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Tags
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10579
1
null
null
4
249
I have 4 groups each consisting of 1000 recent college graduates, and I am studying employment immediately after graduation. 2 groups took a business class in college, and 2 groups took a math course in college. Group 1 is a control that has taken neither a business class nor a math course in college. I want to conduct...
Testing significant effect in 2 by 2 factor design on a binary outcome
CC BY-SA 3.0
null
2011-05-09T22:20:50.180
2011-05-11T15:29:29.850
2011-05-11T15:29:29.850
183
4538
[ "statistical-significance" ]
10580
2
null
10432
5
null
It sounds like any linear classifier will do what you need. Suppose you have $N$ features and the value of feature $i$ is $f_i$. Then a linear classifier will compute a score $$s = \sum_i w_i f_i + o$$ (where $o$ is the offset). Then, if $s > t$ (where $t$ is some threshold), then the feature belongs to a class (a gro...
null
CC BY-SA 3.0
null
2011-05-09T22:51:32.127
2011-05-09T22:58:25.560
2011-05-09T22:58:25.560
3369
3369
null
10581
2
null
10578
39
null
Here I explain why the asymptotic variance of the maximum likelihood estimator is the Cramer-Rao lower bound. Hopefully this will provide some insight as to the relevance of the Fisher information. Statistical inference proceeds with the use of a likelihood function $\mathcal{L}(\theta)$ which you construct from the d...
null
CC BY-SA 3.0
null
2011-05-09T23:09:17.680
2011-05-10T15:09:16.277
2011-05-10T15:09:16.277
3567
3567
null
10582
2
null
10579
3
null
This seems like a classic problem for [logistic regression](http://en.wikipedia.org/wiki/Logistic_regression). Rather than specifying these groups, turn math and business coursework into predictors for employment status. This is easy to code up in pretty much whatever statistical software you have around, although yo...
null
CC BY-SA 3.0
null
2011-05-09T23:28:35.240
2011-05-09T23:28:35.240
null
null
71
null
10583
2
null
10579
3
null
Self-selection problem need to be addressed here. People who choose to take business classes might be more likely to get a job. So, the sample you have is not random, and the inferences you draw might be incorrect. Heckman procedure is used to correct to self-selection bias. I am not sure if it is applicable for discre...
null
CC BY-SA 3.0
null
2011-05-09T23:52:24.900
2011-05-09T23:52:24.900
null
null
4540
null
10585
2
null
10579
2
null
One of the more basic approaches you could take is a [two-way ANOVA](http://udel.edu/~mcdonald/stattwoway.html) (Page from U Delaware), using Math Class = {Y, N} and Business Class = {Y, N} as your two treatments. You would then perform an analysis of variance on the dependent variable (number of people employed) to de...
null
CC BY-SA 3.0
null
2011-05-10T00:59:05.887
2011-05-10T00:59:05.887
null
null
1118
null
10586
2
null
10579
3
null
If @EEE's concern can be addressed and you proceed with an hypothesis test, then rather than logistic regression I'd recommend a chi-square test. For a person fairly new to statistical testing, it'll be dramatically easier to conduct, interpret, and explain to an audience. Plus I think it'll give you just about as mu...
null
CC BY-SA 3.0
null
2011-05-10T00:59:45.170
2011-05-10T00:59:45.170
null
null
2669
null
10587
1
null
null
3
675
I lack knowledge of statistical terminology, so I'll try to thoroughly explain my predicament and hope that it is understandable: I am programming a software for technical analysis of financial markets. This software will receive a variable who's value represents current market conditions. In this particular case the v...
Uniform frequency from non-uniform (exponential) distribution?
CC BY-SA 3.0
null
2011-05-10T01:47:23.723
2011-05-10T01:58:11.990
2020-06-11T14:32:37.003
-1
4542
[ "distributions", "probability", "confidence-interval", "histogram" ]
10588
2
null
10587
3
null
If your data really is [exponentially distributed](http://en.wikipedia.org/wiki/Exponential_random_variable), find the [maximum likelihood estimate of the rate](http://en.wikipedia.org/wiki/Exponential_random_variable#Maximum_likelihood) $\lambda$, then transform the samples $X_n$ to a sequence $Y_n$ uniformly distribu...
null
CC BY-SA 3.0
null
2011-05-10T01:58:11.990
2011-05-10T01:58:11.990
null
null
4479
null
10589
2
null
10578
17
null
One way that I understand the fisher information is by the following definition: $$I(\theta)=\int_{\cal{X}} \frac{\partial^{2}f(x|\theta)}{\partial \theta^{2}}dx-\int_{\cal{X}} f(x|\theta)\frac{\partial^{2}}{\partial \theta^{2}}\log[f(x|\theta)]dx$$ The Fisher Information can be written this way whenever the density $f...
null
CC BY-SA 3.0
null
2011-05-10T07:19:38.177
2018-04-17T04:12:51.770
2018-04-17T04:12:51.770
14396
2392
null
10591
1
10661
null
8
2438
The [Anscombe transform](http://en.wikipedia.org/wiki/Anscombe_transform) is $a(x) = 2\sqrt{x+3/8}$. Can anyone show me how to prove that an Anscombe-transformed version $Y = a(X)$ of a Poisson distributed random variable $X$ is approximately normal distributed (when $\lambda>4$)?
Anscombe transform and normal approximation
CC BY-SA 3.0
null
2011-05-10T10:38:24.523
2011-05-12T13:02:02.343
2011-05-12T13:02:02.343
2970
4496
[ "distributions", "normal-distribution", "poisson-distribution" ]
10592
1
10637
null
9
1080
Given a data matrix $X$ of say 1000000 observations $\times$ 100 features, is there a fast way to build a tridiagonal approximation $A \approx cov(X)$ ? Then one could factor $A = L L^T$, $L$ all 0 except $L_{i\ i-1}$ and $L_{i i}$, and do fast decorrelation (whitening) by solving $L x = x_{white}$. (By "fast" I mean ...
