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Tags
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2823
1
null
null
4
291
I've just been given a stack of polling data to analyse. Some of the questions are obviously leading or present subtle incentives (for the poller or polled) for specific answers. Of other questions I'm not so sure but I have some doubts. I'm also starting to question other factors about how the poll was conducted (envi...
What are good resources/criteria for judging human bias in data collection?
CC BY-SA 2.5
null
2010-09-18T16:14:02.140
2010-09-19T09:30:23.640
2010-09-19T09:30:23.640
183
1343
[ "references", "mathematical-statistics", "survey" ]
2824
1
2853
null
17
4509
A few months ago I posted a question about homoscedasticity tests in R on SO, and Ian Fellows answered that (I'll paraphrase his answer very loosely): Homoscedasticity tests are not a good tool when testing the goodness of fit of your model. With small samples, you don't have enough power to detect departures from ho...
Checking ANOVA assumptions
CC BY-SA 3.0
null
2010-09-18T17:42:06.037
2016-03-11T12:36:01.467
2016-03-11T12:29:57.890
4253
1356
[ "hypothesis-testing", "anova", "nonparametric", "goodness-of-fit", "heteroscedasticity" ]
2825
2
null
2715
53
null
Keep your analysis reproducible. A reviewer or your boss or someone else will eventually ask you how exactly you arrived at your result - probably six months or more after you did the analysis. You will not remember how you cleaned the data, what analysis you did, why you chose the specific model you used... And recons...
null
CC BY-SA 3.0
null
2010-09-18T18:15:49.220
2013-06-17T18:03:39.020
2013-06-17T18:03:39.020
22047
1352
null
2826
2
null
2823
1
null
Possibly [Benford's Law](http://en.wikipedia.org/wiki/Benford%27s_law) might help. Check the Application section on the wiki
null
CC BY-SA 2.5
null
2010-09-18T18:33:13.560
2010-09-18T20:43:30.903
2010-09-18T20:43:30.903
795
364
null
2827
2
null
2715
8
null
For histograms, a good rule of thumb for number of bins in a histogram: square root of the number of data points
null
CC BY-SA 2.5
null
2010-09-18T19:49:37.593
2010-09-18T19:49:37.593
null
null
438
null
2828
1
2890
null
24
14703
How can we compare complexity of two models with the same number of parameters? Edit 09/19: To clarify, model complexity is a measure of how hard it is to learn from limited data. When two models fit existing data equally well, a model with lower complexity will give lower error on future data. When approximations are ...
Measures of model complexity
CC BY-SA 2.5
null
2010-09-18T20:20:10.293
2017-06-09T02:49:27.430
2010-09-19T22:06:26.193
511
511
[ "model-selection" ]
2829
2
null
527
1
null
I agree with @drnexus. In addition, I might recommend a Morgan-Pitman test for the equality of variances of the two methods. This would tell you if one method has more variance than the other. This in itself might not be a bad thing because presumably the two tests have different bias-variance tradeoffs (for example, o...
null
CC BY-SA 2.5
null
2010-09-18T20:41:05.413
2010-09-18T20:41:05.413
null
null
795
null
2830
2
null
2828
5
null
I think it would depend on the actual model fitting procedure. For a generally applicable measure, you might consider Generalized Degrees of Freedom described in [Ye 1998](http://www.jstor.org/pss/2669609) -- essentially the sensitivity of change of model estimates to perturbation of observations -- which works quite ...
null
CC BY-SA 2.5
null
2010-09-18T20:41:57.250
2010-09-18T20:41:57.250
null
null
251
null
2831
2
null
2715
30
null
One rule per answer ;-) Talk to the statistician before conducting the study. If possible, before applying for the grant. Help him/her understand the problem you are studying, get his/her input on how to analyze the data you are about to collect and think about what that means for your study design and data requirement...
null
CC BY-SA 2.5
null
2010-09-18T21:07:17.487
2010-09-18T21:07:17.487
null
null
1352
null
2832
2
null
1815
4
null
[Experimental Design for the Life Sciences](http://ukcatalogue.oup.com/product/9780199285112.do), by Ruxton & Colegrave. Aimed primarily at undergraduates.
null
CC BY-SA 2.5
null
2010-09-18T21:07:17.843
2010-09-18T21:07:17.843
null
null
266
null
2833
2
null
2824
11
null
A couple of graphs will usually be much more enlightening than the p value from a test of normality or homoskedasticity. Plot observed dependent variables against independent variables. Plot observations against fits. Plot residuals against independent variables. Investigate anything that looks strange on these plots. ...
null
CC BY-SA 2.5
null
2010-09-18T21:27:13.180
2010-09-18T21:27:13.180
null
null
1352
null
2834
2
null
527
16
null
The simple correlation approach isn't the right way to analyze results from method comparison studies. There are (at least) two highly recommended books on this topic that I referenced at the end (1,2). Briefly stated, when comparing measurement methods we usually expect that (a) our conclusions should not depend on th...
null
CC BY-SA 3.0
null
2010-09-18T21:29:59.203
2016-07-13T08:11:16.300
2016-07-13T08:11:16.300
1352
930
null
2835
2
null
2585
2
null
A slight variation on Jeromy's theme: time on the horizontal axis, price on the vertical axis. Plot multiple lines: one connecting the minimum prices, one connecting the 10% quantiles of prices, one connecting the 25% quantiles of prices. Plot these lines in varying shades of gray: large amounts of product available at...
null
CC BY-SA 4.0
null
2010-09-18T21:46:28.497
2023-03-09T10:11:48.967
2023-03-09T10:11:48.967
362671
1352
null
2836
2
null
2828
3
null
[Minimum Description Length](http://en.wikipedia.org/wiki/Minimum_description_length) may be an avenue worth pursuing.
