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Tags
list
6243
1
null
null
2
322
When computing the difference between means I can resolve a new mean, variance, standard error of the mean, and margin of error, but is there a way to compute a new/composite sample size value? I ask because I use the difference between means as a way to calibrate the mean and later when comparing other calibrated mean...
Computing the difference between means and resolving a new/composite sample size
CC BY-SA 4.0
null
2011-01-14T08:09:04.757
2023-03-03T10:40:58.100
2023-03-03T10:39:58.870
362671
2634
[ "sample-size", "mean" ]
6244
2
null
6239
8
null
Also useful, if you are combining multiple time series and don't want to have to have to `window` every one to get them to match, `ts.union` and `ts.intersect`.
null
CC BY-SA 2.5
null
2011-01-14T09:35:20.220
2011-01-14T09:35:20.220
null
null
1195
null
6245
1
null
null
4
273
In a field experiment involving crops, what is the difference in considering block as random or otherwise as fixed factor? As far as I understood, random means that conclusion can be extended to other levels not included in the study; fixed factor on the contrary restricts the analysis only to a specific experiment.
How can I treat blocks in a split plot design?
CC BY-SA 2.5
null
2011-01-14T10:56:04.463
2011-01-14T19:32:48.250
2011-01-14T19:32:48.250
449
2779
[ "anova", "mixed-model", "random-variable", "experiment-design", "split-plot" ]
6246
2
null
1455
3
null
Generally, with a large sample size it is assumed as reasonable approximation that all estimators (or some opportune functions of them) have a normal distribution. So, if you only need the p-value corresponding to the given confidence interval, you can simply proceed as follows: - transform $OR$ and the corresponding...
null
CC BY-SA 3.0
null
2011-01-14T12:10:06.210
2012-10-18T17:42:31.303
2012-10-18T17:42:31.303
7290
1219
null
6247
1
6251
null
3
2469
I have a problem. I am creating a wide barplot (50x grouped 4 columns) and printing it to ps. However the figure does not fit to printed ps - the x axis goes out of a page. It would fit if only I could remove a large left margin on yaxis. But I have no idea how to move picture left and reduce the margin. I have spend s...
Postscript in R: How to remove a large left margin (on y axis)
CC BY-SA 2.5
null
2011-01-14T13:47:37.963
2011-01-14T15:39:25.757
2011-01-14T15:39:25.757
1389
1389
[ "r", "data-visualization", "barplot" ]
6248
2
null
6247
2
null
Excerpt from the help page of function par: `mar`: A numerical vector of the form `c(bottom, left, top, right)` which gives the number of lines of margin to be specified on the four sides of the plot. The default is `c(5, 4, 4, 2) + 0.1`. So try something like ``` par(mar=c(5,1,4,2)) ``` ...
null
CC BY-SA 2.5
null
2011-01-14T13:52:32.007
2011-01-14T13:52:32.007
null
null
2116
null
6249
2
null
6247
2
null
You could look after the par() function's mar(gin) paramater. A nice brief can be found in [efg's Research Notes](http://research.stowers-institute.org/efg/R/Graphics/Basics/mar-oma/index.htm).
null
CC BY-SA 2.5
null
2011-01-14T13:53:55.810
2011-01-14T13:53:55.810
null
null
2714
null
6251
2
null
6247
4
null
I quite like the suggestion made by [Andrew Gelman](http://www.stat.columbia.edu/~cook/movabletype/archives/2010/10/could_someone_p.html) for the default setting of `par`. Namely, ``` par(mar=c(3,3,2,1), mgp=c(2,.7,0), tck=-.01) ```
null
CC BY-SA 2.5
null
2011-01-14T13:59:06.693
2011-01-14T13:59:06.693
null
null
8
null
6252
1
null
null
26
33963
I have a clustering algorithm (not k-means) with input parameter $k$ (number of clusters). After performing clustering I'd like to get some quantitative measure of quality of this clustering. The clustering algorithm has one important property. For $k=2$ if I feed $N$ data points without any significant distinction am...
Clustering quality measure
CC BY-SA 2.5
null
2011-01-14T14:06:06.030
2022-05-12T13:08:10.357
2011-01-14T19:33:53.787
255
255
[ "clustering" ]
6253
1
null
null
5
360
You are in an exam, and are presented with the following question: > Write down what mark do you expect to take in this exam... If you get it right in range of +/-10 % then you will take 10% bonus... if wrong (or not answered) you will lose 5% Assume that you have no idea of how you are going to perform in t...