How to calculate tridiagonal approximate covariance matrix, for fast decorrelation?
CC BY-SA 3.0
null
2011-05-10T10:38:49.923
2022-05-24T19:37:35.363
2011-05-15T09:34:53.137
557
557
[ "variance", "approximation", "covariance-matrix" ]
10593
2
null
10594
4
null
Suppose you have a cumulative distribution function $F$ of the variable in question. Suppose the value given is $x$, and the range is $[r_1,r_2]$ with $x\in[r_1,r_2]$. Then if you select the amount of values falling into that range $N$, the following should hold: $$F(r_1)-F(r_2)=\frac{N}{500 000}$$ This is an equation ...
null
CC BY-SA 3.0
null
2011-05-10T11:06:58.780
2011-05-10T11:06:58.780
null
null
2116
null
10594
1
10595
null
6
11951
I have 500,000 values for a variable derived from financial markets. This variable has a arbitrary distribution. I need a formula that will allow me to select a range around any value of this variable such that an equal (or close to it) amount of values fall within that range. From what I understand, this means that I ...
Converting arbitrary distribution to uniform one
CC BY-SA 3.0
null
2011-05-10T09:23:10.113
2011-05-10T15:00:17.433
2020-06-11T14:32:37.003
-1
4544
[ "probability", "matlab" ]
10595
2
null
10594
10
null
If $X$ has the (cumulative) distribution function $F(x)=P(X<x)$, then $F(X)$ has a uniform distribution on $[0,1]$. You don't know what $F$ is, but with N = 500,000 data points you could simply use the empirical distribution function: $$\hat{F}(x) = \frac{1}{N} \sum_{i=1}^N 1[x_i\leq x]$$ where $1[A]$ is the indicator ...
null
CC BY-SA 3.0
null
2011-05-10T10:11:43.367
2011-05-10T10:26:19.683
null
null
2425
null
10597
1
null
null
4
2239
Is there a reasonable way to quantify the amount of local correlations in an image? For example, I want to justify the correlations between a neighbourhood of pixels is much higher than the correlations between pixels in entirely different regions of the image. Would showing the xcorr2(A,A) as the 2-d autocorrelation ...
Valid method to analyze spatial correlations in images?
CC BY-SA 3.0
null
2011-05-10T13:55:45.370
2011-05-10T21:03:06.407
2011-05-10T15:47:44.150
1036
4547
[ "correlation", "spatial", "image-processing" ]
10598
1
14771
null
9
2449
Various forms of the correlation, e.g., $r = \frac{\Sigma_i x_i * y_i}{\sigma_x \sigma_y}$ or $r = \frac{\Sigma_i (x_i-\bar{x}) * (y_i-\bar{y})}{\sigma_x \sigma_y}$ are popular similarity measures in many applications. Is there a probabilistic interpretation for this such that either $r$ or $r^2$ is an approximate l...
Correlation as a likelihood measure
CC BY-SA 3.0
null
2011-05-10T14:19:14.667
2011-08-24T19:32:05.150
2011-05-10T14:30:19.253
2728
2728
[ "probability", "correlation", "interpretation", "likelihood" ]
10599
2
null
10597
2
null
One straightforward way of doing this is to consider arbitrarily-sized patches of the image. For example, let's say we are interested in all 9*9 regions of pixels that can be taken from the image. Extract each of these image patches, and transform each image patch to a row vector. Consider the entire set of image pa...
null
CC BY-SA 3.0
null
2011-05-10T15:14:59.910
2011-05-10T15:14:59.910
null
null
3595
null
10600
2
null
10526
2
null
I don't think that using CCA will help you. It appears to me that you have a number of endogenous series ( abundance of species n in number ) and a number of exogenous series ( variety of food resources m in number ). I would suggest constructing n transfer functions each one optimized to fully utilize the information ...
null
CC BY-SA 3.0
null
2011-05-10T15:57:42.317
2011-05-10T15:57:42.317
null
null
3382
null
10601
2
null
10564
1
null
If I understand things correctly, you're testing if the mean value of predictor $A$ associated with outcome $1$ differ from the mean value of predictor A associated with outcome $2$. Even if they don't differ, this result says nothing to your research question. What it says is only that in your sample, the average valu...
null
CC BY-SA 3.0
null
2011-05-10T16:09:36.753
2011-05-10T20:31:29.040
2011-05-10T20:31:29.040
3058
3058
null
10602
1
null
null
0
676
I have a design where birds of 1, 3, 5 week of age are placed in 2 chambers(independent) with 4 treatments( light technology) for 4 days. for example, x no of birds of 1 weeks of age are kept for 4 days and then new birds of 3 week age are placed in both chambers and so on...readings are taken for their position, feed ...
Sample size determination for block design with repeated measurement in SAS
CC BY-SA 3.0
null
2011-05-10T16:28:07.593
2011-05-10T17:14:40.017
null
null
4550
[ "anova" ]
10603
1
null
null
2
2924
I have a very basic question on when a discrete distribution might be called a symmetric distribution. Let say I have a r.v. $X$ that can take two possible values $(x1, x2)$ with $x1 \neq x2$ and corresponding probabilities $(0.4, 0.6)$. Then can I say that $X$ is symmetric? Thanks,
How to characterize symmetric discrete distribution?
CC BY-SA 3.0
null
2011-05-10T16:55:47.630
2012-05-23T11:33:55.457
2011-05-10T20:59:45.283
930
4551
[ "distributions", "discrete-data" ]
10604
1
11499
null
7
8670
I'm trying to forecast using ARIMAX with two exogenous (input) variables. I'm using PROC ARIMA, but I can't figure out from the SAS documentation whether my code is producing the parameterization I want. I want to extend an ARI(12,1) model so that it also includes the last 12 terms of each of the two exogenous variable...
How do I ensure PROC ARIMA is performing the correct parameterization of input variables?
