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2477 | 2 | null | 125 | 12 | null | I have read some parts of [A First Course in Bayesian Statistical Methods](http://rads.stackoverflow.com/amzn/click/0387922997) by Peter Hoff, and I found it easy to follow. (Example R-code is provided throughout the text)
| null | CC BY-SA 3.0 | null | 2010-09-08T10:28:33.510 | 2012-01-25T05:18:00.047 | 2012-01-25T05:18:00.047 | 7497 | 339 | null |
2478 | 2 | null | 2476 | 24 | null | For text documents, the feature vectors can be very high dimensional and sparse under any of the standard representations (bag of words or TF-IDF etc). Measuring distances directly under such a representation may not be reliable since it is a known fact that in very high dimensions, distance between any two points star... | null | CC BY-SA 2.5 | null | 2010-09-08T10:49:23.317 | 2010-09-08T10:58:25.990 | 2010-09-08T10:58:25.990 | 881 | 881 | null |
2481 | 1 | 2495 | null | 7 | 4273 | I have found the term "asymptotic power of a statistical test" only related to the Kolmogorov-Smirnov test (to be precise: asyptotic power = 1). What does this term acctually mean? In my opinion it should be someting like this: "if the alternative hypothesis is true, than for every significance level alpha there exists... | Asymptotic power | CC BY-SA 2.5 | null | 2010-09-08T11:33:12.393 | 2019-01-16T15:02:26.317 | 2019-01-16T15:02:26.317 | 11887 | 1215 | [
"hypothesis-testing",
"statistical-significance",
"statistical-power",
"asymptotics"
] |
2482 | 2 | null | 2466 | 10 | null | How's the Garvan?
The problem is we don't know how many zero counts are observed. We have to estimate this. A classic statistical procedure for situations like this is the Expectation-Maximisation algorithm.
A simple example:
Assume we draw from an unknown population (of 1,000,000) with a poisson constant of 0.2.
```
c... | null | CC BY-SA 2.5 | null | 2010-09-08T11:44:25.410 | 2010-09-08T13:35:34.850 | 2010-09-08T13:35:34.850 | null | 521 | null |
2483 | 1 | 2539 | null | 2 | 459 | I have reformulated the problem from a "dog barking warning system" to something else which hopefully, has less ambiguity. Instead, I will repose the problem as follows:
Let's assume that my neighbour is a "mad scientist", who claims to have invented a "terrorist event" forecasting machine. The machine has three colore... | How to model and test a decision support system (e.g. a terrorist warning system)? | CC BY-SA 3.0 | null | 2010-09-08T11:49:25.087 | 2016-08-09T13:08:57.997 | 2016-08-09T13:08:57.997 | 22468 | 1216 | [
"confidence-interval",
"modeling",
"model-selection",
"experiment-design"
] |
2486 | 2 | null | 2481 | 3 | null | As I understood it, the asymptotic power is the hypothetical power when the effect size goes to zero and the sample size to infinity. Basically it should be 0 or 1, indicating whether the test cannot or can distinguish an arbitrary small deviation from the null hypothesis when the sample size is sufficiently large.
| null | CC BY-SA 2.5 | null | 2010-09-08T12:54:35.677 | 2010-09-08T12:54:35.677 | null | null | 1124 | null |
2487 | 2 | null | 2481 | 1 | null | Yes, you are right. I would only replace "there exists a sample size n that the selected test would reject the null hypothesis" with "for every e>0 there exists a sample size n_0 such that the probability to reject the null hypothesis is greater than 1-e for all n>n_0".
| null | CC BY-SA 2.5 | null | 2010-09-08T13:43:43.877 | 2010-09-08T13:43:43.877 | null | null | 1219 | null |
2489 | 2 | null | 2483 | 3 | null | I have thought about this question a while and have come to the following rather vague answer to a, in my eyes, rather vague question. Despite the asker's wish I don't use the word model as I didn't get it into my thinking on this problem. Sorry for that.
- What is your hypothesis?
I see three different possible inter... | null | CC BY-SA 2.5 | null | 2010-09-08T15:43:01.230 | 2010-09-08T15:49:37.677 | 2010-09-08T15:49:37.677 | 442 | 442 | null |
2490 | 2 | null | 2483 | 2 | null | Count sucesses an failures when the barking patterns occur and get a contingency table. Then do a Chi squared test against 50/50 occurences (ie null hypothesis is that barking is not correlated with getting the correct weather pattern).
Of course, there is also the other side of this to consider: what barking pattern p... | null | CC BY-SA 2.5 | null | 2010-09-08T16:31:59.693 | 2010-09-08T16:31:59.693 | null | null | 229 | null |
2491 | 2 | null | 321 | 6 | null | The second paper you cite seems to contain the answer to your question. To recap; mathematically, the main difference is in the shape of the loss function being used. Friedman, Hastie, and Tibshirani's loss function being easier to optimize at each iteration. –
| null | CC BY-SA 2.5 | null | 2010-09-08T17:30:41.103 | 2010-09-08T17:30:41.103 | null | null | 603 | null |
2492 | 1 | 2498 | null | 371 | 140129 | A former colleague once argued to me as follows:
>
We usually apply normality tests to the results of processes that,
under the null, generate random variables that are only
asymptotically or nearly normal (with the 'asymptotically' part dependent on some quantity which we cannot make large); In the era of
chea... | Is normality testing 'essentially useless'? | CC BY-SA 3.0 | null | 2010-09-08T17:47:21.820 | 2019-02-03T14:17:07.813 | 2016-01-16T19:01:05.907 | 100906 | 795 | [
"hypothesis-testing",
"normality-assumption",
"philosophical"
] |
2493 | 1 | 2497 | null | 16 | 1651 | I'm looking for the appropriate theoretical framework or speciality to help me deal with understanding how to deal with the errors that the GPS system has - especially when dealing with routes.
Fundamentally, I'm looking for the requirements on the data and any algorithms to use to be able to establish the length of a ... | Managing error with GPS routes (theoretical framework?) | CC BY-SA 4.0 | null | 2010-09-08T19:48:42.110 | 2022-11-28T05:22:50.090 | 2022-11-28T05:22:50.090 | 362671 | 1227 | [
"error",
"sampling"
] |
2495 | 2 | null | 2481 | 7 | null | The definition above (a fixed alternative, sample size going to infinity) is more precisely related to the consistency (or not) of a hypothesis test. That is, a test is consistent against a fixed alternative if the power function approaches 1 at that alternative.