null
CC BY-SA 2.5
null
2010-09-18T21:50:53.100
2010-09-18T21:50:53.100
null
null
1352
null
2837
2
null
113
2
null
John, I am not sure my suggestion may be of help. But, in any case the book [Intuitive Biostatistics](http://rads.stackoverflow.com/amzn/click/0199730067) by Harvey Motulsky may be of assistance. Chapter 37 'Choosing a Test' has a pretty good table on page 298 that tells you given the nature of the data set and probl...
null
CC BY-SA 2.5
null
2010-09-19T00:27:18.983
2010-10-08T23:57:02.170
2010-10-08T23:57:02.170
1329
1329
null
2838
2
null
913
1
null
Many have already made excellent suggestions regarding transforming the variables and using robust regression methods. But, when looking at the scatter plot, I observe two separate data sets. One set has a very strong linear relationship where the correlation is a lot higher than the overall 0.6. And, visually it lo...
null
CC BY-SA 2.5
null
2010-09-19T00:52:52.930
2010-09-19T00:52:52.930
null
null
1329
null
2839
2
null
913
0
null
Like the others have said, some sort of transformation is recommended. Your data seems highly clustered, and could be roughly linear, but it's difficult to tell with all the other points around it. Others have suggested trying a log transformation, but it might also be a good idea to try a [Box-Cox Transformation](http...
null
CC BY-SA 2.5
null
2010-09-19T01:47:02.270
2010-09-19T01:47:02.270
null
null
1118
null
2840
2
null
2824
4
null
QQ Plots are pretty good ways to detect non-normality. For homoscedasticity, try Levene's test or a Brown-Forsythe test. Both are similar, though BF is a little more robust. They are less sensitive to non-normality than Bartlett's test, but even still, I've found them not to be the most reliable with small sample size...
null
CC BY-SA 3.0
null
2010-09-19T02:09:59.820
2016-03-11T12:36:01.467
2016-03-11T12:36:01.467
22047
1118
null
2841
2
null
2823
4
null
In regards to the leading questions, here are several options of how I would attempt to investigate if your suspicions are true; 1 - Conduct your own experiment. One of your conditions will be to mimic the leading questions in the prior surveys, the other condition will be a survey constructed with functionally similar...
null
CC BY-SA 2.5
null
2010-09-19T03:24:26.727
2010-09-19T03:24:26.727
null
null
1036
null
2842
2
null
2824
4
null
The are some very good web guides to checking the assumptions of ANOVA & what to do if the fail. [Here](http://quality-control-plan.com/StatGuide/oneway_anova_ass_viol.htm) is one. [This](http://homepage.mac.com/bradthiessen/stats/m301/4a.pdf) is another. Essentially your eye is the best judge, so do some [explorator...
null
CC BY-SA 2.5
null
2010-09-19T04:34:21.487
2010-09-19T04:34:21.487
null
null
521
null
2843
2
null
328
0
null
I like [Risk and Asset Allocation](http://books.google.com/books?id=Qc8KWWtUokcC&lpg=PR1&dq=risk%20and%20asset%20allocation%20meucci&pg=PR1#v=onepage&q&f=false) by A. Meucci. This book is a bit more advanced than Ruppert's book, but still very user-friendly.
null
CC BY-SA 2.5
null
2010-09-19T05:41:03.267
2010-09-19T05:41:03.267
null
null
795
null
2844
1
2847
null
11
8113
Example code: ``` (pc.cr <- princomp(USArrests)) summary(pc.cr) loadings(pc.cr) ## note that blank entries are small but not zero ``` I am getting different outputs from each, and I am not sure I understand what the difference is. Here is the output: ``` > summary(pc.cr) Importance of components: ...
What is the difference between summary() and loadings() for princomp() object in R?
CC BY-SA 3.0
null
2010-09-19T09:21:07.803
2016-05-24T20:54:37.147
2016-05-24T20:54:37.147
253
253
[ "r", "pca" ]
2845
2
null
1815
2
null
[Experimental Design in Biotechnology](http://rads.stackoverflow.com/amzn/click/0824778812) by Perry D. Haaland, ed Marcel Dekker.
null
CC BY-SA 2.5
null
2010-09-19T09:24:48.077
2010-09-19T09:34:20.480
2010-09-19T09:34:20.480
null
null
null
2846
1
2850
null
13
10140
I have read and seen a lot of Parallel coordinates plots. Can someone answer the following set of questions: - What are parallel coordinates plots (PCP) in simple words, so that a layman can understand? - A mathematical explanation with some intuition if possible - When are PCP useful and when to use them? - When a...
An easy explanation for the parallel coordinates plot
CC BY-SA 2.5
null
2010-09-19T09:32:28.610
2014-05-04T04:23:06.427
2010-09-19T09:37:17.790
183
1307
[ "r", "data-visualization" ]
2847
2
null
2844
4
null
The first output is the correct and most useful one. Calling `loadings()` on your object just returns a summary where the SS are always equal to 1, hence the % variance is just the SS loadings divided by the number of variables. It makes sense only when using Factor Analysis (like in `factanal`). I never use `princomp`...
null
CC BY-SA 2.5
null
2010-09-19T10:45:31.837
2010-09-19T11:40:21.617
2010-09-19T11:40:21.617
930
930
null
2848
2
null
1708
3
null
It looks like you are referring to eigenanalysis for SNPs data and the article from Nick Patterson, [Population Structure and Eigenanalysis](http://www.plosgenetics.org/article/info%3adoi/10.1371/journal.pgen.0020190) (PLoS Genetics 2006), where the first component explains the largest variance on allele frequency wrt....
null
CC BY-SA 2.5
null
2010-09-19T11:24:58.573
2010-09-26T20:55:20.310
2010-09-26T20:55:20.310
930
930
null
2849
1
null
null
3
718
I have a static panel data model with small T (T=5) that makes it impossible for me to use granger causality as it requires a long time span. So my question: - Is there any alternative solution to test for causation even in a small T context? Any hint will be highely appreciated!