CC BY-SA 3.0
null
2011-05-10T17:02:08.347
2011-06-03T07:32:50.997
2011-05-10T17:12:45.243
1583
1583
[ "time-series", "sas", "dynamic-regression" ]
10605
2
null
10603
4
null
No, it only would be symmetric if the corresponding probabilities were (0.5,0.5). Also, with binary or categorical distributions, the concept of symmetry does not have much meaning.
null
CC BY-SA 3.0
null
2011-05-10T17:11:08.470
2011-05-10T20:46:21.960
2011-05-10T20:46:21.960
3595
3595
null
10606
2
null
10602
1
null
When problems get more complicated than the simple cases that have nice canned sample size solutions I turn to simulation. The basic steps: - Decide what you think your data will look like (including things you may want to change, e.g. sample size(s)) - Decide how you will analyze the data - create some code that s...
null
CC BY-SA 3.0
null
2011-05-10T17:14:40.017
2011-05-10T17:14:40.017
null
null
4505
null
10607
1
10620
null
8
12128
I am running a logistic model. In SAS Entreprise Miner, I noticed there's a link function that has three possible options: `logit`, `probit` and `cll` (complementary log-log). Can you please shed light on the following questions: - Can we use any of these link function to carry out a logistic regression? - Are there ...
How to choose the link function when performing a logistic regression?
CC BY-SA 3.0
null
2011-05-10T17:23:17.073
2021-12-07T15:31:28.437
2021-12-07T15:31:28.437
11887
1763
[ "regression", "logistic", "sas", "link-function" ]
10608
1
10610
null
9
2544
I have a question concerning feature selection and classification. I will be working with R. I should start by saying that I am not very familiar with data mining techniques, aside from a brief glimpse provided by an undergraduate course on multivariate analysis, so forgive me if I am lacking in details regarding my qu...
Questions about variable selection for classification, and different classification techniques
CC BY-SA 3.0
null
2011-05-10T17:29:14.633
2011-05-11T16:23:22.990
2017-04-13T12:44:40.883
-1
2252
[ "r", "machine-learning", "classification", "dimensionality-reduction" ]
10610
2
null
10608
14
null
Feature selection does not necessarily improve the performance of modern classifier systems, and quite frequently makes performance worse. Unless finding out which features are the most important is an objective of the analysis, it is often better not even to try and to use regularisation to avoid over-fitting (select...
null
CC BY-SA 3.0
null
2011-05-10T18:04:24.603
2011-05-10T18:04:24.603
null
null
887
null
10611
2
null
10608
6
null
On dimensionality reduction, a good first choice might be [principal components analysis](http://en.wikipedia.org/wiki/Principal_components_analysis). Apart from that, i don't have too much to add, except that if you have any interest in data mining, I strongly recommend you read [the elements of statistical learning](...
null
CC BY-SA 3.0
null
2011-05-10T18:04:58.020
2011-05-10T18:04:58.020
null
null
656
null
10612
2
null
10531
4
null
There is no simple yes or no answer. People constantly attempt to make inferences about causal relationships. The question is what assumptions you have to make, and how sensitive your inferences are to changing those assumptions. The causal effects you can identify with the fewest assumptions are the effects of the...
null
CC BY-SA 3.0
null
2011-05-10T18:22:00.337
2011-05-10T18:22:00.337
null
null
3748
null
10613
1
10617
null
161
90704
Recently, I have found in a [paper by Klammer, et al.](http://pubs.acs.org/doi/abs/10.1021/pr8011107) a statement that p-values should be uniformly distributed. I believe the authors, but cannot understand why it is so. Klammer, A. A., Park, C. Y., and Stafford Noble, W. (2009) [Statistical Calibration of the SEQUEST ...
Why are p-values uniformly distributed under the null hypothesis?
CC BY-SA 3.0
null
2011-05-10T18:26:26.630
2022-03-31T13:53:07.677
2017-10-19T22:56:56.347
44269
4552
[ "p-value", "uniform-distribution" ]
10614
2
null
9299
5
null
You can use this module of the [pysal](http://pysal.org/1.1/library/spreg/ols.html) python library for the spatial data analysis methods I discuss below. Your description of how each person's attitude is influenced by the attitudes of the people surrounding her can be represented by a [spatial autoregressive model (SAR...
null
CC BY-SA 3.0
null
2011-05-10T18:59:18.107
2011-05-11T03:57:17.720
2017-04-13T12:44:27.570
-1
4329
null
10615
1
null
null
2
482
I'd be too happy, if someone could post a code snippet, which explains how to compute mean and variance of a set of records, which contain frequencies? Suppose we have records like (FORMAT F) ``` - GroupA, 6 x Grade 1, 5 x Grade 2, 10 x Grade 3 - GroupB, 2 x Grade 1, 7 x Grade 2, 18 x Grade 3 - GroupA, 23 x Grade 1, 5 ...
Variance based on given frequencies using SPSS
CC BY-SA 3.0
null
2011-05-10T19:28:40.657
2011-05-15T22:31:54.813
2011-05-15T22:31:54.813
4554
4554
[ "spss" ]
10617
2
null
10613
114
null
To clarify a bit. The p-value is uniformly distributed when the null hypothesis is true and all other assumptions are met. The reason for this is really the definition of alpha as the probability of a type I error. We want the probability of rejecting a true null hypothesis to be alpha, we reject when the observed $...
null
CC BY-SA 3.0
null
2011-05-10T19:45:10.343
2016-03-23T07:19:27.883
2016-03-23T07:19:27.883
null
4505
null
10619
1
10626
null
1
704
I am using Matlab to try and find a good fit for this curve: ![cumulative distribution](https://i.stack.imgur.com/pF3lz.png) None of the built-in formulas seem to work well. Any suggestions?
What regression formula would best fit this curve?