Increasing Exam Expected Mark
CC BY-SA 2.5
null
2011-01-14T15:02:59.787
2011-01-15T21:41:48.193
2011-01-14T15:24:06.853
8
2599
[ "probability", "expected-value" ]
6254
1
null
null
7
1158
I have a very unbalanced sample set, e.g. 99% true and 1% false. Is it reasonable to select a balanced subset with a 50/50-distribution for neural network training? The reason for this is, that I guess training on the original data set may induce a bias on the true-samples. Can you suggest me some literature that cove...
Balanced sampling for network training?
CC BY-SA 3.0
null
2011-01-14T15:13:26.037
2018-01-09T08:52:39.037
2018-01-09T08:52:39.037
128677
null
[ "neural-networks", "sampling", "references" ]
6255
2
null
6253
7
null
First a couple of assumptions: 1. All marks are equally likely. 1. If you guess your mark to be 95 and you get 95, your return mark is 100 not 105. 1. Similarly, if your exam mark is 1 and you guess 50 (say), then your return mark is 0 not -4. 1. I'm only considering discrete marks, that is, values 0, ..., 100. S...
null
CC BY-SA 2.5
null
2011-01-14T15:17:31.510
2011-01-15T21:41:48.193
2011-01-15T21:41:48.193
8
8
null
6256
2
null
6254
7
null
Yes, it is reasonable to select a balanced dataset, however if you do your model will probably over-predict the minority class in operation (or on the test set). This is easily overcome by using a threshold probability that is not 0.5. The best way to choose the new threshold is to optimise on a validation sample tha...
null
CC BY-SA 2.5
null
2011-01-14T15:41:24.823
2011-01-14T15:41:24.823
null
null
887
null
6257
2
null
6252
5
null
Since clustering is unsupervised, it's hard to know a priori what the best clustering is. This is research topic. Gary King, a well-known quantitative social scientist, has a [forthcoming article](http://gking.harvard.edu/publications/general-purpose-computer-assisted-clustering-methodology) on this topic.
null
CC BY-SA 2.5
null
2011-01-14T16:47:59.270
2011-01-14T16:47:59.270
null
null
null
null
6258
2
null
6245
3
null
The way you are thinking is one of the ways most people interpret blocks. But the bigger picture which sometimes people don't notice is: Blocks are a way to model a correlation structure. They let us "eliminate" or control for factors which we know influence the outcomes but are not really of interest. However, your co...
null
CC BY-SA 2.5
null
2011-01-14T17:22:49.567
2011-01-14T17:30:57.563
2011-01-14T17:30:57.563
1307
1307
null
6260
2
null
6253
6
null
I'm not sure if this would be a funny game or your professor is mildly sadistic. It would be torturous for students who are right on the edge of passing (which we may expect them to be the worst guessers!) Sorry not an answer but I couldn't help myself. ![alt text](https://i.stack.imgur.com/MuDBB.jpg)
null
CC BY-SA 2.5
null
2011-01-14T18:37:22.030
2011-01-14T18:37:22.030
null
null
1036
null
6261
2
null
6232
2
null
Sounds like a mixed effects ANOVA. If you have a continuous treatment variable (i.e., harvesting intensity), then an ANCOVA is warranted (or, really, just a mixed effects/hierarchical general linear model) (or generalized linear model if your response variable better fits that framework).
null
CC BY-SA 2.5
null
2011-01-14T19:57:45.567
2011-01-14T19:57:45.567
null
null
101
null
6262
2
null
6074
10
null
This game looks similar to 20 questions at [http://20q.net](http://20q.net), which the creator reports is based on a neural network. Here's one way to structure such network, similar to the neural network described in [Concept description vectors and the 20 question game](http://citeseerx.ist.psu.edu/viewdoc/summary?d...
null
CC BY-SA 2.5
null
2011-01-14T21:57:51.143
2011-01-15T19:41:21.880
2011-01-15T19:41:21.880
511
511
null
6265
1
null
null
3
2861
I would like some help with the following problem. I have 40 subjects. On each subject I take a measurement at 25 body sites. The measurement is a continuous variable that varies between 0 and 1 and appears to be normally distributed. I want do a test to see if body site statistically significantly affects the measur...