How to test for causation in a static panel data model with small t?
CC BY-SA 2.5
null
2010-09-19T12:46:28.310
2010-11-10T07:40:11.763
2010-11-10T07:40:11.763
930
1251
[ "econometrics", "causality", "panel-data" ]
2850
2
null
2846
6
null
It seems to me that the main function of PCP is to highlight homogeneous groups of individuals, or conversely (in the dual space, by analogy with PCA) specific patterns of association on different variables. It produces an effective graphical summary of a multivariate data set, when there are not too much variables. Va...
null
CC BY-SA 2.5
null
2010-09-19T12:57:26.100
2010-09-19T16:55:34.567
2017-04-13T12:44:40.807
-1
930
null
2851
2
null
2446
2
null
Concerning your more specific question (i.e. how many degrees of freedom): the question is how many replicates do you have. Look at the early pages of chapter 19 of [the R book](http://rads.stackoverflow.com/amzn/click/0470510242) for examples and guidelines for such accounting. We could do the accounting here but i do...
null
CC BY-SA 2.5
null
2010-09-19T13:21:39.003
2010-09-21T20:33:56.847
2010-09-21T20:33:56.847
603
603
null
2852
1
null
null
1
5555
The biological data is listed as following: ``` V1 V2 V3 V4 V5 V6 0.064 0.014 0.016 0.012 0.013 0.023 0.056 0.000 0.000 0.008 0.010 0.000 0.042 0.014 0.024 0.008 0.017 0.023 0.031 0.014 0.016 0.008 0.013 0.023 0.068 0.000 0.008 0.004 0.020 0.000 0.081 0.000 0.000 0.004 0.010 0.000 0.060 0.014 0.016 0...
How to analyze these data?
CC BY-SA 2.5
null
2010-09-19T14:02:26.617
2010-09-20T11:29:59.137
2010-09-20T06:33:04.833
930
null
[ "r", "hypothesis-testing" ]
2853
2
null
2824
12
null
In applied settings it is typically more important to know whether any violation of assumptions is problematic for inference. Assumption tests based on significance tests are rarely of interest in large samples, because most inferential tests are robust to mild violations of assumptions. One of the nice features of g...
null
CC BY-SA 2.5
null
2010-09-19T14:44:17.667
2010-09-19T14:44:17.667
null
null
183
null
2854
1
5646
null
5
1274
Dear all, I was encouraged to ask this question here as well as on stackoverflow and would be very appreciative of any answers... Due to hetereoscedasticity I'm doing bootstrapped linear regression (appeals more to me than robust regression). I'd like to create a plot along the lines of what I've done in the script he...
Calculating probability for bivariate normal distributions based on bootstrapped regression coefficients
CC BY-SA 2.5
null
2010-09-19T15:00:04.550
2010-12-24T11:45:34.523
2010-12-19T17:06:45.113
449
1291
[ "r", "bootstrap", "heteroscedasticity", "ggplot2" ]
2855
2
null
2010
2
null
Almost all statistics implicitly condition on N. We treat N as a constant that can come out from the expression $\mathbb{E}\left[\frac{1}{N}\sum_{i=1}^{N}{x_i}\right]$, for example. For that to be appropriate, N has to be a fixed value, which we get by conditioning. Without conditioning on N, as you said, we'd need to ...
null
CC BY-SA 2.5
null
2010-09-19T16:41:11.350
2010-09-19T16:41:11.350
null
null
401
null
2856
2
null
2846
4
null
In regards to questions 3, 4, and 5 I would suggest you check out this work [Perceiving patterns in parallel coordinates: determining thresholds for identification of relationships by: Jimmy Johansson, Camilla Forsell, Mats Lind, Matthew Cooper in Information Visualization, Vol. 7, No. 2. (2008), pp. 152-162.](http://...
null
CC BY-SA 2.5
null
2010-09-19T17:10:15.873
2010-09-19T17:28:17.197
2010-09-19T17:28:17.197
1036
1036
null
2857
2
null
2852
1
null
For most of your variables (e.g. `V2`), some observations have identical values, hence the warning message thrown by R: unique ranks cannot be computed for all observations, and there are ties, precluding the computation of an exact p-value. For your variable named `V2`, there are in fact only two distinct values (out ...
null
CC BY-SA 2.5
null
2010-09-19T17:36:12.660
2010-09-19T17:36:12.660
null
null
930
null
2858
2
null
2846
4
null
Please visit [http://www.cs.tau.ac.il/~aiisreal/](http://www.cs.tau.ac.il/~aiisreal/) and also look at the new book Parallel Coordinates - This book is about visualization, systematically incorporating the fantastic human pattern recognition into the problem-solving process... www.springer.com/math/cse/book/978-0-387-2...
null
CC BY-SA 2.5
null
2010-09-19T17:57:05.217
2010-09-19T17:57:05.217
null
null
1366
null
2859
2
null
2852
5
null
Sometimes a formal statistical test is overkill. Row by row, the entries in the first column are the largest. Draw a picture to make this apparent: side-by-side boxplots or dotplots would work nicely. Although this is a post-hoc comparison, if the initial intent had been to compare the first column against the rest f...
null
CC BY-SA 2.5
null
2010-09-19T18:11:38.943
2010-09-19T18:11:38.943
null
null
919
null
2860
1
null
null
5
3572
We know that the projection matrix learned by PCA can be applied to out-of-sample data points to get their low-dimensional embedding. However, how reliable are these embeddings expected to be, as compared to the embedding obtained from PCA with these out-of-sample points combined with the original data? Consider this ...