Asymptotic power is something different. As Joris rema... | null | CC BY-SA 2.5 | null | 2010-09-08T20:23:12.640 | 2010-09-11T00:47:08.027 | 2010-09-11T00:47:08.027 | null | null | null |
2496 | 2 | null | 2446 | 2 | null | This a very simple multi-level (a.k.a. hierarchical) model. Douglas Bate his currently working on a book on the subject (draft avalaible here: [http://lme4.r-forge.r-project.org/book/](http://lme4.r-forge.r-project.org/book/)). While there are many books on this subject, Doug's has the added benefit of being designed a... | null | CC BY-SA 2.5 | null | 2010-09-08T21:21:58.237 | 2010-09-08T21:27:01.180 | 2010-09-08T21:27:01.180 | 603 | 603 | null |
2497 | 2 | null | 2493 | 8 | null | This is a well studied problem in geospatial science--you can find discussions of it on GIS forums.
First, note that the wiggles do not necessarily increase the route's length, because many of them actually cut inside curves. (I have evaluated this by having an entire classroom of students digitize the same path and t... | null | CC BY-SA 2.5 | null | 2010-09-08T22:10:12.760 | 2010-09-08T22:10:12.760 | null | null | 919 | null |
2498 | 2 | null | 2492 | 273 | null | It's not an argument. It is a (a bit strongly stated) fact that formal normality tests always reject on the huge sample sizes we work with today. It's even easy to prove that when n gets large, even the smallest deviation from perfect normality will lead to a significant result. And as every dataset has some degree of ... | null | CC BY-SA 3.0 | null | 2010-09-08T22:23:19.163 | 2018-03-05T07:03:51.740 | 2018-03-05T07:03:51.740 | 197523 | 1124 | null |
2499 | 1 | 2506 | null | 85 | 25263 | There are several distinct usages:
- kernel density estimation
- kernel trick
- kernel smoothing
Please explain what the "kernel" in them means, in plain English, in your own words.
| What is a "kernel" in plain English? | CC BY-SA 3.0 | null | 2010-09-09T00:15:07.943 | 2018-07-30T10:14:22.703 | 2015-04-23T05:52:50.573 | 9964 | 74 | [
"kernel-trick",
"kernel-smoothing"
] |
2500 | 2 | null | 2499 | 50 | null | There appear to be at least two different meanings of "kernel": one more commonly used in statistics; the other in machine learning.
In statistics "kernel" is most commonly used to refer to [kernel density estimation](http://en.wikipedia.org/wiki/Kernel_density_estimation) and [kernel smoothing](http://en.wikipedia.org... | null | CC BY-SA 4.0 | null | 2010-09-09T01:21:55.677 | 2018-07-30T10:14:22.703 | 2018-07-30T10:14:22.703 | 121522 | 521 | null |
2501 | 2 | null | 2492 | 209 | null | When thinking about whether normality testing is 'essentially useless', one first has to think about what it is supposed to be useful for. Many people (well... at least, many scientists) misunderstand the question the normality test answers.
The question normality tests answer: Is there convincing evidence of any devi... | null | CC BY-SA 2.5 | null | 2010-09-09T02:35:31.153 | 2010-09-09T21:37:22.197 | 2010-09-09T21:37:22.197 | 25 | 25 | null |
2504 | 1 | 2511 | null | 31 | 4050 | Is it possible to test for finiteness (or existence) of the variance of a random variable given a sample? As a null, either {the variance exists and is finite} or {the variance does not exist/is infinite} would be acceptable. Philosophically (and computationally), this seems very strange because there should be no diff... | Test for finite variance? | CC BY-SA 2.5 | null | 2010-09-09T06:01:05.300 | 2017-04-07T23:18:53.103 | 2011-11-02T13:27:19.020 | 6961 | 795 | [
"hypothesis-testing",
"variance",
"central-limit-theorem"
] |
2506 | 2 | null | 2499 | 44 | null | In both statistics (kernel density estimation or kernel smoothing) and machine learning (kernel methods) literature, kernel is used as a measure of similarity. In particular, the kernel function $k(x,.)$ defines the distribution of similarities of points around a given point $x$. $k(x,y)$ denotes the similarity of poin... | null | CC BY-SA 3.0 | null | 2010-09-09T06:09:23.923 | 2015-04-23T06:19:47.650 | 2015-04-23T06:19:47.650 | 35989 | 881 | null |
2507 | 2 | null | 2492 | 15 | null | Let me add one small thing:
Performing a normality test without taking its alpha-error into account heightens your overall probability of performing an alpha-error.