Consequence of violating independence assumption of ANOVA
CC BY-SA 2.5
null
2011-01-15T00:02:52.923
2011-01-16T10:24:07.540
2011-01-15T07:57:33.163
449
2788
[ "anova", "repeated-measures", "missing-data", "manova" ]
6266
2
null
6253
2
null
Use the bootstrap! Take lots of practice exams and estimate what your score will be on the real exam. If it does not improve your estimate, it will probably be good preparation!
null
CC BY-SA 2.5
null
2011-01-15T03:50:50.530
2011-01-15T03:50:50.530
null
null
795
null
6267
2
null
6252
5
null
Here you have a couple of measures, but there are many more: SSE: sum of the square error from the items of each cluster. Inter cluster distance: sum of the square distance between each cluster centroid. Intra cluster distance for each cluster: sum of the square distance from the items of each cluster to its centroid. ...
null
CC BY-SA 2.5
null
2011-01-15T04:15:14.430
2011-01-15T04:15:14.430
null
null
1808
null
6268
1
6398
null
11
810
I'm searching how to (visually) explain simple linear correlation to first year students. The classical way to visualize would be to give an Y~X scatter plot with a straight regression line. Recently, I came by the idea of extending this type of graphics by adding to the plot 3 more images, leaving me with: the scatter...
How to present the gain in explained variance thanks to the correlation of Y and X?
CC BY-SA 3.0
null
2011-01-15T06:36:34.710
2016-04-07T10:50:34.987
2016-04-07T10:50:34.987
2910
253
[ "r", "data-visualization", "regression", "correlation" ]
6269
2
null
6268
1
null
Not answering to your exact question, but the followings could be interesting by visualizing one possible pitfall of linear correlations based on an [answer](https://stackoverflow.com/questions/4666590/remove-outliers-from-correlation-coefficient-calculation/4668720#4668720) from [stackoveflow](https://stackoverflow.co...
null
CC BY-SA 2.5
null
2011-01-15T09:00:39.090
2011-01-15T09:00:39.090
2017-05-23T12:39:26.203
-1
2714
null
6270
2
null
6252
17
null
The choice of metric rather depends on what you consider the purpose of clustering to be. Personally I think clustering ought to be about identifying different groups of observations that were each generated by a different data generating process. So I would test the quality of a clustering by generating data from kn...
null
CC BY-SA 2.5
null
2011-01-15T10:16:53.073
2011-01-15T10:16:53.073
null
null
887
null
6271
2
null
2691
9
null
Why so eigenvalues/eigenvectors ? When doing PCA, you want to compute some orthogonal basis by maximizing the projected variance on each basis vector. Having computed previous basis vectors, you want the next one to be: - orthogonal to the previous - norm 1 - maximizing projected variance, i.e with maximal covarianc...
null
CC BY-SA 2.5
null
2011-01-15T12:25:12.660
2011-01-15T12:31:57.020
2011-01-15T12:31:57.020
null
null
null
6273
2
null
6243
1
null
I just think you are making it just too complex -- it is a JS benchmark for other programmers, not a clinical trial or Higgs boson search that will be peer reviewed by bloodthirsty referees and later have a great impact. Just make a non-small number of repetitions (30), of both test and empty test, subtract the means, ...
null
CC BY-SA 4.0
null
2011-01-15T13:46:04.417
2023-03-03T10:40:58.100
2023-03-03T10:40:58.100
362671
null
null
6274
2
null
6243
1
null
How are you comparing the calibrated means? If you're looking at differences between them, and testing if that's zero using a $t$-test, then surely the mean of the empty loop ($\bar{x}_0$, say) will simply cancel out: $$(\bar{x}_1 - \bar{x}_0) - (\bar{x}_2 - \bar{x}_0) = \bar{x}_1 - \bar{x}_2$$
null
CC BY-SA 2.5
null
2011-01-15T13:58:40.187
2011-01-15T13:58:40.187
null
null
449
null
6275
1
6278
null
17
4962
I am currently collecting data for an experiment into psychosocial characteristics associated with the experience of pain. As part of this, I am collecting GSR and BP measurements electronically from my participants, along with various self-report and implicit measures. I have a psychological background and am comforta...