CC BY-SA 3.0
null
2011-05-10T20:21:47.193
2011-05-10T23:37:39.147
2011-05-10T20:23:56.783
919
4544
[ "distributions", "matlab" ]
10620
2
null
10607
4
null
I don't know of SAS, so i'll just answer based on the statistics side of the question. About the software you mays ask at the sister site, stackoverflow. - If the link function is different (logistic, probit or Clog-log), than you will get different results. For logistic, use logistic. - About the real differences of...
null
CC BY-SA 3.0
null
2011-05-10T20:30:24.190
2011-05-10T21:14:00.837
2011-05-10T21:14:00.837
3058
3058
null
10621
1
null
null
4
4072
I'm interested in fitting a conditional Poisson regression model using PROC GENMOD in SAS to analyze a matched cohort study. However, it's not quite clear to me how I should exactly go about it. My impression is that a REPEATED statement should be used along with the events/trials syntax, but if so then how does one a...
How does one fit conditional Poisson regression in SAS?
CC BY-SA 3.0
null
2011-05-10T21:02:18.387
2017-03-17T18:23:09.137
2011-05-11T07:30:51.817
930
4555
[ "regression", "poisson-distribution", "sas", "matching" ]
10623
1
10624
null
4
202
If I have a sample of k successes and n-k failures, there are standard techniques (Agresti-Coull, Clopper, etc.) for finding a confidence interval of the probability of an individual success. What if I want to find a confidence interval for the probability of getting at least k' out of n' instead? Obviously it can be...
Binomial testing with probability estimated from sample
CC BY-SA 3.0
null
2011-05-10T21:42:26.387
2011-05-11T00:46:47.260
null
null
1378
[ "confidence-interval", "binomial-distribution" ]
10624
2
null
10623
3
null
I believe you are looking for the [beta binomial distribution](https://secure.wikimedia.org/wikipedia/en/wiki/Beta-binomial_distribution), which reduces the pdf of of interest ($\pi(k\prime)$) to $\pi(k\prime|n\prime,n,k) = {n\prime \choose k\prime} \frac{B(k\prime+k+1,n\prime-k\prime+n-k+1)}{B(k+1,n-k+1)}$ For motivat...
null
CC BY-SA 3.0
null
2011-05-10T21:59:57.487
2011-05-10T21:59:57.487
null
null
2728
null
10625
2
null
10619
1
null
Check out [Eureqa](http://creativemachines.cornell.edu/eureqa) for a neat evolutionary approach to finding the mathematical form of an otherwise ambiguous function. It's native to Windows but works fine on Linux & Mac via Wine (in which case I'd suggest you use [winebottler](http://winebottler.kronenberg.org)).
null
CC BY-SA 3.0
null
2011-05-10T22:13:21.433
2011-05-10T22:13:21.433
null
null
364
null
10626
2
null
10619
2
null
Looking at the charts in your first question, this looks slightly like the absolute value of a standard normal distribution, what Wikipedia calls a [half-normal distribution](http://en.wikipedia.org/wiki/Half-normal_distribution), and your curve here looks like the top half of the cdf of a normal distribution. One wa...
null
CC BY-SA 3.0
null
2011-05-10T23:37:39.147
2011-05-10T23:37:39.147
null
null
2958
null
10627
2
null
73
3
null
I use `lattice`, `ggplot2`, `lubridate`, `reshape`, `boot`, `e1071`, `car`, `forecast`, and `zoo` a lot.
null
CC BY-SA 3.0
null
2011-05-10T23:50:24.527
2011-05-10T23:50:24.527
null
null
1764
null
10629
2
null
10607
2
null
All 3 link functions are s-shaped and are not going to be that different. Li and Duan showed that if the predictor variables are well behaved (elliptically symmetric predictors are a subset of the well behaved group) then changing the link function will change the coefficients by a multiplicitive constant. Even if th...
null
CC BY-SA 4.0
null
2011-05-11T00:35:33.890
2018-07-24T04:36:38.033
2018-07-24T04:36:38.033
11887
4505
null
10630
2
null
10623
3
null
If you are happy with your confidence interval on the unknown proportion of a single success, then just plug both of those values into the above formula. Since k and n are known constants (rather than random variables) and the probability of k or more out of n is monotone, you can just transform the ends of your confi...
null
CC BY-SA 3.0
null
2011-05-11T00:46:47.260
2011-05-11T00:46:47.260
null
null
4505
null
10631
1
null
null
3
1264
I have a data set with a distribution of one variable against the other resembling a cubic one (rises to some point and then falls to a steady level without a consequent rise). I know in which cases to use log-linear, log-lin, lin-log, and reciprocal or log reciprocal linear models, but I am not sure what to do here (I...
What is the best linear regression model to use when the shape of the data resembles a cubic distribution?
CC BY-SA 3.0
null
2011-05-11T00:51:20.380
2011-05-11T13:31:27.083
null
null
4560
[ "regression", "econometrics" ]
10632
2
null
10579
0
null
you could use the Agresti-Caffo simultaneous confidence interval or (Simultaneous Score Intervals for Difference of Proportions) to compare differences in proportions (Agresti et al. 2008. Simultaneous confidence intervals for comparing binomial parameters, Biometrics 64, 1270-1275). The corresponding R code is availa...
null
CC BY-SA 3.0
null
2011-05-11T00:58:52.337
2011-05-11T00:58:52.337
null
null
4559
null
10633
2
null
10544
3
null
You would need to use the "Simultaneous Score Intervals for Difference of Proportions" to solve your question. The reference is " Agresti et al. 2008. Simultaneous confidence interval for comparing binomial parameters. Biometrics 64, 1270-1275. The corresponding R code is available in [http://www.stat.ufl.edu/~aa/cda/...
null
CC BY-SA 3.0
null
2011-05-11T01:09:17.860
2011-05-11T01:09:17.860
null
null
4559
null
10634
2
null
10562
0
null
You might want to try "model-based clustering". This algorithm uses "BIC" to determine the number of clusters. Sincerely
null
CC BY-SA 3.0
null
2011-05-11T01:13:16.013
2011-05-11T01:13:16.013
null
null
4559
null
10636
2
null
10607
4
null
I have a question/comment. I thought that by definition, logistic regression uses the logit link. If you are using the probit or complementary log-log link, then I do not think that is logistic regression. What you are doing is fitting generalized linear models on a binary outcome, which is assumed to follow a Bernou...