You shall never forget that each additional test does this as long as you don't control for alpha-error accumulation. Hence, another good reason to dismis... | null | CC BY-SA 2.5 | null | 2010-09-09T08:59:38.777 | 2010-09-09T08:59:38.777 | null | null | 442 | null |
2509 | 2 | null | 1923 | 5 | null | I think the standard solution goes as follows. I'll just do the scalar case, the multi parameter case is similar. Your objective function is $g_N(p,X_1,\dots,X_N)$
where $p$ is the parameter you want to estimate and $X_1,\dots,X_N$ are the observed random variables. For notational simplicity I will just write the obj... | null | CC BY-SA 3.0 | null | 2010-09-09T12:02:48.057 | 2013-11-19T21:13:50.550 | 2013-11-19T21:13:50.550 | 352 | 352 | null |
2510 | 1 | 2521 | null | 4 | 1032 | For the more mathematically minded,
we have $x \in \mathbb{R}^2$ and the function $h(x)$ defined as:
$h(x)=\alpha_1x_1^2+\alpha_2x_2^2+\alpha_3x_1+\alpha_4x_2+\alpha_5x_1x_2+\alpha_6$
and the vector of alpha's is known and further guaranteed to be such that $h(x)$ is a general
elliptic paraboloid (i.e. a convex funct... | Can we approximate this function by a polynomial? | CC BY-SA 2.5 | null | 2010-09-09T12:33:53.397 | 2010-09-09T20:15:54.960 | 2010-09-09T19:21:26.227 | 603 | 603 | [
"approximation"
] |
2511 | 2 | null | 2504 | 14 | null | No, this is not possible, because a finite sample of size $n$ cannot reliably distinguish between, say, a normal population and a normal population contaminated by a $1/N$ amount of a Cauchy distribution where $N$ >> $n$. (Of course the former has finite variance and the latter has infinite variance.) Thus any fully ... | null | CC BY-SA 2.5 | null | 2010-09-09T12:57:35.380 | 2010-09-09T12:57:35.380 | null | null | 919 | null |
2513 | 1 | 2530 | null | 8 | 4148 | I have 2560 paired observations from an experiment in which participants provided two ratings for a set of objects, at two different points in time. Half of the objects in the set had the value of an attribute A changed between the two time points, half did not. Of the objects that were changed in each participant's ... | Pitman's test of equality of variance and testing for regression to the mean: am I doing the right thing? | CC BY-SA 2.5 | null | 2010-09-09T15:04:28.853 | 2010-09-28T02:27:31.433 | 2010-09-10T11:50:47.273 | 266 | 266 | [
"regression",
"standard-deviation",
"variance"
] |
2516 | 1 | 2519 | null | 176 | 52251 | In a [recent article](http://magazine.amstat.org/blog/2010/09/01/statrevolution/) of Amstat News, the authors (Mark van der Laan and Sherri Rose) stated that "We know that for large enough sample sizes, every study—including ones in which the null hypothesis of no effect is true — will declare a statistically significa... | Are large data sets inappropriate for hypothesis testing? | CC BY-SA 2.5 | null | 2010-09-09T18:21:30.200 | 2021-10-15T14:16:05.627 | 2019-11-29T13:29:23.393 | 11887 | 666 | [
"hypothesis-testing",
"statistical-significance",
"dataset",
"sample-size",
"large-data"
] |
2517 | 2 | null | 2516 | 2 | null | I think what they mean is that one often makes an assumption about the probability density of the null hypothesis which has a 'simple' form but does not correspond to the true probability density.
Now with small data sets, you might not have enough sensitivity to see this effect but with a large enough data set you wi... | null | CC BY-SA 2.5 | null | 2010-09-09T18:42:48.590 | 2010-09-09T18:42:48.590 | null | null | 961 | null |
2518 | 2 | null | 2516 | 10 | null | In a certain sense, [all] many null hypothesis are [always] false (the group of people living in houses with odd numbers does never exactly earn the same on average as the group of people living in houses with even numbers).
In the frequentist framework, the question that is asked is whether the difference in income b... | null | CC BY-SA 2.5 | null | 2010-09-09T18:55:04.400 | 2010-09-09T19:55:14.900 | 2010-09-09T19:55:14.900 | 603 | 603 | null |
2519 | 2 | null | 2516 | 115 | null | It is not true. If the null hypothesis is true then it will not be rejected more frequently at large sample sizes than small. There is an erroneous rejection rate that's usually set to 0.05 (alpha) but it is independent of sample size. Therefore, taken literally the statement is false. Nevertheless, it's possible that... | null | CC BY-SA 3.0 | null | 2010-09-09T18:59:36.507 | 2017-08-05T07:36:50.280 | 2017-08-05T07:36:50.280 | 601 | 601 | null |
2520 | 2 | null | 2510 | 1 | null | Note that $h(x)$ itself is a polynomial in $x_1$ and $x_2$ and $g(x)$ is what I would call a truncated polynomial.
The region where $h(x)$ is negative, $g(x)$ will be zero. You can approximate this region where $h(x)$ is flat by a non-constant polynomial (non-constant because you also need to approximate the region wh... | null | CC BY-SA 2.5 | null | 2010-09-09T19:00:45.007 | 2010-09-09T19:00:45.007 | null | null | 961 | null |
2521 | 2 | null | 2510 | 6 | null | The $L^2$ distance between $g$ and a polynomial approximation will be finite if and only if the polynomial approximation behaves asymptotically like $g$, which means it behaves asymptotically like $h$, which implies it must equal $h$. Therefore $h$ is the unique $L^2$ approximator.
Thus:
(1) Yes; the global approximat... | null | CC BY-SA 2.5 | null | 2010-09-09T19:27:32.943 | 2010-09-09T20:15:54.960 | 2010-09-09T20:15:54.960 | 919 | 919 | null |
2522 | 2 | null | 2516 | 35 | null | I agree with the answers that have appeared, but would like to add that perhaps the question could be redirected. Whether to test a hypothesis or not is a research question that ought, at least in general, be independent of how much data one has. If you really need to test a hypothesis, do so, and don't be afraid of ... | null | CC BY-SA 2.5 | null | 2010-09-09T19:42:26.763 | 2010-09-09T19:42:26.763 | null | null | 919 | null |
2524 | 2 | null | 1646 | 4 | null | I think (1) is not a statistical question but a subject-area one. E.g., in the described example it would be up to those who study group psychology to determine appropriate language for the strength of ICCs. This is analogous to a Pearson correlation -- what constitutes 'strong' differs depending on whether one is wor... | null | CC BY-SA 2.5 | null | 2010-09-09T20:39:15.037 | 2010-09-09T20:39:15.037 | null | null | 1107 | null |
2525 | 2 | null | 363 | 12 | null | Long ago, Jack Kiefer's little monograph ["Introduction to Statistical Inference"](http://rads.stackoverflow.com/amzn/click/0387964207) peeled away the mystery of a great deal of classical statistics and helped me get started with the rest of the literature. I still refer to it and warmly recommend it to strong studen... | null | CC BY-SA 2.5 | null | 2010-09-09T22:52:29.493 | 2011-02-20T02:32:14.440 | 2011-02-20T02:32:14.440 | 159 | 919 | null |
2526 | 2 | null | 1520 | -1 | null | You're right about the expectation.
You actually also have the right answer to the probability of getting more than your original stake back, although not the right proof. Consider, instead of the raw amount of money you have, its base-2 logarithm. This turns out to be the number of times you've doubled your money, mi... | null | CC BY-SA 2.5 | null | 2010-09-09T23:09:59.063 | 2010-09-09T23:09:59.063 | null | null | 98 | null |
2528 | 2 | null | 2516 | 17 | null | A (frequentist) hypothesis test, precisely, address the question of the probability of the observed data or something more extreme would be likely assuming the null hypothesis is true. This interpretation is indifferent to sample size. That interpretation is valid whether the sample is of size 5 or 1,000,000.