PCA on out-of-sample data
CC BY-SA 2.5
null
2010-09-19T18:53:35.410
2022-05-03T12:10:00.487
2010-09-21T12:01:56.170
183
881
[ "machine-learning", "pca", "dimensionality-reduction" ]
2861
2
null
2615
0
null
I am not sure what the real question is, but suppose instead of changing every non-diagonal element, you changed just 2 (to keep the resulting matrix symmetric). That is let $\hat{C}$ be $C$ with $\hat{C_{i,j}} = C_{i,j} + \Delta C / 2= \hat{C_{j,i}},$ for some choice of $i,j$ with $i \ne j$. (alternatively, imagine $\...
null
CC BY-SA 2.5
null
2010-09-19T20:09:26.417
2010-09-20T01:50:20.380
2010-09-20T01:50:20.380
795
795
null
2863
1
2864
null
6
13782
I want to assess item-total correlations on a 19-item questionnaire (some of the questions are meant to be reverse-scored). My question is: - Do I reverse score the items PRIOR to calculating the item-total correlations (in order to eliminate any variables that do not correlate with the total at >.40)? - Addition...
Should I reverse score items before running reliability analyses (item-total correlation) and factor analysis?
CC BY-SA 3.0
null
2010-09-19T22:35:50.730
2020-02-29T20:40:23.440
2011-06-06T13:54:23.937
183
null
[ "correlation", "factor-analysis", "reliability" ]
2864
2
null
2863
5
null
Yes, you should reverse score all items as needed to ensure that a particular score means the same thing on all items. You should do this for all types of analysis. For example, you have 'propensity to shoplift' measured via 3 items on a scale of 1 to 5 (where 1 is low propensity to shoplift and 5 is high). Suppose th...
null
CC BY-SA 2.5
null
2010-09-19T22:56:29.170
2010-09-19T22:56:29.170
null
null
null
null
2872
2
null
195
2
null
I have been told many times that the Anderson Darling (AD) test is much better than the Kolmogorov-Smirnov (KS) one because AD does a better job at fitting the tails of the distribution. KS is only good at fitting the mid-range of the distribution; but, is not better than AD even in this regard. I think the main adva...
null
CC BY-SA 2.5
null
2010-09-20T00:29:57.047
2010-09-20T00:29:57.047
null
null
1329
null
2873
2
null
2860
1
null
I have never done this but my intuition suggests that the answer would depend to the extent to which the covariance matrix for the 500 data points is 'different' from the out-of-sample data. If the out-of-sample covariance matrix is very different then clearly the projection matrix of those points would be different th...
null
CC BY-SA 2.5
null
2010-09-20T00:38:48.693
2010-09-20T00:38:48.693
null
null
null
null
2875
1
null
null
3
261
My friend and I are working on a project on distributed datastructures. We were wondering how much is nearest neighbor information used in modern recommendation systems and whether it would be worthwhile to work on a distributed datastructure (say a kd-tree) for that purpose. Thanks
Nearest neighbor information for recommendation engines
CC BY-SA 2.5
null
2010-09-20T01:19:26.897
2013-08-20T00:03:06.297
2013-08-20T00:03:06.297
22468
250
[ "k-nearest-neighbour", "recommender-system" ]
2877
2
null
2860
2
null
This isn't unlike a model selection problem where the goal is to arrive at something close to the "true dimensionality" of the data. You could try a cross validation approach, say 5-fold CV with your 500 data points. This will give you a reasonable metric of generalization error for out-of-sample data. The following...
null
CC BY-SA 4.0
null
2010-09-20T03:38:03.447
2022-05-03T12:10:00.487
2022-05-03T12:10:00.487
79696
251
null
2878
2
null
2863
9
null
Reliability Analysis: Yes, you should reverse score the reversed items. Factor Analysis: It does not matter so much. Eigenvalues and associated indices (e.g., variance explained by factors, rules of thumb regarding number of factors to extract, etc.) should be the same. The sign of factor loadings will flip based on wh...
null
CC BY-SA 2.5
null
2010-09-20T04:07:18.163
2010-09-20T04:07:18.163
null
null
183
null
2883
2
null
2061
4
null
[BIOSTATISTICS VS. LAB RESEARCH](http://www.xtranormal.com/watch/6878253/): A funny/sad video on statistics consulting.
null
CC BY-SA 2.5
null
2010-09-20T06:05:15.013
2010-09-20T10:34:39.257
2010-09-20T10:34:39.257
183
183
null
2884
2
null
2852
0
null
Thank you very much, chl, whuber and Gaetan Lion. But do you think is there any problem that if I change to caculate the differene among the data using Kruskal-Wallis test instead of comparing the difference between the first column with other columns? > kruskal.test(as.list(Data)) ``` Kruskal-Wallis rank sum te...
null
CC BY-SA 2.5
null
2010-09-20T06:14:15.227
2010-09-20T11:29:59.137
2010-09-20T11:29:59.137
null
null
null
2885
2
null
2828
5
null
Minimum Description Length (MDL) and Minimum Message Length (MML) are certainly worth checking out. As far as MDL is concerned, a simple paper that illustrates the Normalized Maximum Likelihood (NML) procedure as well as the asymptotic approximation is: > S. de Rooij & P. Grünwald. An empirical study of minimum desc...
null
CC BY-SA 2.5
null
2010-09-20T06:20:50.417
2010-09-20T06:20:50.417
null
null
530
null
2886
1
2887
null
8
10898
As title, I am thinking of merging both into "missing data", which is to name it as NA in R. Since I don't see it will make much sense (or even any sense), to separate the "don't know" row out and to compare the information with other rows. Is it OK for me to do so?
How will you deal with "don't know" and "missing data" in survey data?