Good introductions to time series (with R)
CC BY-SA 3.0
null
2011-01-15T14:01:55.437
2018-05-04T12:11:19.117
2018-05-04T12:11:19.117
53690
656
[ "r", "time-series", "references" ]
6276
2
null
6275
6
null
[Time Series Analysis and Its Applications: With R Examples](http://www.stat.pitt.edu/stoffer/tsa3/) by Robert H. Shumway and David S. Stoffer would be a great resource for the subject, but you may find a lot of useful blog entries (e.g. my favorite one: [learnr](http://learnr.wordpress.com/)) and tutorials (e.g. [from...
null
CC BY-SA 2.5
null
2011-01-15T14:14:37.693
2011-01-15T14:20:01.030
2011-01-15T14:20:01.030
2714
2714
null
6277
2
null
6268
1
null
I'd have two two-panel plots, both have the xy plot on the left, and a histogram on the right. In the first plot, a horizontal line is placed at the mean of y and lines extend from this to each point, representing the residuals of y values from the mean. The histogram with this simply plots these residuals. Then in the...
null
CC BY-SA 2.5
null
2011-01-15T14:27:25.763
2011-01-15T14:27:25.763
null
null
364
null
6278
2
null
6275
25
null
This is a very large subject and there are many good books that cover it. These are both good, but Cryer is my favorite of the two: - Cryer. "Time Series Analysis: With Applications in R" is a classic on the subject, updated to include R code. - Shumway and Stoffer. "Time Series Analysis and Its Applications: With R...
null
CC BY-SA 2.5
null
2011-01-15T14:46:59.737
2011-01-15T14:46:59.737
null
null
5
null
6279
1
null
null
2
4859
I am a very beginner of statistic. Recently a project require me to analyse data using logistic regression & SPSS within a specific time frame. Although I have read few books, but still very blur on how to start off. Can someone guide me through? What is the 1st ste and what next? Anyway, I have started some. Once ente...
Steps of data analysis using logistic regression
CC BY-SA 2.5
null
2011-01-15T14:48:52.947
2011-01-16T04:48:53.307
null
null
2793
[ "logistic" ]
6280
2
null
6180
4
null
You ask how to 'formally and usefully' present your conclusions Formally: Your answer is an accurate summary of some of the results from Brown et al. as I understand them. (I note you do not offer their preferred small n method). Usefully: I wonder who you audience is. For professional statisticians, you could state ...
null
CC BY-SA 2.5
null
2011-01-15T15:02:55.903
2011-01-15T15:02:55.903
null
null
1739
null
6281
1
6284
null
6
19662
I'm working through a practice problem for my Stats homework. We're using Confidence Intervals to find a range that the true mean lies within. I'm having trouble understanding how to find the required sample size to estimate the true mean within something like +- 0.5%. I understand how to work the problem when the rang...
How to use Confidence Intervals to find the true mean within a percentage
CC BY-SA 2.5
null
2011-01-15T15:03:39.233
2015-09-24T12:12:15.880
2011-01-15T18:10:18.550
2129
2794
[ "confidence-interval", "self-study" ]
6284
2
null
6281
6
null
I am not sure what kind of variable is being audited, so I give 2 alternatives: - To be able to compute the required sample size to give an acceptable estimate to a continuous variable (= given confidence interval) you have to know a few parameters: mean, standard deviation (and to be precise: population size). If you...
null
CC BY-SA 3.0
null
2011-01-15T18:37:14.230
2015-09-24T12:12:15.880
2015-09-24T12:12:15.880
22228
2714
null
6285
2
null
6243
0
null
Thanks @mbq and @onestop. After running some tests the calibration was a wash. Subtracting the means raised the margin or error to the point that the calibrated and none calibrated test results where indeterminately different. @mbq I will take your advice and reduce the critical value lookup to 30 (as infinity). When c...
null
CC BY-SA 2.5
null
2011-01-15T20:28:57.713
2011-01-15T20:28:57.713
null
null
2634
null
6286
2
null
6265
1
null
You should consider using mixed-effect / multi-level models. The techniques used to fit these models work fine with unbalanced design, which is how it will interpret your missing data. As long as the data is missing at random, this is a reasonable way to proceed. SPSS is able to fit linear mixed-effect models. Mixed-ef...
null
CC BY-SA 2.5
null
2011-01-15T21:30:57.260
2011-01-15T21:30:57.260
null
null
2739
null
6287
1
6289
null
6
838
I'm fooling around with threshold time series models. While I was digging through what others have done, I ran across the CDC's site for flu data. [http://www.cdc.gov/flu/weekly/](http://www.cdc.gov/flu/weekly/) About 1/3 of the way down the page is a graph titled "Pneumonia and Influenza Mortality....". It shows the...