An impo... | null | CC BY-SA 3.0 | null | 2010-09-10T03:51:12.823 | 2018-02-27T21:16:38.203 | 2018-02-27T21:16:38.203 | 485 | 485 | null |
2529 | 2 | null | 36 | 2 | null | The more fire engines sent to a fire, the bigger the damage.
| null | CC BY-SA 2.5 | null | 2010-09-10T07:40:27.233 | 2010-09-10T07:40:27.233 | null | null | 1048 | null |
2530 | 2 | null | 2513 | 3 | null | As far as I know, the Pitman test is formulated as :
$$F=\frac{SD_2}{SD_1} ~with~ SD_2 > SD_1$$
$$T=\frac{(F-1)\sqrt{n-2}}{2\sqrt{F(1-r^2)}} $$ with $r$ the correlation between the scores in sample 1 and sample 2. This is not equivalent to the formula you use and mentioned in the paper. I'm not positive about my formul... | null | CC BY-SA 2.5 | null | 2010-09-10T09:52:48.877 | 2010-09-10T09:52:48.877 | null | null | 1124 | null |
2531 | 2 | null | 2516 | 5 | null | Hypothesis testing for large data should the desired level of difference into account, rather than whether there is a difference or not. You're not interested in the H0 that the estimate is exactly 0. A general approach would be to test whether the difference between the null hypothesis and the observed value is larger... | null | CC BY-SA 2.5 | null | 2010-09-10T10:03:13.960 | 2010-09-10T13:45:11.413 | 2010-09-10T13:45:11.413 | 1124 | 1124 | null |
2532 | 2 | null | 36 | 5 | null | when $x_t$; $y_t$ are stationary time series, then correlation between $y_t$ and $x_{t-1}$ implies causation of $y_t$ by $x_{t-1}$. For some reason it's not mentioned here.
| null | CC BY-SA 2.5 | null | 2010-09-10T10:48:33.617 | 2010-09-10T10:48:33.617 | null | null | 603 | null |
2535 | 2 | null | 1646 | 1 | null | 1) With correlations, you can never really give sensible cut-offs, but the general rules of the normal correlation apply I'd say.
2) Regarding the appropriateness of the ICC : depending on the data, the ICC is equivalent to an F-test (see eg [Commenges & Jacqmin, 1994](http://www.jstor.org/stable/2533395) and [Kistner... | null | CC BY-SA 2.5 | null | 2010-09-10T11:28:41.017 | 2010-09-10T11:28:41.017 | null | null | 1124 | null |
2536 | 2 | null | 534 | 42 | null | I'll just add some additional comments about causality as viewed from an epidemiological perspective. Most of these arguments are taken from [Practical Psychiatric Epidemiology](http://occmed.oxfordjournals.org/content/56/6/434.2.full), by Prince et al. (2003).
Causation, or causality interpretation, are by far the mos... | null | CC BY-SA 2.5 | null | 2010-09-10T12:33:09.340 | 2010-10-02T17:02:16.690 | 2010-10-02T17:02:16.690 | 930 | 930 | null |
2537 | 1 | 2538 | null | 4 | 3566 | Say we have 5 items, and people are asked which item they like. Multiple answers are possible, but also no answer is possible. The people are categorized according to factors like gender, age, and so on. One possible approach to analyze the differences between genders, age groups and so on is making use of the [General... | Confidence intervals on differences in choices in a GEE framework: methods and alternatives? | CC BY-SA 2.5 | null | 2010-09-10T12:51:35.787 | 2010-11-01T11:02:10.263 | 2010-11-01T11:02:10.263 | 930 | 1124 | [
"confidence-interval",
"estimation",
"mixed-model",
"psychometrics",
"random-effects-model"
] |
2538 | 2 | null | 2537 | 5 | null | Well, the [gee](http://cran.r-project.org/web/packages/gee/index.html) package includes facilities for fitting GEE and `gee()` return asymptotic and robust SE. I never used the [geepack](http://cran.r-project.org/web/packages/geepack/index.html) package. From what I saw in the online example, output seems to resemble m... | null | CC BY-SA 2.5 | null | 2010-09-10T14:46:40.440 | 2010-09-10T15:37:00.850 | 2010-09-10T15:37:00.850 | 930 | 930 | null |
2539 | 2 | null | 2483 | 3 | null | I am going to give a simple answer in response to your edit. If my answer does not meet your real needs please include it in the comments and I will change/complexify it a bit.
Let:
$S$ be the severity of the event of interest with higher numbers representing more severity
$W$ be the warning generated by the system.
Th... | null | CC BY-SA 2.5 | null | 2010-09-10T16:30:12.310 | 2010-09-10T18:25:12.273 | 2010-09-10T18:25:12.273 | null | null | null |
2540 | 2 | null | 1520 | 1 | null | Let $S_k$ be the wealth after $k$ plays of this game, where we assume $S_0 = 1.$ The temptation here is to take $X_k = \log{S_k}$, and study $X_k$ as a symmetric random walk, with innovations of size $\pm \log{2}$. This, as it turns out, will be fine for the second question, but not the first. A bit of work will show t... | null | CC BY-SA 2.5 | null | 2010-09-10T16:32:41.367 | 2010-09-11T21:21:57.313 | 2010-09-11T21:21:57.313 | 795 | 795 | null |
2541 | 1 | 2542 | null | 51 | 107639 | I have read/heard many times that the sample size of at least 30 units is considered as "large sample" (normality assumptions of means usually approximately holds due to the CLT, ...). Therefore, in my experiments, I usually generate samples of 30 units. Can you please give me some reference which should be cited when... | What references should be cited to support using 30 as a large enough sample size? | CC BY-SA 3.0 | null | 2010-09-10T17:07:39.130 | 2022-03-15T23:55:20.267 | 2017-12-04T09:46:55.683 | 28666 | 1215 | [
"references",
"sample-size",
"normality-assumption",
"central-limit-theorem",
"rule-of-thumb"
] |
2542 | 2 | null | 2541 | 45 | null | The choice of n = 30 for a boundary between small and large samples is a rule of thumb, only. There is a large number of books that quote (around) this value, for example, Hogg and Tanis' Probability and Statistical Inference (7e) says "greater than 25 or 30".