CC BY-SA 4.0
null
2010-09-20T06:44:20.220
2019-07-25T10:10:37.353
2019-07-25T10:10:37.353
11887
588
[ "multivariate-analysis", "missing-data", "survey" ]
2887
2
null
2886
12
null
Well, you should also considered that "don't know" is at least some kind of answer, whereas non-response is a purely missing value. Now, we often allow for "don't know" response in survey just to avoid forcing people to provide a response anyway (which might bias the results). For example, in the National Health and Nu...
null
CC BY-SA 2.5
null
2010-09-20T07:08:01.583
2010-09-20T07:08:01.583
null
null
930
null
2888
2
null
1856
8
null
I haven't seen this used in outside of bioinformatics/machine learning either, but maybe you can be the first one :) As a good representative of small sample method method from bioinformatics, logistic regression with L1 regularization can give a good fit when number of parameters is exponential in the number of observ...
null
CC BY-SA 2.5
null
2010-09-20T07:29:51.983
2010-10-01T15:56:38.640
2010-10-01T15:56:38.640
511
511
null
2889
2
null
2886
2
null
It depends on the type of question/response in your survey. If they are like "I like", "I dislike", "Don't know", chl answers partially to your question. The first solution is chl's answer. You have to check if "Don't know" doesn't hide anything. You have to analyse separately these values to see if it highlights a sp...
null
CC BY-SA 2.5
null
2010-09-20T07:31:33.540
2010-09-20T07:39:17.980
2010-09-20T07:39:17.980
930
1154
null
2890
2
null
2828
13
null
Besides the various measures of Minimum Description Length (e.g., normalized maximum likelihood, Fisher Information approximation), there are two other methods worth to mention: - Parametric Bootstrap. It's a lot easier to implement than the demanding MDL measures. A nice paper is by Wagenmaker and colleagues: Wagen...
null
CC BY-SA 2.5
null
2010-09-20T08:40:00.997
2010-09-21T08:45:45.537
2017-04-13T12:44:23.203
-1
442
null
2891
1
5695
null
1
188
I'm looking for a simple way to store ratios. For a time component, I must store the average ratio between two behavior. For example the number of people that turn left compared to the number of people that turn right. I have to detect unusual behavior (people that turn right abnormally). How should I mathematically co...
Best value to store ratio data and compare it to time period average
CC BY-SA 2.5
null
2010-09-20T09:07:06.277
2010-12-22T14:22:27.143
2010-12-22T14:22:27.143
1739
null
[ "data-visualization", "multiple-comparisons", "count-data", "logit", "proportion" ]
2892
1
2905
null
17
14638
What is your intuition / interpretation of a distribution of eigenvalues of a correlation matrix? I tend to hear that usually 3 largest eigenvalues are the most important, while those close to zero are noise. Also, I've seen a few research papers investigating how naturally occuring eigenvalue distributions differ from...
Intuition / interpretation of a distribution of eigenvalues of a correlation matrix?
CC BY-SA 2.5
null
2010-09-20T10:26:08.910
2019-02-17T00:32:01.113
null
null
1250
[ "distributions", "correlation" ]
2893
1
2897
null
21
5825
It is usual to use second, third and fourth moments of a distribution to describe certain properties. Do partial moments or moments higher than the fourth describe any useful properties of a distribution?
Moments of a distribution - any use for partial or higher moments?
CC BY-SA 2.5
null
2010-09-20T10:56:57.297
2018-09-04T08:41:06.673
2018-09-04T08:41:06.673
11887
1250
[ "distributions", "moments", "partial-moments" ]
2894
1
null
null
9
415
I am trying to estimate the mean of a more-or-less Gaussian distribution via sampling. I have no prior knowledge about its mean or its variance. Each sample is expensive to obtain. How do I dynamically decide how many samples I need to get a certain level of confidence/accuracy? Alternatively, how do I know when I can ...
Dynamic calculation of number of samples required to estimate the mean
CC BY-SA 2.5
null
2010-09-20T13:24:09.147
2010-09-20T15:51:22.327
2010-09-20T13:29:12.717
1376
1376
[ "estimation", "sample-size" ]
2895
2
null
665
6
null
Probability studies, well, how probable events are. You intuitively know what probability is. Statistics is the study of data: showing it (using tools such as charts), summarizing it (using means and standard deviations etc.), reaching conclusions about the world from which that data was drawn (fitting lines to data et...
null
CC BY-SA 2.5
null
2010-09-20T13:59:30.777
2010-09-20T13:59:30.777
null
null
666
null
2896
2
null
2894
0
null
You would normally want at least 30 to invoke central limit theorem (though this is somewhat arbitrary). Unlike in the case with polls etc, which are modelled using the binomial distribution, you can not determine a sample size beforehand which guarantees a level of accuracy with a Gaussian process - it depends on what...
null
CC BY-SA 2.5
null
2010-09-20T15:19:18.547
2010-09-20T15:44:52.563
2010-09-20T15:44:52.563
229
229
null
2897
2
null
2893
10
null
Aside from special properties of a few numbers (e.g., 2), the only real reason to single out integer moments as opposed to fractional moments is convenience. Higher moments can be used to understand tail behavior. For example, a centered random variable $X$ with variance 1 has subgaussian tails (i.e. $\mathbb{P}(|X| >...
null
CC BY-SA 2.5
null
2010-09-20T15:22:46.340
2011-03-24T18:26:30.237
2011-03-24T18:26:30.237
89
89
null
2898
2
null
2894
2
null
You need to search for 'Bayesian adaptive designs'. The basic idea is as follows: - You initialize the prior for the parameters of interest. Before any data collection your priors would be diffuse. As additional data comes in you re-set the prior to be the posterior that corresponds to the 'prior + data till that poi...
null
CC BY-SA 2.5
null
2010-09-20T15:51:22.327
2010-09-20T15:51:22.327
null
null
null
null
2899
2
null
2893
10
null
I get suspicious when I hear people ask about third and fourth moments. There are two common errors people often have in mind when they bring up the topic. I'm not saying that you are necessarily making these mistakes, but they do come up often. First, it sounds like they implicitly believe that distributions can be b...