null
CC BY-SA 3.0
null
2011-05-11T01:37:41.867
2011-05-11T01:37:41.867
null
null
2312
null
10637
2
null
10592
2
null
Merely computing the covariance matrix--which you're going to need to get started in any event--is $O((Nf)^2)$ so, asymptotically in $N$, nothing is gained by choosing a $O(Nf)$ algorithm for the whitening. There are approximations when the variables have additional structure, such as when they form a time series or re...
null
CC BY-SA 4.0
null
2011-05-11T03:37:27.523
2022-05-24T16:44:55.370
2022-05-24T16:44:55.370
919
919
null
10638
2
null
10592
2
null
On a whim, I decided to try computing (in R) the covariance matrix for a dataset of about the size mentioned in the OP: ``` z <- rnorm(1e8) dim(z) <- c(1e6, 100) vcv <- cov(z) ``` This took less than a minute in total, on a fairly generic laptop running Windows XP 32-bit. It probably took longer to generate `z` in the...
null
CC BY-SA 3.0
null
2011-05-11T04:00:43.317
2011-05-11T04:00:43.317
null
null
1569
null
10639
1
10722
null
3
3323
According to [Wikipedia](http://en.wikipedia.org/wiki/Wilks%27_lambda_distribution), Wilks' Lambda distribution generalizes Hotelling's distribution. I am having some problems seeing how this works. I can see how Hotelling's distribution generalizes Student's t-distribution (a RV distributed as Hotelling's law with $p=...
How exactly does Wilks' Lambda distribution generalize the Hotelling distribution?
CC BY-SA 3.0
null
2011-05-11T04:34:34.790
2017-04-28T19:39:29.567
2017-04-28T19:39:29.567
28666
795
[ "distributions", "t-distribution", "hotelling-t2" ]
10640
1
10709
null
5
2132
I'm trying to design an experiment where I measure a variable as a function of 5 two-level factors, labelled A, B, C, D and E. I'm trying to understand how to best design this experiment so I can conduct it in 8 runs. I've tried to follow the guidance given in Box, Hunter & Hunter, and found two experimental $2^{5-2}$ ...
How to design an 8-run experiment in 5 factors?
CC BY-SA 3.0
null
2011-05-11T07:09:00.243
2013-09-24T18:50:43.890
2011-05-11T15:36:41.373
26
4370
[ "experiment-design" ]
10641
2
null
10639
2
null
[These NCSU course notes](http://faculty.chass.ncsu.edu/garson/PA765/manova.htm) say > Multivariate tests in contrast to the overall F test, answer the question, "Is each effect significant?" or more specifically, "Is each effect significant for at least one of the dependent variables?" That is, where the F...
null
CC BY-SA 3.0
null
2011-05-11T07:19:46.017
2011-05-11T07:19:46.017
null
null
2958
null
10642
2
null
10640
2
null
I do not have the book at hand, so I cannot comment on the reasoning to find these models. However, it is reasonable to expect in this type of setting that: - Different designs might better achieve different optimality criteria: perhaps you want the design with 8 runs that has best overall predictive ability, perhaps ...
null
CC BY-SA 3.0
null
2011-05-11T07:47:29.803
2011-05-11T07:47:29.803
null
null
4257
null
10643
1
10686
null
2
278
I'm measuring distances of various samples from a reference point. The distance is defined as a non-negative number, where $d=0$ means that the test case is identical to the reference. My general question is: Given a set of "typical" distances, what is the proper way to tell whether a given $d_1$ "too large", compare...
How to properly analyze distance from a reference?
CC BY-SA 3.0
null
2011-05-11T09:01:45.637
2011-05-11T23:04:01.823
2011-05-11T09:50:04.673
930
1496
[ "distributions", "hypothesis-testing", "distance-functions" ]
10644
1
null
null
10
2362
In PCA eigenvalues determine the order of components. In ICA I am using kurtosis to obtain the ordering. What are some accepted methods to assess the number, (given I have the order) of components that are singificant apart from prior knowledge about the signal?
Using kurtosis to assess significance of components from independent component analysis
CC BY-SA 3.0
null
2011-05-11T09:27:52.943
2017-10-15T02:25:18.827
2015-02-12T07:02:41.553
53618
4563
[ "statistical-significance", "pca", "kurtosis", "independent-component-analysis" ]
10645
2
null
10643
1
null
Can you not use the empirical distribution's 95% (or whichever you prefer) confidence limit? If your sample size is big enough, this ought to be a reasonable approximation.
null
CC BY-SA 3.0
null
2011-05-11T09:54:22.177
2011-05-11T09:54:22.177
null
null
4257
null
10646
2
null
73
1
null
Some packages are very useful in R. I will just recommand kernlab for Kernel-based Machine Learning Lab and e1071 for SVM and ggplot2 for graphics
null
CC BY-SA 3.0
null
2011-05-11T10:03:37.470
2011-05-11T10:03:37.470
null
null
4531
null
10647
2
null
9756
0
null
I have worked on active learning in classification and in SVM, that problem was same for me, if the boundary you found out by first model isn't that good the probability to have a good label for new points will decrease. If you have any other method to labelize your new generated points rather than using the boundary t...
null
CC BY-SA 3.0
null
2011-05-11T10:15:49.427
2011-05-11T10:15:49.427
null
null
4531
null
10649
1
null
null
4
6662
How can one obtain confidence limits of predicted values in ARIMA?
How to obtain confidence limits of predicted values in ARIMA?