That said, the story told to me was that the only reason 30... | null | CC BY-SA 2.5 | null | 2010-09-10T17:44:58.943 | 2010-09-10T17:44:58.943 | null | null | null | null |
2543 | 2 | null | 146 | 3 | null | If your data is high dimensional and noisy, and you don't have a large number of sample, you run into the danger of overfitting. In such cases, it does make sense to use PCA (which can capture a dominant part of data variance; orthogonality isn't an issue) or factor analysis (which can find the true explanatory variabl... | null | CC BY-SA 2.5 | null | 2010-09-10T18:14:48.727 | 2010-09-10T18:14:48.727 | null | null | 881 | null |
2544 | 2 | null | 2541 | 9 | null | IMO, it all depends on what you want to use your sample for. Two "silly" examples to illustrate what I mean: If you need to estimate a mean, 30 observations is more than enough. If you need to estimate a linear regression with 100 predictors, 30 observations will not be close to enough.
| null | CC BY-SA 2.5 | null | 2010-09-10T18:41:42.803 | 2010-09-10T18:41:42.803 | null | null | 1204 | null |
2545 | 2 | null | 2541 | 10 | null | Mostly arbitrary rule of thumb. This statement depends on a number of factor to be true. For example on the distribution of the data. If the data comes from a Cauchy for example, even 30^30 observations are not enough to estimate the mean (in that case even an infinite number of observations would not be enough to caus... | null | CC BY-SA 3.0 | null | 2010-09-10T19:05:05.227 | 2017-12-04T09:48:55.993 | 2017-12-04T09:48:55.993 | 603 | 603 | null |
2546 | 2 | null | 2541 | 52 | null | Actually, the "magic number" 30 is a fallacy. See Jacob's Cohen's delightful paper, [Things I Have Learned (So Far) (Am. Psych. December 1990 45 #12, pp 1304-1312)](https://pdfs.semanticscholar.org/fa77/0a7fb7c45a59abbc4c2bc7d174fa51e5d946.pdf). This myth is his first example of how "some things you learn aren't so".
>... | null | CC BY-SA 4.0 | null | 2010-09-10T19:42:16.590 | 2019-05-16T11:14:23.453 | 2020-06-11T14:32:37.003 | -1 | 666 | null |
2547 | 1 | 2550 | null | 50 | 96987 |
- If you look at Wolfram Alpha
- Or this Wikipedia page List of countries by median age
Clearly [median](http://en.wikipedia.org/wiki/Median) seems to be the statistic of choice when it comes to ages.
I am not able t... | Why is median age a better statistic than mean age? | CC BY-SA 2.5 | null | 2010-09-10T20:26:56.997 | 2020-07-25T12:06:36.090 | 2020-07-25T12:06:36.090 | 7290 | 285 | [
"mean",
"median",
"types-of-averages"
] |
2548 | 2 | null | 2547 | 18 | null | John gave you a good answer on the sister site.
One aspect he didn't mention explicitly is robustness: median as a measure of central location does better than the mean as it has a higher breakdown point (of 50%) whereas the mean has a very low one of 0 (see wikipedia for details).
Intuitively, it means that individ... | null | CC BY-SA 2.5 | null | 2010-09-10T20:48:49.707 | 2010-09-10T20:48:49.707 | null | null | 334 | null |
2549 | 2 | null | 2547 | 1 | null | John's answer on math.stackexchange can be viewed as the following:
>
When you have a skewed distribution the median may be a better summary statistic than the mean.
Note that when he says that there are more infants than adults he essentially is suggesting that the age distribution is a skewed distribution.
| null | CC BY-SA 2.5 | null | 2010-09-10T21:33:58.017 | 2010-09-10T21:33:58.017 | null | null | null | null |
2550 | 2 | null | 2547 | 53 | null | Statistics does not provide a good answer to this question, in my opinion. A mean can be relevant in mortality studies for example, but ages are not as easy to measure as you might think. Older people, illiterate people, and people in some third-world countries tend to round their ages to a multiple of 5 or 10, for i... | null | CC BY-SA 3.0 | null | 2010-09-10T22:17:24.443 | 2016-10-22T23:06:11.547 | 2016-10-22T23:06:11.547 | 92454 | 919 | null |
2551 | 2 | null | 726 | 11 | null | >
There is no free hunch.
-- Robert Abelson
| null | CC BY-SA 2.5 | null | 2010-09-10T23:05:50.640 | 2010-09-10T23:05:50.640 | null | null | 666 | null |
2552 | 2 | null | 1908 | 1 | null | [European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML PKDD)](http://www.ecmlpkdd2010.org/)
To see the type of papers presented at the conference see the videos of the last confenece on [videolectures.net](http://videolectures.net/ecmlpkdd09_bled/)
| null | CC BY-SA 2.5 | null | 2010-09-10T23:50:38.213 | 2010-09-10T23:50:38.213 | null | null | 1215 | null |
2553 | 2 | null | 2547 | 7 | null | Why is an axe better than a hatchet?
That's similar to your question. They just mean and do different things. If one is talking about medians then the story they are trying to convey, the model they are trying to apply to the data, is different than one with means.
| null | CC BY-SA 2.5 | null | 2010-09-11T00:30:30.430 | 2010-09-11T00:30:30.430 | null | null | 601 | null |
2555 | 1 | 2558 | null | 3 | 618 | In "On Gaussian-like Densities of Order Greater than Two" (Willett, P. Thomas, J. B., 1987), section II, the author state:
$\mathcal{N}(x,y,\rho)=\phi(x)\phi(y)\sum_{n=0}^{\infty}\rho^nH_n(x)H_n(y)$
where
- $\phi(.)$ is the unit normal density,
- $H_n(.)$ is the $n^{th}$ Hermite polynomial,
- $\mathcal{N}(x,y,\rho)$... | Issues using Hermite approximation to bivariate Gaussian in R | CC BY-SA 2.5 | null | 2010-09-11T01:13:44.640 | 2010-09-11T04:44:51.973 | 2010-09-11T01:39:26.823 | 603 | 603 | [
"approximation"
] |
2558 | 2 | null | 2555 | 5 | null | It would appear that you neglected to normalize your Hermite polynomials. Try this:
```
library(PolynomF)
x <- polynom()
H <- polylist(1,x); for(n in 2:10) H[[n+1]] <- x*H[[n]] - (n-1)*H[[n-1]]
for(n in 1:11) H[[n]] <- H[[n]]*exp(-lgamma(n)/2)
Hp <- as.function(H)
#The (normalized) Hermite polynomial of order 10
rho <... | null | CC BY-SA 2.5 | null | 2010-09-11T04:44:51.973 | 2010-09-11T04:44:51.973 | null | null | null | null |
2559 | 1 | 2570 | null | 7 | 912 | The following paper describes an implementation of R in parallel on a graphics processing unit (GPU).