null
CC BY-SA 2.5
null
2010-09-20T15:54:47.243
2010-09-20T17:31:39.423
2010-09-20T17:31:39.423
319
319
null
2900
2
null
1805
9
null
[This page in MathWorld](http://mathworld.wolfram.com/FishersExactTest.html) explains how the calculations work. It points out that the test can be defined in a variety of ways: > To compute the P-value of the test, the tables must be ordered by some criterion that measures dependence, and those tables that rep...
null
CC BY-SA 2.5
null
2010-09-20T16:15:58.623
2010-09-20T16:49:00.773
2010-09-20T16:49:00.773
25
25
null
2901
2
null
2893
3
null
One example of use (interpretation is a better qualifier) of a higher moment: the fifth moment of a univariate distribution measures the asymmetry of its tails.
null
CC BY-SA 2.5
null
2010-09-20T16:42:10.380
2010-09-20T20:07:31.340
2010-09-20T20:07:31.340
603
603
null
2903
2
null
2730
7
null
Gelman has a good discussion paper on [ANOVA](http://projecteuclid.org/euclid.aos/1112967698) Analysis of variance—why it is more important than ever
null
CC BY-SA 2.5
null
2010-09-20T16:54:56.517
2010-09-20T16:54:56.517
null
null
603
null
2904
1
null
null
7
1091
I am attempting to estimate a model of the following form: ``` W = alphaH * H + alphaM * M + alphaL * L + X * beta ``` where `H, M, L` are indicators for a discrete choice variable, and `beta` is something like 35-dimensional. Because we believe our data/model has endogeneity issues, we have expanded the model to ``` ...
How can I work around "lumpiness" in simulated maximum likelihood estimation?
CC BY-SA 2.5
null
2010-09-20T17:45:15.683
2010-11-16T23:35:41.633
2010-11-16T23:35:41.633
159
53
[ "matlab", "stata", "maximum-likelihood", "optimization" ]
2905
2
null
2892
6
null
I tend to hear that usually 3 largest eigenvalues are the most important, while those close to zero are noise You can test for that. See the paper linked in [this](https://stats.stackexchange.com/questions/2860/pca-on-out-of-sample-data/2877#2877) post for more detail. Again if your dealing with financial times series ...
null
CC BY-SA 2.5
null
2010-09-20T18:49:08.317
2010-09-21T11:59:13.977
2017-04-13T12:44:46.433
-1
603
null
2906
1
2908
null
20
1181
Nassim Taleb, of [Black Swan](http://rads.stackoverflow.com/amzn/click/081297381X) fame (or infamy), has elaborated on the concept and developed what he calls ["a map of the limits of Statistics"](http://www.edge.org/3rd_culture/taleb08/taleb08_index.html). His basic argument is that there is one kind of decision probl...
What is the community's take on the Fourth Quadrant?
CC BY-SA 2.5
null
2010-09-20T18:57:24.617
2010-09-20T19:13:08.843
null
null
666
[ "distributions", "modeling", "random-variable" ]
2907
2
null
2686
1
null
I would start with robust time series [filters](http://cran.r-project.org/web/packages/robfilter/index.html) (i.e. time varying medians) because these are more simple and intuitive. Basically, the robust time filter is to time series smoothers what the median is to the mean; a summary measures (in this case a time vary...
null
CC BY-SA 2.5
null
2010-09-20T19:11:45.167
2010-09-22T12:44:41.213
2010-09-22T12:44:41.213
603
603
null
2908
2
null
2906
28
null
I was at a meeting of the ASA (American Statistical Association) a couple years ago where Taleb talked about his "fourth quadrant" and it seemed his remarks were well received. Taleb was much more careful in his language when addressing an auditorium of statisticians than he has been in his popular writing. Some sta...
null
CC BY-SA 2.5
null
2010-09-20T19:13:08.843
2010-09-20T19:13:08.843
null
null
319
null
2909
1
4033
null
9
1133
I am interested in the distribution of the maximum drawdown of a random walk: Let $X_0 = 0, X_{i+1} = X_i + Y_{i+1}$ where $Y_i \sim \mathcal{N}(\mu,1)$. The maximum drawdown after $n$ periods is $\max_{0 \le i \le j \le n} (X_i - X_j)$. A paper by [Magdon-Ismail et. al.](http://www.alumni.caltech.edu/~amir/drawdown-jr...
Computing the cumulative distribution of max drawdown of random walk with drift
CC BY-SA 2.5
null
2010-09-20T19:59:31.487
2018-08-27T16:10:00.043
2018-08-27T16:10:00.043
11887
795
[ "distributions", "cumulative-distribution-function", "finance", "random-walk" ]
2910
1
3191
null
92
23330
We often hear of project management and design patterns in computer science, but less frequently in statistical analysis. However, it seems that a decisive step toward designing an effective and durable statistical project is to keep things organized. I often advocate the use of R and a consistent organization of file...
How to efficiently manage a statistical analysis project?
CC BY-SA 2.5
null
2010-09-20T20:39:08.183
2018-06-09T04:04:28.840
2016-08-10T15:26:11.967
7290
930
[ "project-management" ]
2911
2
null
2910
21
null
This doesn't specifically provide an answer, but you may want to look at these related stackoverflow questions: - "Workflow for statistical analysis and report writing" - "Organizing R Source Code" - "How to organize large R programs?" - "R and version control for the solo data analyst" - "How does software devel...
null
CC BY-SA 2.5
null
2010-09-20T20:42:21.877
2010-09-25T10:59:17.233
2017-05-23T12:39:26.167
-1
5
null
2912
2
null
2892
4
null
One way I have studied this problem in the past is to construct the 'eigenportfolios' of the correlation matrix. That is, take the eigenvector associated with the $k$th largest eigenvalue of the correlation matrix and scale it to a gross leverage of 1 (i.e. make the absolute sum of the vector equal to one). Then see if...
