Re: Cauchy PDF + Parameter Estimate
On 25 Feb 2002 07:56:56 -0800, [EMAIL PROTECTED] (kjetil halvorsen) wrote: >It isstraightforward tlo write down the loglikelihood, and then whatever >optimization routine (there must be one in Matlab) will help you! Just be careful when searching, because Cauchy likelihoods are frequently multi-modal. Duncan Murdoch = 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: The meaning of the p value
On 2 Feb 2001 01:12:59 -0800, [EMAIL PROTECTED] (Will Hopkins) wrote: >I've been involved in off-list discussion with Duncan Murdoch. At one >stage there I was about to retire in disgrace. But sighs of relief... his >objection is Bayesian. Just to clarify, I don't think this is a valid summary of what I said. What I said offline was just a longer version of what I said online in <[EMAIL PROTECTED]>. Duncan Murdoch = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: unequal n's: quadratic weights
On Tue, 30 Jan 2001 23:22:51 -0500, "K. Bloom" <[EMAIL PROTECTED]> wrote: >If your answer IS the correct answer >to my question, perhaps you would kindly explain it to me in a more concrete >way suitable to my simple knowledge of the problem. My means are 2.05, >6.38, and 12.08 for the three groups respectively. In other words.. what >does one calculate and how? I'm still not sure I understand your question completely, but what I think you're asking is this: You have 3 groups of observations. You'd graph them with x-coordinates equal to -1, 0 and +1. The y-coordinates would be the observed data. The means for those three groups are 2.05, 6.38, and 12.08, based on different numbers of observations in each group. You want the quadratic curve that provides the least-squares fit to your data. If that's the case, then the numbers of observations in each group doesn't matter. There's a quadratic curve that goes exactly through each group mean, and you can't find a better fit than that. To find it, do this. Suppose the quadratic curve is A x^2 + B x + C. Then you've got three equations: A (-1)^2 + B (-1) + C = 2.05 A (0)^2 + B (0) + C = 6.38 A (1)^2 + B (1) + C = 12.08 There's a unique solution to these equations; it is C = 6.38, A = (12.08+2.05)/2, B = (12.08-2.05)/2.Those are the least-squares parameter estimates. If you have more than three groups, then you won't be able to find an exact solution like this (you've only got three parameters to play with), and then the least-squares solution *does* depend on the group sizes. In general, you should solve linear least-squares problems using "multiple linear regression"; there are a ton of texts on that and I'd suggest you use one of those. In particular, with unequal group sizes you probably want to use "weighted least squares", with the weights equal to the group sizes. Duncan Murdoch = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: unequal n's: quadratic weights
Serve me right for not checking my work. Here's a correction: On Wed, 31 Jan 2001 12:37:13 GMT, [EMAIL PROTECTED] (Duncan Murdoch) wrote: >To find it, do this. Suppose the quadratic curve is A x^2 + B x + C. >Then you've got three equations: > > A (-1)^2 + B (-1) + C = 2.05 > A (0)^2 + B (0) + C = 6.38 > A (1)^2 + B (1) + C = 12.08 > There's a unique solution to these equations; it is C = 6.38, A = (12.08+2.05)/2-C, B = (12.08-2.05)/2-C.Those are the least-squares parameter estimates. Duncan Murdoch = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: unequal n's: quadratic weights
On Tue, 30 Jan 2001 19:53:03 -0500, "K. Bloom" <[EMAIL PROTECTED]> wrote: >Could someone please tell me how to calculate quadratic coefficients for >unequal sample sizes (equal intervals, three groups)? The formula is not in >the SPSS algorithm notes. Maybe I'm misunderstanding the question, but if you only have 3 groups, your estimates will interpolate the group means. Just solve the 3 linear equations in 3 unknowns, using whatever equation solving method you like. Duncan Murdoch = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: article on Excel errors
On Sun, 28 Jan 2001 16:01:54 GMT, [EMAIL PROTECTED] (Duncan Murdoch) wrote in message <[EMAIL PROTECTED]>: >On 28 Jan 2001 04:04:04 -0800, [EMAIL PROTECTED] (Konrad >Halupka) wrote: >>Look up three papers which have been previously published in the PCPRo, >>all by the same author, I guess. >> >>http://www.woodleyside.co.uk/stats.htm I responded: >The first of those quotes the McCullough and Wilson paper; that's the >only part of the articles that really has any validity. The rest is a >fairly ignorant rant about the fact that Excel and VBA are actually >different languages (e.g. precedence of operators is different, so >"-2^2" is interpreted as 4 in one, as -4 in the other). The author of those articles is Jon Honeyball (you can get his email address from his web page); I've had a short discussion with him by email about my comment above. He's convinced me that it's actually not a "fairly ignorant rant" after all. His main point is that for his audience (business users of Excel), subtleties like operator precedence are just not understood. Microsoft has extensive help systems and offers lots of hints about possible errors, and they *should* warn users when there are potential errors like these. Moreover, the new versions of both Excel and VBA are likely to be incompatible with the old ones in many ways; they should take this opportunity to make them compatible with one another. Duncan Murdoch = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: article on Excel errors