- Buckner et al., The gputools package enables GPU computing in R, BIOINFORMATICS, Vol. 26 no. 1 2010, pages 134–135
In the experimental section, on a 4-core computer, they compare the performance of the program run... | Gputools for R: how to interpret the experimental procedure? | CC BY-SA 2.5 | null | 2010-09-11T07:52:28.570 | 2010-09-16T12:27:58.123 | 2010-09-11T08:45:18.317 | 8 | 386 | [
"r",
"gpu",
"parallel-computing"
] |
2560 | 2 | null | 2559 | 7 | null | There is fundamental difference between parallel computing in CPUs and GPUs. Essentially, the [CPU](http://en.wikipedia.org/wiki/Central_processing_unit) has been designed to do clever things on behalf of the programmer. For example, [Instruction level parallelism](http://en.wikipedia.org/wiki/Central_processing_unit#I... | null | CC BY-SA 2.5 | null | 2010-09-11T09:10:29.047 | 2010-09-11T09:10:29.047 | null | null | 8 | null |
2561 | 2 | null | 726 | 12 | null | >
At their best, graphics are instruments for reasoning.
Edward Tufte, www.edwardtufte.com
| null | CC BY-SA 2.5 | null | 2010-09-11T10:26:16.900 | 2010-09-11T21:12:24.913 | 2010-09-11T21:12:24.913 | 930 | 930 | null |
2562 | 2 | null | 726 | 17 | null | May I add this one, because I like Jan's contributions to psychometrics and statistics...
>
Causal interpretation of the results
of regression analysis of
observational data is a risky
business. The responsibility rests
entirely on the shoulders of the
researcher, because the shoulders of
the statistical t... | null | CC BY-SA 2.5 | null | 2010-09-11T10:29:14.257 | 2010-09-11T10:29:14.257 | null | null | 930 | null |
2563 | 1 | 2571 | null | 4 | 5892 | What are some of the best ranking algorithms with inputs as up and down votes?
| What are some of the best ranking algorithms with inputs as up and down votes? | CC BY-SA 2.5 | null | 2010-09-11T13:15:03.890 | 2012-07-07T23:14:55.627 | null | null | 1248 | [
"algorithms"
] |
2564 | 2 | null | 726 | 26 | null | >
We are drowning in information and starving for knowledge.
Rutherford D. Roger
| null | CC BY-SA 2.5 | null | 2010-09-11T13:50:33.270 | 2010-09-11T13:50:33.270 | null | null | 961 | null |
2565 | 2 | null | 2547 | 14 | null | Here's my answer first posted on math.stackexchange:
Median is what many people actually have in mind when they say "mean." It's easier to interpret the median: half the population is above this age and half are below. Mean is a little more subtle.
People look for symmetry and sometimes impose symmetry when it isn't th... | null | CC BY-SA 2.5 | null | 2010-09-11T14:20:43.827 | 2010-09-11T14:20:43.827 | null | null | 319 | null |
2566 | 2 | null | 726 | 32 | null | >
…the statistician knows…that in nature
there never was a normal distribution,
there never was a straight line, yet
with normal and linear assumptions,
known to be false, he can often derive
results which match, to a useful
approximation, those found in the real
world.
George Box (JASA, 1976, Vol. 71,... | null | CC BY-SA 2.5 | null | 2010-09-11T15:18:26.880 | 2010-09-11T15:18:26.880 | null | null | 1107 | null |
2567 | 2 | null | 726 | 9 | null | >
The business of the statistician is to
catalyze the scientific learning
process.
George Box
| null | CC BY-SA 2.5 | null | 2010-09-11T15:27:50.037 | 2010-09-11T15:27:50.037 | null | null | 1107 | null |
2569 | 2 | null | 726 | 6 | null | >
We statisticians, as a police of
science (a label some dislike but I am
proud of...), have
the fundamental duty of helping others
to engage in statistical thinking as a
necessary step of scientific inquiry
and evidence-based policy formulation.
In order to truly fulfill this task,
we must constantly ... | null | CC BY-SA 2.5 | null | 2010-09-11T15:37:55.277 | 2010-09-11T15:37:55.277 | null | null | 1107 | null |
2570 | 2 | null | 2559 | 10 | null | >
But, the experimental conditions for the GPU side is unclear (to me). When using a GPU, for efficiency we should simultaneously make use of the CPUs.
That is not generally true, and in particular is not true for the [gputools](http://cran.r-project.org/package=gputools) R package which offers an 'everything to the... | null | CC BY-SA 2.5 | null | 2010-09-11T16:05:23.110 | 2010-09-16T12:27:58.123 | 2010-09-16T12:27:58.123 | 334 | 334 | null |
2571 | 2 | null | 2563 | 6 | null | David MacIver had a nice post on the algorithm he used for ranking programming languages based on relative rankings from different users for various factors:
- Rank Aggregation in The Right Tool
It's based the [Rank Aggregation Methods for the Web](http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.28.8702) pap... | null | CC BY-SA 2.5 | null | 2010-09-11T18:51:18.540 | 2010-09-11T18:51:18.540 | null | null | 251 | null |
2572 | 1 | 2605 | null | 4 | 1779 | Could you suggest good articles / books / online materials on correlation stress testing?
Correlation stress testing: say, we have a positive semidefinite correlation matrix. We might want to explore the impact on the results if some or all elements of the matrix are increased or a decrease by a given value/s. Of cours... | Correlation stress testing | CC BY-SA 2.5 | null | 2010-09-11T19:05:38.680 | 2010-09-13T10:36:05.453 | null | null | 1250 | [
"correlation"
] |
2573 | 1 | 2621 | null | 20 | 65318 | If we want to visibly see the distribution of a continuous data, which one among histogram and pdf should be used?