null
CC BY-SA 2.5
null
2010-09-20T21:27:28.550
2010-09-20T21:27:28.550
null
null
795
null
2913
2
null
2860
2
null
What computational savings? The PCA computation is based on the covariance (or correlation) matrix, whose size depends on the number of variables, not the number of data points. The calculation of a covariance matrix is fast. Even if you were doing PCA repeatedly (as part of a simulation, for instance), reducing fro...
null
CC BY-SA 2.5
null
2010-09-20T21:29:31.903
2010-09-20T21:29:31.903
null
null
919
null
2914
1
2931
null
14
23534
When you are the one doing the work, being aware of what you are doing you develop a sense of when you have over-fit the model. For one thing, you can track the trend or deterioration in the Adjusted R Square of the model. You can also track a similar deterioration in the p values of the regression coefficients of th...
How to detect when a regression model is over-fit?
CC BY-SA 2.5
null
2010-09-20T21:35:58.207
2021-11-19T14:13:26.137
2017-08-15T21:41:44.853
12359
1329
[ "regression", "multivariate-analysis", "overfitting" ]
2915
1
2928
null
4
276
I am talking about the regression method that measures the impact of several layers of independent variables upon a dependent variable.
What is a good internet based source of information on Hierarchical Modeling?
CC BY-SA 2.5
null
2010-09-20T22:16:05.190
2010-09-21T11:24:20.990
2010-09-21T11:24:20.990
183
1329
[ "modeling", "regression", "multilevel-analysis" ]
2916
2
null
2892
14
null
Eigenvalues give magnitudes of principle components of data spread. [](https://i.stack.imgur.com/PznUT.png) (source: [yaroslavvb.com](http://yaroslavvb.com/upload/eigenvalues.png)) First dataset was generated from Gaussian with covariance matrix $\left(\matrix{3&0\\\\0&1}\right)$ second dataset is the first dataset ro...
null
CC BY-SA 4.0
null
2010-09-20T23:05:48.593
2019-02-17T00:32:01.113
2019-02-17T00:32:01.113
79696
511
null
2917
1
null
null
11
3365
## Background I am conducting a meta-analysis that includes previously published data. Often, differences between treatments are reported with P-values, least significant differences (LSD), and other statistics but provide no direct estimate of the variance. In the context of the model that I am using, an overestima...
Are these formulas for transforming P, LSD, MSD, HSD, CI, to SE as an exact or inflated/conservative estimate of $\hat{\sigma}$ correct?
CC BY-SA 2.5
null
2010-09-20T23:14:27.380
2011-03-17T02:47:49.370
2011-03-17T02:46:32.257
795
1381
[ "multiple-comparisons", "variance", "data-transformation", "meta-analysis" ]
2918
1
null
null
4
1669
Are Lorenz curves and QQ-plots the same? If not, where are the differences? I read about both of them and they appear to be two terms for the same type of plot / statistical technique to compare distributions. I was not able to find any confirmatory source for this. Perhaps you know?
Is Lorenz curve the same as QQ-plot?
CC BY-SA 3.0
null
2010-09-20T23:22:35.163
2014-11-20T01:17:39.007
2014-11-20T01:17:39.007
805
608
[ "data-visualization", "qq-plot", "lorenz-curve" ]
2919
2
null
2915
4
null
I warmly recommend Doug Bate's [book](http://lme4.r-forge.r-project.org/book/)
null
CC BY-SA 2.5
null
2010-09-20T23:37:22.590
2010-09-20T23:37:22.590
null
null
603
null
2920
2
null
2917
7
null
Your LSD equation looks fine. If you want to get back to variance and you have a summary statistic that says something about variability or significance of an effect then you can almost always get back to variance—-you just need to know the formula. For example, in your equation for LSD you want to solve for MSE, MSE...
null
CC BY-SA 2.5
null
2010-09-20T23:42:21.657
2010-09-20T23:42:21.657
null
null
601
null
2921
2
null
2915
7
null
[The Centre for Multilevel Modelling](http://www.cmm.bristol.ac.uk/learning-training/index.shtml) has free online tutorials for multi-level modeling, and they have software tutorials for fitting models in both their MLwiN software and STATA. You will probably want to check out all the questions with the [multilevel ana...
null
CC BY-SA 2.5
null
2010-09-20T23:52:04.230
2010-09-21T02:52:02.937
2017-04-13T12:44:33.310
-1
1036
null
2922
2
null
2904
2
null
Your likelihood function is non-concave (i.e. the Hessian matrix of your likelihood function is not SDN). From this it follows that - You will only find a local maximae to your likelihood function (no garantuee of global optimality) - This maxima will always depend on your choice of starting point. - Your maximizati...
null
CC BY-SA 2.5
null
2010-09-21T00:04:45.017
2010-09-22T22:33:24.393
2010-09-22T22:33:24.393
603
603
null
2924
2
null
2904
3
null
It sounds like you need to use a more robust optimization algorithm that can handle local minima. Particle swarm methods work quite well in this case. Or you could try other evolutionary optimization methods or simulated annealing.
null
CC BY-SA 2.5
null
2010-09-21T00:42:04.910
2010-09-21T00:42:04.910
null
null
159
null
2925
1
2963
null
6
791
Suppose that we want to generate a draw from the following distribution: $P(X=0) = 0.5$ $P(X=1) = 0.5$ There are two constraints though: (a) The draw has to be on the basis of an external event. (b) Related to (a), the draw must be verifiable by a third party. In other words, a third party should be able to verify that...
Is there a verifiable way to generate discrete random variables on the basis of an external event?
