, Herman Rubin wrote: I do not see this. The binomial distribution is a natural one; the normal distribution, while it has lots of mathematical properties, is not. i don't know of any distribution that is natural ... what does that mean? inherent in the universe? all distributions are human made ... in the sense that WE observe events ... and, find some function that links events to probabilities all of mathematics ... and statistics too as an offshoot ... is made up Dennis Roberts, 208 Cedar Bldg., University Park PA 16802 Emailto: [EMAIL PROTECTED] WWW: http://roberts.ed.psu.edu/users/droberts/drober~1.htm AC 8148632401 = Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at http://jse.stat.ncsu.edu/ =
Re: Statistical Distributions
In article [EMAIL PROTECTED], Dennis Roberts [EMAIL PROTECTED] wrote: At 07:34 AM 2/19/02 -0500, Herman Rubin wrote: I do not see this. The binomial distribution is a natural one; the normal distribution, while it has lots of mathematical properties, is not. i don't know of any distribution that is natural ... what does that mean? inherent in the universe? all distributions are human made ... in the sense that WE observe events ... and, find some function that links events to probabilities all of mathematics ... and statistics too as an offshoot ... is made up Yes, but much can be well described with mathematical models. This has been called the unreasonable effectiveness of mathematics. The idea of essentially independent events with the same probability can, I believe, be considered natural. Thus, the number of them in a fixed number of trials, and its distribution, can likewise be considered natural. On the other hand, nobody came up with the idea of something having a normal distribution until long after the distribution was known as an approximation to the binomial, and some other cases of the Central Limit Theorem had been found. Gauss did give some mathematical arguments for the distribution of observational errors to be normal, assuming certain properties of observational errors. These are only approximately correct. Poincare stated that everyone believed in normality of natural observations; the empirical people, because they thought the theorists had proved it had to be the case, and the theorists because the empiricists had found it to be so. It is NOT so. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399 [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 = Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at http://jse.stat.ncsu.edu/ =
Re: Statistical Distributions
In article [EMAIL PROTECTED], Timothy W. Victor [EMAIL PROTECTED] wrote: I also think Alan's idea is sound. I start my students off with some binomial expansion theory. Giving not the formulas for the standard distributions but what types of problems result in these is good. But I believe it is important to start out with what happens when those equally likely or other simplifying assumptions are not met. Students seem to have little difficulty in working with equally likely or identically distributed; it is when these are not the case that they seem unable to cope. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399 [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 = Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at http://jse.stat.ncsu.edu/ =
Re: Statistical Distributions
not to disagree with alan but, my goal was to parallel what glass and stanley did and that is all ...seems like there are all kinds of distributions one might discuss AND, there may be more than one order that is acceptable most books of recent vintage (and g and s was 1970) don't even discuss what g and s did but, just for clarity sake ... are you saying that the nd is a logical SECOND step TO the binomial or, that if you look at the binomial, one could (in many circumstances of n and p) say that the binomial is essentially a nd (very good approximation).. ? the order i had for the nd, chis square, F and t seemed to make sense but, i don't necessarily buy that one NEED to START with the binominal certainly, however, if one talks about the binomial, then the link to the nd is a must At 06:36 PM 2/17/02 -0500, Timothy W. Victor wrote: I also think Alan's idea is sound. I start my students off with some binomial expansion theory. Alan McLean wrote: This is a good idea, Dennis. I would like to see the sequence start with the binomial - in a very real way, the normal occurs naturally as an 'approximation' to the binomial. Dennis Roberts, 208 Cedar Bldg., University Park PA 16802 Emailto: [EMAIL PROTECTED] WWW: http://roberts.ed.psu.edu/users/droberts/drober~1.htm AC 8148632401 = Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at http://jse.stat.ncsu.edu/ =
Re: Statistical Distributions
addendum if one manipulates n and p in a binomial and, gets to a point where a person would say (or we would say as the instructor) that what you see is very similar to ... and might even be approximated well by ... the nd ... this MEANS that the nd came first in the sense that one would have to be familiar with that before you could draw the parallel At 06:36 PM 2/17/02 -0500, Timothy W. Victor wrote: I also think Alan's idea is sound. I start my students off with some binomial expansion theory. Alan McLean wrote: This is a good idea, Dennis. I would like to see the sequence start with the binomial - in a very real way, the normal occurs naturally as an 'approximation' to the binomial. Dennis Roberts, 208 Cedar Bldg., University Park PA 16802 Emailto: [EMAIL PROTECTED] WWW: http://roberts.ed.psu.edu/users/droberts/drober~1.htm AC 8148632401 = Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at http://jse.stat.ncsu.edu/ =
Re: Statistical Distributions