CC BY-SA 3.0
null
2011-05-11T12:28:39.347
2011-05-11T21:10:48.220
2011-05-11T16:51:38.367
2970
4427
[ "forecasting" ]
10650
2
null
73
2
null
For me I am using kernlab for Kernel-based Machine Learning Lab and e1071 for SVM and ggplot2 for graphics
null
CC BY-SA 3.0
null
2011-05-11T12:33:30.563
2011-05-11T12:33:30.563
null
null
4531
null
10651
2
null
10631
2
null
I would have thought a "cubic regression" would work well for a cubic relationship. Call $Y_{i}$ the dependent variable, and $X_{i}$ the independent variable (or regressor). You simply use a polynomial regression: $$Y_{i}=\left(\sum_{j=0}^{p}\beta_{j}X_{i}^{j}\right)+e_{i}$$ I would use BIC to select the value of $p$...
null
CC BY-SA 3.0
null
2011-05-11T12:35:05.150
2011-05-11T12:35:05.150
null
null
2392
null
10652
2
null
7224
3
null
You need to put on an algorithm detecting which person that picture is referring to. You can build a model based on different portrait pictures of famous personality and use classifiers to ensure that this picture is referring to one of your database picture. You need to use a certain classifier based on different para...
null
CC BY-SA 3.0
null
2011-05-11T12:53:49.673
2011-05-11T12:53:49.673
null
null
4531
null
10653
2
null
10604
-1
null
I have reviewed the output and the forecast refelects an AR(12) in the error term which translates to a 12 period weighted forecast using the last 12 values of both your predictor series as the AR polynomial acts a multiplier across all series ( X,Y,Z ). Without getting into it in great detail , your model specificatio...
null
CC BY-SA 3.0
null
2011-05-11T13:26:05.713
2011-05-12T22:10:04.407
2011-05-12T22:10:04.407
3382
3382
null
10654
2
null
10631
4
null
Restricted cubic splines (natural splines) are an excellent choice. These are piecewise cubic polynomials that can fit any shape given enough knots. The following code in R shows how to fit such relationships and to plot the fit with confidence bands. ``` require(rms) dd <- datadist(mydata); options(datadist='dd') f ...
null
CC BY-SA 3.0
null
2011-05-11T13:31:27.083
2011-05-11T13:31:27.083
null
null
4253
null
10655
1
10706
null
4
2432
I have a scatter plot of (for example) height against age. How does one calculate for an individual point the percentile of the height for a given age? Suggestions in R would be most appreciated. Thanks!
How to calculate a percentile of y for a given x given a series of (x, y)?
CC BY-SA 3.0
null
2011-05-11T13:33:07.000
2011-05-12T21:10:18.593
null
null
1991
[ "quantiles" ]
10656
1
null
null
2
902
i just wanted to know if i could use factor scores and crosstab it with demographics (i.e. gender, age, etc.)? I have 69 likert-scale variables and run factor analysis on SPSS. It gave me 10 new variables (types of personality. i just wanted to see the demographics of each new variables. Thanks!!!
Crosstab factor scores generated by factor analysis
CC BY-SA 3.0
null
2011-05-11T13:44:50.520
2011-05-11T19:34:00.410
2011-05-11T19:34:00.410
null
4565
[ "factor-analysis" ]
10657
1
null
null
3
196
In relation to web usage mining from a log file, can you cluster data without performing User and/or Session identification? I mean,let's say I have these entries: > 123.234.324.122 [timestamp] "GET /cars/sport/porsche.jpg" 200 23432 "http://topgear.com/cars" "Mozilladsfsd" 120.23.324.122 [timestamp] "GET /bikes/sport...
Can one cluster web log data without performing user or session identification?
CC BY-SA 3.0
null
2011-05-11T13:55:41.987
2011-05-11T20:07:20.180
2020-06-11T14:32:37.003
-1
4402
[ "clustering" ]
10658
2
null
10062
5
null
Package [Mclust](http://cran.r-project.org/web/packages/mclust/mclust.pdf) is nice. The mclust function fits a mixture of normals distribution to data. You can automatically choose the number of components based on BIC (mclustmodel) or specify the number of components. There is also no need to convert your data into...
null
CC BY-SA 3.0
null
2011-05-11T13:57:14.200
2011-09-24T02:16:05.507
2011-09-24T02:16:05.507
2310
2310
null
10659
2
null
10655
1
null
'The' percentile for a given age implies some sort of regression (i.e. you can find 'the' mean predicted height from a given age). Once you have found this, the result depends on your assumptions: if you want no assumptions (besides the regression's), find how many of the heights in your original data are smaller than ...
null
CC BY-SA 3.0
null
2011-05-11T14:18:39.307
2011-05-11T14:18:39.307
null
null
4257
null
10660
2
null
10657
1
null
If you don't identify your sessions/users, you are clustering different things: one user who is an insane adept of any given car and looks at its picture dayly could have a huge impact on your results, though you're probably not interested in this.
null
CC BY-SA 3.0
null
2011-05-11T14:58:55.840
2011-05-11T14:58:55.840
null
null
4257
null
10661
2
null
10591
9
null
Here is a sketch of a proof which combines three ideas: (a) the delta method, (b) variance-stabilization transformations and (c) the closure of the Poisson distribution under independent sums. First, let's consider a sequence of iid Poisson random variables $X_1, X_2, \ldots$ with mean $\lambda > 0$. Then, the Central ...
null
CC BY-SA 3.0
null
2011-05-11T15:28:51.700
2011-05-12T12:56:29.837
2011-05-12T12:56:29.837
2970
2970
null
10662
1
10663
null
4
465
I'm working with a lot of data that was collected by obstetricians regarding the health of infants (birth weight, gestational age at delivery, mother's BMI), and I am trying to connect this data with geometric measurements performed on microscopic slide scans for each associated placenta (area, perimeter, number of blo...
What to do with a small (27) medical dataset?