CC BY-SA 2.5
null
2010-09-21T00:47:15.803
2020-06-29T21:36:10.710
null
null
null
[ "random-variable" ]
2926
2
null
305
4
null
Two reasons I can think of: - Regular Student's T is pretty robust to heteroscedasticity if the sample sizes are equal. - If you believe strongly a priori that the data is homoscedastic, then you lose nothing and might gain a small amount of power by using Studen'ts T instead of Welch's T. One reason that I would...
null
CC BY-SA 2.5
null
2010-09-21T01:36:24.877
2010-09-21T01:36:24.877
null
null
1347
null
2927
2
null
2914
7
null
When I'm fitting a model myself I generally use information criteria during the fitting process, such as [AIC](http://en.wikipedia.org/wiki/Akaike_information_criterion) or [BIC](http://en.wikipedia.org/wiki/Bayesian_information_criterion), or alternatively [Likelihood-ratio tests](http://en.wikipedia.org/wiki/Likeliho...
null
CC BY-SA 2.5
null
2010-09-21T02:14:36.227
2010-09-21T02:14:36.227
null
null
521
null
2928
2
null
2915
6
null
UCLA has some good resources: - Papers on multilevel modelling - Textbook examples (see multilevel modelling) - A free textbook on multilevel modelling by Harvey Goldstein - and more...
null
CC BY-SA 2.5
null
2010-09-21T02:25:20.493
2010-09-21T02:25:20.493
null
null
183
null
2929
2
null
2918
11
null
The Lorenz curve is just a cumulative distribution function for a random variable bounded between 0 and 1, e.g., a proportion. In economics, the Lorenz curve asks, "what fraction of income is earned by the lowest x% of earners?" Typically, it is compared to the uniform distribution over [0,1], a distribution that would...
null
CC BY-SA 2.5
null
2010-09-21T02:46:15.140
2010-09-21T02:46:15.140
null
null
401
null
2930
2
null
2910
4
null
[van Belle](http://rads.stackoverflow.com/amzn/click/0470144483) is the source for the rules of successful statistical projects.
null
CC BY-SA 2.5
null
2010-09-21T03:00:47.613
2010-09-21T03:00:47.613
null
null
666
null
2931
2
null
2914
17
null
Cross validation is a fairly common way to detect overfitting, while regularization is a technique to prevent it. For a quick take, I'd recommend Andrew Moore's tutorial slides on the use of [cross-validation](https://www.cs.cmu.edu/%7E./awm/tutorials/overfit.html) ([mirror](https://web.archive.org/web/20170815214245/...
null
CC BY-SA 4.0
null
2010-09-21T03:32:23.540
2021-11-19T14:13:26.137
2021-11-19T14:13:26.137
322742
251
null
2932
1
null
null
6
765
Does the use of metric spaces to describe the support of a random variable provide any greater illumination? I ask this after reading about how metrics spaces have been used to unify the mathematical measure theoretic nature of probability and the physical intuition that most associate with probability. You can read my...
Metric spaces and the support of a random variable
CC BY-SA 2.5
null
2010-09-21T03:38:50.050
2012-01-08T17:18:07.957
2010-09-24T14:00:05.347
930
null
[ "random-variable" ]
2934
1
null
null
4
852
I have distributional data which I represent as a density. The data represents frequencies of user activities on a computer screen (e.g. amount of clicks on the y or x-axis of that screen but also other activities that can be related to coordinates and can therefore be binned by those coordinates (e.g. 5 pixels bins))....
Using Lorenz curve / Gini coefficient for (non-ecomoical) distribution data
CC BY-SA 2.5
null
2010-09-21T04:08:56.927
2010-09-21T04:57:20.413
null
null
608
[ "distributions" ]
2935
2
null
1735
5
null
Here is my suggestion. Rerun your model(s) using one single regression. And, the Summer/Winter variable would be simply a single dummy variable (1,0). This way you would have a coefficient for Summer to differentiate it from Winter. And, the regression coefficients for your three other variables would be consistent...
null
CC BY-SA 2.5
null
2010-09-21T04:29:35.863
2010-09-21T04:29:35.863
null
null
1329
null
2936
2
null
2925
3
null
This reminds me of a question from Algorithms class a long time ago. Let the external event be a (preferrably continuous) random variable $Y$. To generate a value of $X$, take two independent observations of $Y$ and let $X$ be $1$ if the first observation of $Y$ is greater than the second, let it be $0$ if the second i...
null
CC BY-SA 2.5
null
2010-09-21T04:48:37.157
2010-09-21T16:21:35.873
2010-09-21T16:21:35.873
795
795
null
2937
2
null
2934
2
null
You can use a [2-sample Kolmogorov-Smirnov test](http://en.wikipedia.org/wiki/Kolmogorov_Smirnov_Test#Two-sample_Kolmogorov.E2.80.93Smirnov_test) to compare the two distributions. Other tests for comparing 2-samples are the Anderson-Darling test (although the 2-sample form of this is less frequently used), and the Baum...
null
CC BY-SA 2.5
null
2010-09-21T04:57:20.413
2010-09-21T04:57:20.413
null
null
795
null
2938
1
null
null
12
2568
The qq-plot can be used to visualize how similar two distributions are (e.g. visualizing the similarity of a distribution to a normal distribution, but also to compare two artibrary data distributions). Are there any statistics that generate a more objective, numerical measure that represent their similarity (preferabl...
Quantifying QQ plot
CC BY-SA 3.0
null
2010-09-21T05:15:16.743
2017-04-13T01:52:10.793
2014-11-20T09:49:31.713
22047
608
[ "distributions", "qq-plot" ]
2939
2
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As I say in response to your comment on your previous question, check out the Kolmogorov-Smirnov test. It uses the maximum absolute distance between two cumulative distribution functions (alternatively conceived as the maximum absolute distance of the curve in the QQ plot from the 45-degree line) as a statistic. The KS...
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CC BY-SA 2.5
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2010-09-21T05:35:11.600
2010-09-21T05:35:11.600
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