What are the differences, not formula wise, between histogram and pdf?
| Difference between histogram and pdf? | CC BY-SA 2.5 | null | 2010-09-11T19:36:38.390 | 2015-07-14T13:18:08.613 | 2010-10-06T14:33:18.633 | 8 | null | [
"distributions",
"density-function",
"histogram"
] |
2574 | 2 | null | 2573 | 13 | null | A histogram is pre-computer age estimate of a density. A density estimate is an alternative.
These days we use both, and there is a rich literature about which defaults one should use.
A pdf, on the other hand, is a closed-form expression for a given distribution. That is different from describing your dataset with a... | null | CC BY-SA 2.5 | null | 2010-09-11T19:40:11.540 | 2010-09-11T19:40:11.540 | null | null | 334 | null |
2575 | 2 | null | 2573 | 6 | null | There's no hard and fast rule here. If you know the density of your population, then a PDF is better. On the other hand, often we deal with samples and a histogram might convey some information that an estimated density covers up. For example, Andrew Gelman makes this point:
>
Variations on the histogram
A key bene... | null | CC BY-SA 2.5 | null | 2010-09-11T20:00:52.923 | 2010-09-11T20:00:52.923 | 2020-06-11T14:32:37.003 | -1 | 251 | null |
2576 | 1 | null | null | 7 | 2691 | I'm working with the results of a survey which has multiple questions. All answers (in this case) are categorical and ordinal (such as very unhappy, unhappy, neutral, happy, very happy).
I'm looking for a way to sort the questions from those with "worst results" to those with "best results". Getting the extremes is som... | How to rank the results of questions with categorical answers? | CC BY-SA 2.5 | 0 | 2010-09-11T20:20:34.950 | 2010-11-04T20:10:51.363 | 2010-11-04T15:49:14.910 | 930 | 840 | [
"categorical-data",
"scales",
"survey"
] |
2577 | 2 | null | 2576 | 2 | null | >
If I plot the distribution of answers for each question, I can identify which questions have lots of 'good' answers (distribution is negatively skewed) or those with lots of 'bad' answers (positively skewed histogram). So picking the extremes is easy but this is also dependent on the data.
Is an absolute ranking n... | null | CC BY-SA 2.5 | null | 2010-09-11T20:38:07.827 | 2010-09-11T20:38:07.827 | null | null | 251 | null |
2578 | 2 | null | 2576 | 3 | null | Recoding your data with numerical values seems ok, provided the assumption of an ordinal scale holds. This is often the case for Likert-type item, but see these related questions:
- Is it appropriate to treat n-point Likert scale data as n trials from a binomial process?
- Under what conditions should Likert scales b... | null | CC BY-SA 2.5 | null | 2010-09-11T21:08:54.290 | 2010-11-04T15:51:20.853 | 2017-04-13T12:44:36.923 | -1 | 930 | null |
2579 | 1 | null | null | 0 | 1171 | I have a question related to the time fixed effects when using Swamy Random coefficient model, as you may know in the fixed and random effect context, we use a set of time dummies to estimate the time fixed effects, and I would like if we can use the same approch whith swamy?
| Swamy Random Coefficient Model and time fixed effects | CC BY-SA 4.0 | null | 2010-09-11T23:08:48.143 | 2022-05-08T13:22:59.407 | 2022-05-08T13:22:59.407 | 94889 | 1251 | [
"econometrics",
"panel-data"
] |
2580 | 1 | 2606 | null | 11 | 1499 | I have data with a double peak that I'm trying to model, and there's enough overlap between the peaks that I can't treat them independently. A histogram of the data might look something like this:
I've created two models for this: one uses two Poisson distributions, and ... | Measuring goodness-of-fit in a model that combines two distributions | CC BY-SA 2.5 | null | 2010-09-11T23:12:23.770 | 2013-06-18T08:07:02.577 | 2013-06-18T08:07:02.577 | 805 | 54 | [
"modeling",
"histogram",
"kolmogorov-smirnov-test",
"negative-binomial-distribution",
"likelihood-ratio"
] |
2581 | 2 | null | 2572 | 0 | null | The answer may depend on why you want to do stress testing but here is one partial idea:
You can do a [eigendecompostion](http://en.wikipedia.org/wiki/Eigendecomposition_of_a_matrix) of your current matrix, The eigenvectors are aligned with the axis of the ellipsoid corresponding to the correlation matrix and the eigen... | null | CC BY-SA 2.5 | null | 2010-09-11T23:57:36.683 | 2010-09-12T02:11:56.117 | 2010-09-12T02:11:56.117 | 183 | null | null |
2582 | 2 | null | 2576 | 4 | null | If all your questions have the same response scale and they are standard Likert items, scaling the item 1,2,3,4,5 and taking the mean is generally fine.
You can investigate the robustness of the rank ordering by experimenting with different scaling procedures (e.g., 0, 0, 0, 1, 1 is common where you want to assess the ... | null | CC BY-SA 2.5 | null | 2010-09-12T02:48:34.503 | 2010-09-12T02:48:34.503 | null | null | 183 | null |
2583 | 2 | null | 2352 | 7 | null | >
This paper is somewhat controversial, and somewhat ignored
Not really, it's well regarded where the theory of model selection is concerned, though it's certainly misinterpreted. The real issue is how relevant it is to the practice of modeling in the wild. Suppose you perform the simulations for the cases you pro... | null | CC BY-SA 2.5 | null | 2010-09-12T03:25:19.597 | 2010-09-12T04:19:37.793 | 2010-09-12T04:19:37.793 | 251 | 251 | null |
2584 | 2 | null | 2547 | 4 | null | For a concrete example, consider the mean ages for the Congo (DRC) and Japan. One is devastated by civil war, the other is well developed with an ageing population. The mean isn't terribly interesting for an apples to apples comparison. On the other hand, the median can be informative as a measure of central tendenc... | null | CC BY-SA 2.5 | null | 2010-09-12T05:01:58.287 | 2010-09-12T05:01:58.287 | null | null | 251 | null |
2585 | 1 | null | null | 2 | 227 | I have a large sample of market data - that is the prices and amount of goods being sold by vendors at specific, but inconsistent, points in time. Assuming I am a buyer and the quality of the goods are constant across the entire market (consumable goods by one manufacturer, let's say), how would you graph this data? Ke... | Graphing low-end prices of goods in a market over time | CC BY-SA 2.5 | null | 2010-09-12T05:04:04.770 | 2023-03-09T10:11:48.967 | 2010-09-16T06:31:51.467 | null | 1253 | [
"time-series",
"data-visualization"
] |
2586 | 2 | null | 2585 | 3 | null | You could create a scatterplot with time on the x-axis and price on the y-axis.