Threshold models and flu epidemic recognition
CC BY-SA 2.5
null
2011-01-15T23:09:06.293
2022-05-30T12:30:56.767
2011-01-16T12:23:18.243
null
2775
[ "r", "time-series", "epidemiology", "threshold" ]
6288
2
null
6279
1
null
Generally large beta coefficients signal multi-collinearity. You should look for marginals that are zero in your cross-tabulations. You should also pay attention to mpiktas's comment. Testing for linearity (and transforming to categorical) is not generally needed if you have been setting up your data correctly.
null
CC BY-SA 2.5
null
2011-01-15T23:48:40.987
2011-01-15T23:48:40.987
null
null
2129
null
6289
2
null
6287
6
null
The CDC uses the epidemic threshold of > 1.645 standard deviations above the baseline for that time of year. The definition may have multiple sorts of detection or mortality endpoints. (The one you are pointing to is pneumonia and influenza mortality. The lower black curve is not really a series, but rather a model...
null
CC BY-SA 4.0
null
2011-01-16T01:18:19.567
2019-02-02T02:23:34.853
2019-02-02T02:23:34.853
11887
2129
null
6290
2
null
6268
1
null
I think what you propose is good, but I would do it in three different examples 1) X and Y are completely unrelated. Simply remove "x" from the r code that generates y (y1<-rnorm(50)) 2) The example you posted (y2 <- x+rnorm(50)) 3) The X are Y are the same variable. Simply remove "rnorm(50)" from the r code that gen...
null
CC BY-SA 2.5
null
2011-01-16T04:00:33.937
2011-01-16T04:00:33.937
null
null
2392
null
6291
2
null
6279
1
null
The large value of "B" would be a coefficient of a variable usually called "X" in your model. Usually, "X" has a real world meaning (could be income, could be a measured volume of something, etc.). So the job is to interpret this "B" in terms of "X". The usual definition (in ordinary least squares) is that a ONE UNI...
null
CC BY-SA 2.5
null
2011-01-16T04:48:53.307
2011-01-16T04:48:53.307
null
null
2392
null
6292
2
null
6265
3
null
Billy, From the comment about the data being rejected if the light is below a certain intensity, does this correspond to why you have missing records? Because if you do, then you do not have total "missingness", but rather "censoring" because you know that the response is below a certain threshold. This does have an i...
null
CC BY-SA 2.5
null
2011-01-16T10:24:07.540
2011-01-16T10:24:07.540
null
null
2392
null
6293
2
null
6281
2
null
It does seem a bit odd for this problem, because there does not appear to be a pivotal statistic or if there is, it isn't the usual Z or T statistic. Here's why I think this is the case. The problem of estimating the population mean, say $\mu$, to within $\pm $ 0.5% obviously depends on the value of $\mu$ (a pivotal st...
null
CC BY-SA 2.5
null
2011-01-16T11:31:53.067
2011-01-18T10:51:39.927
2011-01-18T10:51:39.927
2392
2392
null
6294
1
6295
null
6
3316
What analyses can be used to find an interaction effect in a 2-factor design, with one ordinal and one categorical factor, with binary-valued data? Specifically, are there any types of analyses that are capable of dealing with a 2 factor design 5(ordinal) x 2(categorical), where the outcomes are either true or false? O...
Interaction between ordinal and categorical factor
CC BY-SA 2.5
null
2011-01-16T11:51:10.763
2011-01-16T13:54:38.253
2011-01-16T12:26:17.087
null
2800
[ "interaction" ]
6295
2
null
6294
3
null
I'd stick with logistic or probit regression, enter both factors as covariates, but enter the ordinal factor as if it was continuous. To test for interaction, do a [likelihood-ratio test](http://en.wikipedia.org/wiki/Likelihood-ratio_test) comparing models with and without an interaction between the two factors. This t...
null
CC BY-SA 2.5
null
2011-01-16T12:43:29.283
2011-01-16T12:43:29.283
null
null
449
null
6297
2
null
2715
18
null
Always ask yourself "what do these results mean and how will they be used?" Usually the purpose of using statistics is to assist in making decisions under uncertainty. So it is important to have at the front of your mind "What decisions will be made as a result of this analysis and how will this analysis influence the...
null
CC BY-SA 2.5
null
2011-01-16T13:48:53.937
2011-01-16T13:48:53.937
null
null
2392
null
6298
1
10760
null
28
5942
[Google Prediction API](https://cloud.google.com/prediction/docs) is a cloud service where user can submit some training data to train some mysterious classifier and later ask it to classify incoming data, for instance to implement spam filters or predict user preferences. But what is behind the scenes?