CC BY-SA 3.0
null
2011-05-11T15:37:13.417
2011-05-11T19:46:48.087
2011-05-11T19:43:51.520
null
5129
[ "hypothesis-testing", "data-mining", "small-sample", "exploratory-data-analysis" ]
10663
2
null
10662
5
null
If you're looking for statistical significance I wouldn't hold out hope unless you have a very targeted hypothesis and/or there is a very strong effect. But certainly you could generate some new hypotheses with this data via some exploratory analysis. With 6 variables overall I'm not sure I'd start with any sophisticat...
null
CC BY-SA 3.0
null
2011-05-11T15:57:01.233
2011-05-11T19:46:48.087
2011-05-11T19:46:48.087
26
26
null
10664
1
null
null
2
578
I am trying to analyse a group of 4 questions that are on a 5 point scale. I need to group the answers for each question based on age. There are three different ages. How would I go about doing this?
How to examine group differences on several 5-point items using SPSS?
CC BY-SA 3.0
null
2011-05-11T16:17:56.080
2011-05-12T10:58:56.187
2011-05-12T01:47:22.627
183
4567
[ "spss", "likert" ]
10665
2
null
10649
4
null
One idea would be to use the [forecast](http://cran.r-project.org/web/packages/forecast/index.html) package in [R](http://www.r-project.org/): ``` library(forecast) fit <- auto.arima(WWWusage) fit f <- forecast(fit,h=20) f plot(f) ``` You can also give auto.arima parameters to use, rather than allowing it to fit its o...
null
CC BY-SA 3.0
null
2011-05-11T16:40:47.500
2011-05-11T16:48:50.180
2011-05-11T16:48:50.180
2817
2817
null
10666
2
null
10656
4
null
In SPSS, choose Analyze...Descriptive Statistics...Explore. The factor scores will be your dependents, and a demographic grouping will be your "factor" in this procedure. I'd choose Plots Only to start with and request boxplots. You can get either factor levels together or dependents together: you can experiment. ...
null
CC BY-SA 3.0
null
2011-05-11T16:43:02.240
2011-05-11T16:43:02.240
null
null
2669
null
10667
1
10670
null
2
1734
I have to assess for each product p, the odds ratio associated (success/failure). The data are in this table: ``` N_success N_trials p1 p2 p3 p4 p5 5 310 n n n n n 17 700 n y n n y 12 650 y y y n n 27 2...
Odds ratios multiple comparisons
CC BY-SA 3.0
null
2011-05-11T16:58:07.793
2011-05-11T18:52:39.843
2011-05-11T18:18:03.137
919
4569
[ "logistic", "multiple-comparisons", "odds-ratio" ]
10668
2
null
10369
1
null
Observe that the random variable $i_j$ is a function of $\mathbf{Z} = (Z_1, \ldots, Z_n)$ only. For an $n$-vector, $\mathbf{z}$, we write $i_j(\mathbf{z})$ for the index of the $j$th largest coordinate. Let also $P_z(A) = P(X_1 \in A \mid Z_1 = z)$ denote the conditional distribution of $X_1$ given $Z_1$. If we break ...
null
CC BY-SA 3.0
null
2011-05-11T18:22:17.520
2011-05-11T18:22:17.520
null
null
4376
null
10669
1
10685
null
2
1089
I am running a model for which I am getting a very bad percentage detection of events in the confusion matrix (basically my true positives). Obviously that implies my false negatives are too hight. When I gave these dataset to a neural network node or a decision tree node, I see that the percentage detection by these...
Decision tree output -- learning
CC BY-SA 3.0
null
2011-05-11T18:37:16.257
2011-05-12T13:51:27.850
2011-05-12T13:51:27.850
183
1763
[ "cart" ]
10670
2
null
10667
0
null
I believe you could use "simultaneous score confidence interval for OR" to analyze your question. The reference is Agresti et al. 2008 Simultaneous confidence intervals for comparing binomial parameters. Biometrics 64 1270-1275. The R code is available in [http://www.stat.ufl.edu/~aa/cda/software.html](http://www.stat...
null
CC BY-SA 3.0
null
2011-05-11T18:52:39.843
2011-05-11T18:52:39.843
null
null
4559
null
10671
2
null
10662
1
null
I agree with JMS, you will need to plot each of your variable first because PCA requires the normality assumption. If your variables are not normally distributed then it is not appropriate to use PCA before transforming the variables. I think you will need to ask yourself, what you really want to know from this data se...
null
CC BY-SA 3.0
null
2011-05-11T19:11:30.590
2011-05-11T19:11:30.590
null
null
4559
null
10672
1
10757
null
13
1828
I've read about a number of algorithms for solving n-armed bandit problems like $\epsilon$-greedy, softmax, and UCB1, but I'm having some trouble sorting through what approach is best for minimizing regret. Is there a known optimal algorithm for solving the n-armed bandit problem? Is there a choice of algorithm that se...
Optimal algorithm for solving n-armed bandit problems?
CC BY-SA 3.0
null
2011-05-11T19:57:03.987
2012-07-09T16:32:29.370
2012-07-09T16:32:29.370
4872
4281
[ "machine-learning", "reinforcement-learning", "multiarmed-bandit" ]
10673
2
null
10657
0
null
Cluster analysis does not involve hypothesis testing per se, but is really just a collection of different similarity algorithms for exploratory analysis. You can force hypothesis testing somewhat but the results are often inconsistent, since cluster changes are very sensitive to changes in parameters. So the answer is ...
null
CC BY-SA 3.0
null
2011-05-11T20:07:20.180
2011-05-11T20:07:20.180
null
null
3489
null
10674
1
null
null
0
904
I have a two-dimensional data set that looks like $(t, x)$ where $t$ is a time in seconds when event $X$ happened. $X$ ranges from $[0, 200]$. I want to visualize the frequency of each $x$ at time $t$ over some time period. I guess this would be a bar graph with $x$-axis being event #, $y$-axis being frequency, and $z...
Modeling frequency over time
CC BY-SA 3.0
null
2011-05-11T20:07:34.483
2013-05-15T04:33:18.643
2013-05-15T04:33:18.643
805
4571
[ "r", "data-visualization" ]
10676
1
10677
null
8
10107
Lets say I have a highly dimensional classification problem with a lot of noise, and I want to improve my results by removing some of the noisy variables. I've [read](http://research.microsoft.com/pubs/69946/tr-2002-63.pdf) [several](http://www.andrew.cmu.edu/user/minhhoan/papers/SVMFeatureWeight_PR.pdf) [papers](http...