You could make the size of the points proportional to the amount sold (or some function of amount sold such as log of amount sold). You could add a line that passed through the minimum values or some estimate of the minimum, where the data ... | null | CC BY-SA 2.5 | null | 2010-09-12T08:12:21.863 | 2010-09-12T08:12:21.863 | null | null | 183 | null |
2587 | 1 | 2595 | null | 5 | 719 | Are the two synonymous? The reason I am asking is that I have a paper that calculates a certain p-value as the upper tail of the hypergeometric distribution:
$\Sigma_{k}^{m} = \frac{\binom{m}{k}\binom{N-m}{n-k}}{\binom{N}{n}}$
I want to implement their proposal using Python. [Scipy offers a hypergeometric distribution]... | Is the survival function the same as the upper tail? | CC BY-SA 2.5 | null | 2010-09-12T11:22:28.790 | 2010-09-12T17:00:58.643 | null | null | 977 | [
"distributions"
] |
2588 | 2 | null | 2587 | 0 | null | Yes it is the same as upper tail. See: [http://en.wikipedia.org/wiki/Survival_function](http://en.wikipedia.org/wiki/Survival_function)
| null | CC BY-SA 2.5 | null | 2010-09-12T11:29:59.453 | 2010-09-12T11:29:59.453 | null | null | null | null |
2589 | 2 | null | 2576 | 2 | null | A small additional point to the answers already given:
Without assuming your ordinal data is interval, you can compare any convenient quantiles - e.g. medians.
Or, when comparing X vs Y which are both ordered categorical, you can estimate something like P(Y>X) - P(X>Y) or P(Y>X) + 0.5 * P(Y=X) (etc.), where you estimat... | null | CC BY-SA 2.5 | null | 2010-09-12T13:42:31.060 | 2010-09-12T13:42:31.060 | null | null | 805 | null |
2591 | 1 | 2593 | null | 10 | 7569 | If one is testing assumption of homoscedasticity, parametric (Bartlett Test of Homogeneity of Variances, `bartlett.test`) and non-parametric (Figner-Killeen Test of Homogeneity of Variances, `fligner.test`) tests are available. How to tell which kind to use? Should this depend on e.g. normality of the data?
| When to use (non)parametric test of homoscedasticity assumption? | CC BY-SA 2.5 | null | 2010-09-12T15:12:02.687 | 2017-04-23T21:59:03.103 | 2017-04-23T21:59:03.103 | 11887 | 144 | [
"r",
"variance",
"heteroscedasticity",
"misspecification"
] |
2592 | 1 | 2596 | null | 25 | 41915 | After performing principal component analysis (PCA), I want to project a new vector onto PCA space (i.e. find its coordinates in the PCA coordinate system).
I have calculated PCA in R language using `prcomp`. Now I should be able to multiply my vector by the PCA rotation matrix. Should principal components in this matr... | How to project a new vector onto PCA space? | CC BY-SA 3.0 | null | 2010-09-12T16:11:22.923 | 2020-02-03T22:42:25.733 | 2015-07-18T07:47:56.437 | 1739 | 1260 | [
"r",
"pca"
] |
2593 | 2 | null | 2591 | 12 | null | It seems that the FK test is to be prefered in case of strong departure from the normality (to which the Bartlett test is sensible). Quoting the on-line help,
>
The Fligner-Killeen (median) test has
been determined in a simulation study
as one of the many tests for
homogeneity of variances which is most
robus... | null | CC BY-SA 2.5 | null | 2010-09-12T16:18:40.850 | 2010-09-12T16:18:40.850 | null | null | 930 | null |
2594 | 2 | null | 2592 | 3 | null | I believe that the eigenvectors (i.e., the principal components) should be arranged as columns.
| null | CC BY-SA 2.5 | null | 2010-09-12T16:24:34.503 | 2010-09-12T16:24:34.503 | null | null | null | null |
2595 | 2 | null | 2587 | 4 | null | Yes. By definition, the survival function is $S(X = x) = Pr(X > x) = 1 - F(X = x)$ where $F$ is the CDF.
| null | CC BY-SA 2.5 | null | 2010-09-12T17:00:58.643 | 2010-09-12T17:00:58.643 | null | null | 251 | null |
2596 | 2 | null | 2592 | 31 | null | Well, @Srikant already gave you the right answer since the rotation (or loadings) matrix contains eigenvectors arranged column-wise, so that you just have to multiply (using `%*%`) your vector or matrix of new data with e.g. `prcomp(X)$rotation`. Be careful, however, with any extra centering or scaling parameters that ... | null | CC BY-SA 2.5 | null | 2010-09-12T17:03:16.110 | 2010-09-12T17:03:16.110 | null | null | 930 | null |
2597 | 1 | 2599 | null | 34 | 23939 | I have found extensive literature proposing all sorts of criteria (e.g. [Glenn et al. 1985](http://vohweb.chem.ucla.edu/voh/classes%5Cwinter08%5C160BID48%5CNumClusters.pdf)(pdf) and [Jung et al. 2002](http://www.cc.gatech.edu/~hpark/papers/cluster_JOGO.pdf)(pdf)). However, most of these are not that easy to implement (... | What stop-criteria for agglomerative hierarchical clustering are used in practice? | CC BY-SA 2.5 | null | 2010-09-12T19:49:25.443 | 2010-09-13T08:26:14.417 | null | null | 977 | [
"clustering"
] |
2598 | 1 | null | null | 2 | 143 | Let's pretend there are 10 doors in front of me. Behind one of them, there is a treasure and nothing behind all the others. Intuitively, I can easily determine I have 1 chance out of 10 the pick open the right door (the one with the treasure). I repeat this 5 times (i.e. all door closed, open one door). What are my cha... | Probability to find the treasure five times in row | CC BY-SA 2.5 | null | 2010-09-12T20:18:16.740 | 2010-09-13T12:38:17.643 | null | null | 64 | [
"probability"
] |
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