What is behind Google Prediction API?
CC BY-SA 3.0
null
2011-01-16T14:01:00.537
2016-01-25T14:09:42.297
2016-01-25T14:09:42.297
null
null
[ "machine-learning" ]
6299
2
null
5903
3
null
Given that simple linear regression is analytically identical between classical and Bayesian analysis with Jeffrey's prior, both of which are analytic, it seems a bit odd to resort to a numerical method such as MCMC to do the Bayesian analysis. MCMC is just a numerical integration tool, which allows Bayesian methods t...
null
CC BY-SA 2.5
null
2011-01-16T14:47:21.463
2011-01-16T14:52:45.937
2011-01-16T14:52:45.937
2392
2392
null
6300
2
null
6225
5
null
For me, the decision theoretical framework presents the easiest way to understand the "null hypothesis". It basically says that there must be at least two alternatives: the Null hypothesis, and at least one alternative. Then the "decision problem" is to accept one of the alternatives, and reject the others (although ...
null
CC BY-SA 2.5
null
2011-01-16T15:35:37.147
2011-01-16T15:35:37.147
null
null
2392
null
6301
2
null
4663
41
null
When used in stage-wise mode, the LARS algorithm is a greedy method that does not yield a provably consistent estimator (in other words, it does not converge to a stable result when you increase the number of samples). Conversely, the LASSO (and thus the LARS algorithm when used in LASSO mode) solves a convex data fit...
null
CC BY-SA 3.0
null
2011-01-16T17:42:01.520
2012-11-06T18:12:52.440
2012-11-06T18:12:52.440
16049
1265
null
6302
1
6303
null
8
4407
NOTE: I purposely did not label the axis due to pending publications. The line colors represent the same data in all three plots. I fitted my data using a negative binomial distribution to generate a pdf. I am happy with the pdf and meets my research needs. PDF plot: ![alt text](https://i.stack.imgur.com/ttDnS.png) --...
Use Empirical CDF vs Distribution CDF?
CC BY-SA 2.5
null
2011-01-16T20:56:43.303
2011-01-18T12:42:18.770
2011-01-16T23:09:09.193
449
559
[ "distributions", "data-visualization", "density-function", "cumulative-distribution-function" ]
6303
2
null
6302
5
null
Personally, I'd favour instead showing the fit of the theoretical to the empirical distribution using a set of [P-P plots](http://en.wikipedia.org/wiki/P-P_plot) or [Q-Q plots](http://en.wikipedia.org/wiki/Q-Q_plot).
null
CC BY-SA 2.5
null
2011-01-16T23:07:41.130
2011-01-17T11:19:01.070
2011-01-17T11:19:01.070
449
449
null
6304
1
6307
null
22
5530
Let $t_i$ be drawn i.i.d from a Student t distribution with $n$ degrees of freedom, for moderately sized $n$ (say less than 100). Define $$T = \sum_{1\le i \le k} t_i^2$$ Is $T$ distributed nearly as a chi-square with $k$ degrees of freedom? Is there something like the Central Limit Theorem for the sum of squared rando...
What is the sum of squared t variates?
CC BY-SA 2.5
null
2011-01-17T03:34:38.283
2021-02-07T03:23:59.257
2021-02-07T03:23:59.257
11887
795
[ "central-limit-theorem", "t-distribution", "chi-squared-distribution", "sums-of-squares" ]
6305
2
null
6304
8
null
I'll answer second question. The central limit theorem is for any iid sequence, squared or not squared. So in your case if $k$ is sufficiently large we have $\dfrac{T-kE(t_1)^2}{\sqrt{kVar(t_1^2)}}\sim N(0,1)$ where $Et_1^2$ and $Var(t_1^2)$ is respectively the mean and variance of squared Student t distribution with $...
null
CC BY-SA 2.5
null
2011-01-17T04:07:32.863
2011-01-17T04:07:32.863
null
null
2116
null
6306
1
null
null
41
1112
Although this question is somewhat subjective, I hope it qualifies as a good subjective question according to the [faq guidelines](http://blog.stackoverflow.com/2010/09/good-subjective-bad-subjective/). It is based on a question that Olle Häggström asked me a year ago and although I have some thoughts about it I do not...