Hi Dennis, Dennis Roberts wrote: not to disagree with alan but, my goal was to parallel what glass and stanley did and that is all ...seems like there are all kinds of distributions one might discuss AND, there may be more than one order that is acceptable Sure, I realised that your goal was limited to paralleling GS - but you did ask for suggestions for developing it, and a natural extension of the coverage is one possibility. (And someone recently has been advocating discussion of relationships between the distributions.) It occurs to me that fitting the Poisson into the set also might be a good idea - that would more or less cover the 'basic' distributions. most books of recent vintage (and g and s was 1970) don't even discuss what g and s did but, just for clarity sake ... are you saying that the nd is a logical SECOND step TO the binomial or, that if you look at the binomial, one could (in many circumstances of n and p) say that the binomial is essentially a nd (very good approximation).. ? The former. the order i had for the nd, chis square, F and t seemed to make sense but, i don't necessarily buy that one NEED to START with the binominal certainly, however, if one talks about the binomial, then the link to the nd is a must What I had in mind is something I have thought for a long time (not at all actively, I confess!) but have never seen dealt with, so maybe it is totally off track. That is the idea that a normal distribution can *always* be seen as a limiting expression of a binomial. The binomial is clearly a more basic distribution than the normal, in the sense that it applies to a nominal variable - more specifically, to a dummy variable defined for one value of the nominal variable. It is concerned with whether the value occurs or does not. This registration of occurrence is more primitive than measuring a numerical value of a numeric variable. I believe that the idea expressed above is so, but I am having problems defining it. If anyone has come across this idea, I would be delighted to find a reference to it. Regards, Alan At 06:36 PM 2/17/02 -0500, Timothy W. Victor wrote: I also think Alan's idea is sound. I start my students off with some binomial expansion theory. Alan McLean wrote: This is a good idea, Dennis. I would like to see the sequence start with the binomial - in a very real way, the normal occurs naturally as an 'approximation' to the binomial. Dennis Roberts, 208 Cedar Bldg., University Park PA 16802 Emailto: [EMAIL PROTECTED] WWW: http://roberts.ed.psu.edu/users/droberts/drober~1.htm AC 8148632401 = Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives 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, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at http://jse.stat.ncsu.edu/ =
Re: Statistical Distributions
This is a good idea, Dennis. I would like to see the sequence start with the binomial - in a very real way, the normal occurs naturally as an 'approximation' to the binomial. Alan Dennis Roberts wrote: Back in 1970, Glass and Stanley in their excellent Statistical Methods in Education and Psychology book, Prentice-Hall ... had an excellent chapter on several of the more important distributions used in statistical work (normal, chi square, F, and t) and developed how each was derived from the other(s). Most recent books do not develop distributions in this fashion anymore: they tend to discuss distributions ONLY when a specific test is discussed. I have found this to be a more disjointed treatment. Anyway, I have developed a handout that parallels their chapter, and have used Minitab to do simulation work that supplements what they have presented. The first form of this can be found in a PDF file at: http://roberts.ed.psu.edu/users/droberts/papers/statdist2.PDF Now, there is still some editing work to do AND, working with the spacing of text. Acrobat does not allow too much in the way of EDITING features and, trying to edit the original document and then convert to pdf, is also somewhat of a hit and miss operation. When I get an improved version with better spacing, I will simply copy over the file above. In the meantime, I would appreciate any feedback about this document and the general thrust of it. Feel free to pass the url along to students and others; copy freely and use if you find this helpful. Dennis Roberts, 208 Cedar Bldg., University Park PA 16802 Emailto: [EMAIL PROTECTED] WWW: http://roberts.ed.psu.edu/users/droberts/drober~1.htm AC 8148632401 = Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives 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, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at http://jse.stat.ncsu.edu/ =
Re: Statistical Distributions
I also think Alan's idea is sound. I start my students off with some binomial expansion theory. Alan McLean wrote: This is a good idea, Dennis. I would like to see the sequence start with the binomial - in a very real way, the normal occurs naturally as an 'approximation' to the binomial. Alan Dennis Roberts wrote: Back in 1970, Glass and Stanley in their excellent Statistical Methods in Education and Psychology book, Prentice-Hall ... had an excellent chapter on several of the more important distributions used in statistical work (normal, chi square, F, and t) and developed how each was derived from the other(s). Most recent books do not develop distributions in this fashion anymore: they tend to discuss distributions ONLY when a specific test is discussed. I have found this to be a more disjointed treatment. Anyway, I have developed a handout that parallels their chapter, and have used Minitab to do simulation work that supplements what they have presented. The first form of this can be found in a PDF file at: http://roberts.ed.psu.edu/users/droberts/papers/statdist2.PDF Now, there is still some editing work to do AND, working with the spacing of text. Acrobat does not allow too much in the way of EDITING features and, trying to edit the original document and then convert to pdf, is also somewhat of a hit and miss operation. When I get an improved version with better spacing, I will simply copy over the file above. In the meantime, I would appreciate any feedback about this document and the general thrust of it. Feel free to pass the url along to students and others; copy freely and use if you find this helpful. Dennis Roberts, 208 Cedar Bldg., University Park PA 16802 Emailto: [EMAIL PROTECTED] WWW: http://roberts.ed.psu.edu/users/droberts/drober~1.htm AC 8148632401 = Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives 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, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at http://jse.stat.ncsu.edu/ = -- Tim Victor Policy Research, Evaluation, and Measurement Psychology in Education Division Graduate School of Education University of Pennsylvania = Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at http://jse.stat.ncsu.edu/ =