Using an SVM for feature selection
CC BY-SA 3.0
null
2011-05-11T20:32:04.700
2011-05-12T09:22:47.270
null
null
2817
[ "r", "svm" ]
10677
2
null
10676
5
null
As I understand them, SVMs have built-in regularization because they tend to penalize large weights of predictors which amounts to favor simpler models. They're often used with [recursive feature elimination](http://www.brainvoyager.com/bvqx/doc/UsersGuide/WebHelp/Content/MVPATools/Recursive_Feature_Elimination.htm) (i...
null
CC BY-SA 3.0
null
2011-05-11T20:47:54.837
2011-05-11T20:47:54.837
null
null
930
null
10678
2
null
10649
3
null
The confidence limits for an ARIMA forecast are based upon the PSI WEIGHTS . The PSI WEIGHTS are easily computed by representing the ARIMA MODEL as a pure MOVING AVERAGE MODEL. One should not be dependent upon software ( any software ! ) for answers.
null
CC BY-SA 3.0
null
2011-05-11T21:10:48.220
2011-05-11T21:10:48.220
null
null
3382
null
10679
2
null
10664
3
null
Here are 3 options; hard brackets need to be filled in, while braces contain optional subcommands: ``` cross [varlist] by age {/cells count col row}. means [varlist] by age {/stat anova}. ``` summarize command - best obtained through the menus via Analyze...Reports...Case Summaries. Then you may need to double-click...
null
CC BY-SA 3.0
null
2011-05-11T22:19:51.593
2011-05-12T01:55:53.997
2011-05-12T01:55:53.997
183
2669
null
10680
1
10724
null
15
981
This is sort of an open ended question but I wanna be clear. Given a sufficient population you might be able to learn something (this is the open part) but whatever you learn about your population, when is it ever applicable to a member of the population? From what I understand of statistics it's never applicable to a ...
How to NOT use statistics
CC BY-SA 3.0
null
2011-05-11T17:47:50.800
2014-07-20T01:01:54.527
2014-07-20T00:13:05.307
22468
4576
[ "teaching", "validity" ]
10681
2
null
10680
9
null
Unless the people in the room are a random sample of the world's population, any conclusions based on statistics about the world's population are going to be very suspect. One out of every 5 people in the world is Chinese, but none of my five children are...
null
CC BY-SA 3.0
null
2011-05-11T17:56:10.473
2011-05-11T17:56:10.473
null
null
null
null
10682
2
null
10680
6
null
- To address overapplication of statistics to small samples, I recommend countering with well-known jokes ("I am so excited, my mother is pregnant again and my baby sibling will be Chinese." "Why?" "I have read that every fourth baby is Chinese."). - Actually, I recommend jokes to address all kinds of misconception i...
null
CC BY-SA 3.0
null
2011-05-11T17:57:05.260
2011-05-11T17:57:05.260
null
null
17823
null
10683
2
null
10680
3
null
There is an interesting article by Mary Gray on misuse of statistics in court cases and things like that... Gray, Mary W.; Statistics and the Law. Math. Mag. 56 (1983), no. 2, 67–81
null
CC BY-SA 3.0
null
2011-05-11T18:09:30.407
2011-05-11T18:09:30.407
null
null
42201
null
10684
2
null
10680
0
null
Hypothesis: $A$ (Textbook) Result: Do no reject $A$ ($\sigma = c$) Your Statement: $A$ holds with probability $\sigma$! Correct would be: In this case, you know nothing. If you want to "prove" $A$, your hypothesis has to be $\neg A$; reject it with $\sigma$ to get the desired statement.
null
CC BY-SA 3.0
null
2011-05-11T20:27:27.100
2011-05-11T20:27:27.100
null
null
12868
null
10685
2
null
10669
2
null
I see that you've accepted answers to just 3 of 9 questions... Are you using the type of Decision Tree known as CHAID? If so, you will obtain an indication of one main effect and then any number of so-called interaction effects. You can try these effects in a regression, ANOVA, or general linear model. You build in ...
null
CC BY-SA 3.0
null
2011-05-11T22:48:58.137
2011-05-11T22:48:58.137
2017-04-13T12:44:24.677
-1
2669
null
10686
2
null
10643
2
null
My first instinct is to say that it would be silly to make such a determination absent any knowledge of the topic. "Too large" for what, or for whom? But perhaps what you're looking for is really a test for outliers in the distribution--not that you're likely to find any in the one you've shown. Check out Dixon's Te...
null
CC BY-SA 3.0
null
2011-05-11T23:04:01.823
2011-05-11T23:04:01.823
null
null
2669
null
10687
1
null
null
22
63713
I know correlation does not imply causation but instead the strength and direction of the relationship. Does simple linear regression imply causation? Or is an inferential (t-test, etc.) statistical test required for that?
Does simple linear regression imply causation?
CC BY-SA 3.0
null
2011-05-11T23:05:00.207
2022-05-07T10:19:43.723
2011-05-12T06:44:00.000
930
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[ "regression", "correlation", "causality" ]
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I was using "[Fundamentals of Clinical Trials](https://link.springer.com/book/10.1007/978-3-319-18539-2)" when I was in PhD program.
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CC BY-SA 4.0
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2011-05-11T23:19:08.927
2022-12-06T02:54:37.377
2022-12-06T02:54:37.377
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The quick answer is, no. You can easily come up with non-related data that when regressed, will pass all sorts of statistical tests. Below is an old picture from Wikipedia (which, for some reason has recently been removed) that has been used to illustrate data-driven "causality". We need more pirates to cool the...
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CC BY-SA 3.0
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2011-05-11T23:44:00.907
2011-05-11T23:57:04.897
2011-05-11T23:57:04.897
2775
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