On 28 Jan 2001 04:04:04 -0800, [EMAIL PROTECTED] (Konrad Halupka) wrote: >Look up three papers which have been previously published in the PCPRo, >all by the same author, I guess. > >http://www.woodleyside.co.uk/stats.htm > >(no passwords, but even quoting is "strictly forbidden") The first of those quotes the McCullough and Wilson paper; that's the only part of the articles that really has any validity. The rest is a fairly ignorant rant about the fact that Excel and VBA are actually different languages (e.g. precedence of operators is different, so "-2^2" is interpreted as 4 in one, as -4 in the other). I've never heard of PCPro, where these articles were printed, but I assume from the context and style that it's a UK popular computing magazine. If that's the case, then I would think *they* should be pointing out basic things like this: the fact that operator precedence does vary from language to language, and so do definitions of MOD, and ROUND, etc. Don't blame Microsoft for this. (But do blame them for the crappy statistical routines.) Finally, that copyright notice, which I quote here *without authorization*: "All content is Copyright Woodleyside IT Ltd © 2000 unless otherwise stated. Unauthorised copying, reproduction, emailing, quoting is strictly forbidden. Contact [EMAIL PROTECTED] for more information." What nonsense. Short quotes from published articles are "fair use". He has no authority to forbid me to quote that material. Duncan Murdoch = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Florida votes and statistical errors (fwd)
On 9 Dec 2000 17:28:28 -0800, [EMAIL PROTECTED] (Bob Hayden) wrote: >It's not clear how you split 25 electors among 2 candidates when you >don't know the popular vote, nor if you assume it was a tie. (You >might then have a lawsuit over which elector will be split in two!-) > >There are lots of solutions that seem common-sensical if they >guarantee a pre-determined outcome you find attractive. That's why I >favor tossing a coin. Gore would win if you gave 13 of the votes to Bush, so he'd probably be gracious and give away the undetermined one. Would he still have a lead if the same procedure was used in every state? He got a lot of votes from California based on a very close popular vote. Duncan Murdoch = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Is the vote brouhaha due to statistical falicy?
Surely some voters would choose to leave the ballot blank. If I didn't like any of the presidential candidates, but I thought that some more local election was worth voting in, I might do that. In fact, in the local municipal election that we just had, I was allowed to vote for as many as 4 candidates, but only chose to vote for 2. I would hope that the recount is an attempt to correct counting errors, not to create votes where there were none. Duncan Murdoch On Sun, 19 Nov 2000 09:32:31 -0500, Bob Wheeler <[EMAIL PROTECTED]> wrote: >The model is simplified, but I assume that (B) >votes will be counted by "divining the voter's >intent" through chance imperfections in the >ballots. Thus the probability is 0.50. > >Duncan Murdoch wrote: >> >> On Sat, 18 Nov 2000 22:49:41 -0500, Bob Wheeler <[EMAIL PROTECTED]> >> wrote: >> >> >There are two possibilities: (A) a vote was >> >attempted; (B) no vote was attempted. Let us >> >assume that for (A) the probability of a Gore vote >> >is 0.62, and 0.50 for (B), >> >> If no vote was attempted, then surely the probability that a vote for >> Gore was attempted is 0, not 0.50. >> >> Duncan Murdoch = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Is the vote brouhaha due to statistical falicy?
On Sat, 18 Nov 2000 22:49:41 -0500, Bob Wheeler <[EMAIL PROTECTED]> wrote: >There are two possibilities: (A) a vote was >attempted; (B) no vote was attempted. Let us >assume that for (A) the probability of a Gore vote >is 0.62, and 0.50 for (B), If no vote was attempted, then surely the probability that a vote for Gore was attempted is 0, not 0.50. Duncan Murdoch = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: What is standard deviation exactly?
On Mon, 22 May 2000 13:24:25 +1000, "Glen Barnett"
<[EMAIL PROTECTED]> wrote:
>I assume you're talking about sample standard deviations,
>not population standard deviations (though interpretation
>of what it represents is similar).
>
> ...
>
>Note that the standard deviation can't exceed half the range
>(largest value minus smallest value).
That's true for the n denominator ("population standard deviation"),
but not for n-1 ("sample standard deviation"). For example, if your
sample is just the two points 0 and 1, the sample standard deviation
is 0.71, and the range is 1.
Duncan Murdoch
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