whuber

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bio website quantdec.com location Northeastern US age 13 member for 3 years, 4 months seen 9 hours ago profile views 15,173

Consultant (environmental and spatial stats a specialty), expert witness, and teacher. I can be reached through (outdated but still valid) links posted on my web site.

9,933 Comments

 13h comment Why is the scatter diagram always symmetric around the SD line? The first half of this answer (through the statement "Choosing an angle of 45 degrees makes the ellipse symmetric around the square's diagonal (part of the line y=x)") explains this geometrically, perhaps in much more detail than you really wanted :-). 16h comment What's the best way to test the uniformity of location data? Which version of the multivariate Kolmogorov-Smirnov test did you implement? 16h comment How to test whether the variance of two distributions is different if the distributions are not normal Bootstrapping is appealing, but it is not at all clear how it should be conducted, given that no specific statistical model has been proposed in the question. Some kind of model appropriate for the data is essential because (at a minimum) these time series will likely exhibit strong serial correlation. Other details are almost as important: how does one determine which peaks are "small" and which are not? Should the peak widths be measured at half-height or at some other point? What degree of smoothing should be used for the lowess fit? (There is at least one arbitrary parameter to set.) 16h comment How to test whether the variance of two distributions is different if the distributions are not normal Many peer reviewers would point out that (a) these CIs are not CIs for the peak widths and (b) even if they were, direct comparison of CIs is not a legitimate statistical procedure with known Type I and Type II error rates. Whence the original question: how does one formally test the visually apparent differences? 16h comment Goodness of fit test for a normal distribution Suppose there were no observations in one of the middle categories--say, in the interval $(32,34]$. That would be a glaring departure from a Normal distribution, wouldn't it? So should you or should you not include that interval in your calculation? 16h comment How to test whether the variance of two distributions is different if the distributions are not normal Welcome to our site and thank you for posting a clear, well-illustated answer. This looks like a good approach and a promising technique. It appears to fall short of answering the question, however: just how would you go about (a) identifying "peaks" and (b) formally testing their widths? 16h comment How to Reduce Error Term To get useful help, please revise this question to provide some context. Your readers will want to know something about the data, the model, and what options you have in terms of modifying the dataset or the model. 18h comment What's the best way to test the uniformity of location data? Thanks. Because your question explicitly refers to the interval "$(0,1]$," it looks like a 1D question. Please edit it to avoid confusion. When you do so, it would be a good idea to say something about the 2D region you wish to test and how that region is determined (that will influence the answer). 1d comment How to find the leaders in order to apply The Meggitt algorithm This question appears to be off-topic because it is not about statistics, data analysis, or machine learning. 1d comment What's the best way to test the uniformity of location data? What is the dimension of your "space"? What do you mean by a "path"? 1d comment What's the best way to test the uniformity of location data? How does this apply to spatial data? 1d comment What is the meaning of angle brackets? The angle brackets usually denote an expectation. 1d comment Central limit theorem and the law of large numbers @subhash See en.wikipedia.org/wiki/Law_of_large_numbers#Weak_law. 2d comment Test to measure the significane of performance enhancement The use of any test on this dataset is questionable. In what sense could the results be modeled as iid samples from two populations? Dec6 comment Stats is not maths? (And I fully agree about the terminology problems. My pet peeve concerns references to non-existent "populations" in many applications. Ah... there's some linguistic evidence that some of the roots of statistics lie in sampling rather than observations of the cosmos.) Dec6 comment Stats is not maths? Diaconis the magician? I wouldn't conflate gambling with showmanship! You have a point, but you could push back a little better by suggesting that many "investors" are actually gamblers, whence many theoreticians in mathematical finance might truly be motivated by that form of gambling. Just a thought... Anyway, it is clear that by the time Huygens published his little treatise in 1657 that people were creating a theory of probability (and statistics) for reasons much more profound and far-reaching than doing better at the gambling tables. Dec6 comment Differences in power in regression versus mean of a ratio Neither: the Cauchy arises as the ratio of two zero-mean normal variates. See en.wikipedia.org/wiki/…. Dec6 comment Differences in power in regression versus mean of a ratio It's rarely a matter of what distribution is appropriate, but rather of what distribution actually pertains in any given problem. In some contexts a symmetrical distribution of errors for y~x-1 may be appropriate while in others a symmetrical distribution for y/x~1 may be suitable and in yet others something else is needed. Dec6 comment Stats is not maths? You're thinking of Jacobus Bernoulli, posthumous author of ars conjectandi (ed. Nicholaus Bernoulli, 1713). Probably the last people who seemed to be motivated by gambling problems were Pascal and Fermat in 1654, but even then it appears they were using certain gambling problems (the "problem of the points") only as a motivational example and not as the focus of their investigation. (Modern scholarship actually traces the problem of the points to Islamic contract law c. 1200.) The last mathematician of note who truly was motivated by gambling probably was Cardano (1501-1576). Dec6 comment Stats is not maths? That last statement is a more plausible and interesting hypothesis, but it does not hold up well in light of simple examples. For instance, the terminology of "regression" comes from biology and anthropometry, not physics. Stigler's thesis is that astronomers were early adopters of statistical techniques because it made sense to them that observations could be combined in a meaningful way, whereas it was not at all apparent that averaging data about any number of human beings had any meaning whatsoever. That reveals statistics as a tool of the sciences, but not a branch of any one of them.