Are there statistical lessons from the "Bible Code" episode
CC BY-SA 2.5
null
2011-01-17T09:18:09.130
2022-04-16T00:02:12.807
2020-06-11T14:32:37.003
-1
1148
[ "hypothesis-testing", "data-mining" ]
6307
2
null
6304
15
null
Answering the first question. We could start from the fact noted by mpiktas, that $t^2 \sim F(1, n)$. And then try a more simple step at first - search for the distribution of a sum of two random variables distributed by $F(1,n)$. This could be done either by calculating the convolution of two random variables, or calc...
null
CC BY-SA 2.5
null
2011-01-17T10:44:06.310
2011-01-17T10:44:06.310
null
null
2645
null
6308
1
6310
null
20
2690
I am referring to this article: [http://www.nytimes.com/2011/01/11/science/11esp.html](http://www.nytimes.com/2011/01/11/science/11esp.html) > Consider the following experiment. Suppose there was reason to believe that a coin was slightly weighted toward heads. In a test, the coin comes up heads 527 times out of 1,000...
Article about misuse of statistical method in NYTimes
CC BY-SA 2.5
null
2011-01-17T11:11:10.560
2016-09-15T00:28:09.350
2016-09-15T00:28:09.350
28666
230
[ "hypothesis-testing", "bayesian", "statistics-in-media" ]
6309
1
6311
null
12
10028
I was reading through a paper and I saw a table with a comparison between PPV (Positive Predictive Value) and NPV (Negative Predictive Value). They did some kind of statistical test for them, this is a sketch of the table: ``` PPV NPV p-value 65.9 100 < 0.00001 ... ``` Every rows refers to a particular cont...
Statistical test for positive and negative predictive value
CC BY-SA 3.0
null
2011-01-17T11:25:59.540
2012-08-26T22:55:52.843
2012-08-26T22:55:52.843
null
2719
[ "epidemiology", "contingency-tables", "p-value" ]
6310
2
null
6308
31
null
I will answer the first question in detail. > With a fair coin, the chances of getting 527 or more heads in 1,000 flips is less than 1 in 20, or 5 percent, the conventional cutoff. For a fair coin the number of heads in 1000 trials follows the [binomial distribution](http://en.wikipedia.org/wiki/Binomial_distr...
null
CC BY-SA 2.5
null
2011-01-17T13:22:38.390
2011-01-17T19:48:13.903
2011-01-17T19:48:13.903
2116
2116
null
6311
2
null
6309
17
null
Assuming a cross-classification like the one shown below (here, for a screening instrument) ![alt text](https://i.stack.imgur.com/HCmDE.png) we can define four measures of screening accuracy and predictive power: - Sensitivity (se), a/(a + c), i.e. the probability of the screen providing a positive result given that d...
null
CC BY-SA 2.5
null
2011-01-17T13:57:31.230
2011-01-17T14:10:13.687
2011-01-17T14:10:13.687
930
930
null
6312
1
null
null
14
1335
A signal detection experiment typically presents the observer (or diagnostic system) with either a signal or a non-signal, and the observer is asked to report whether they think the presented item is a signal or non-signal. Such experiments yield data that fill a 2x2 matrix: ![alt text](https://i.stack.imgur.com/JktFQ....
Is it valid to analyze signal detection data without employing metrics derived from signal detection theory?
CC BY-SA 2.5
null
2011-01-17T14:15:04.320
2014-06-01T02:11:56.710
null
null
364
[ "diagnostic", "signal-detection" ]
6314
1
10976
null
23
2050
In 1999, Beyer et al. asked, [When is "Nearest Neighbor" meaningful?](http://www.cis.temple.edu/~vasilis/Courses/CIS750/Papers/beyer99when_17.pdf) Are there better ways of analyzing and visualizing the effect of distance flatness on NN search since 1999? > Does [a given] data set provide meaningful answers to the 1-NN...
When is "Nearest Neighbor" meaningful, today?
CC BY-SA 2.5
null
2011-01-17T15:12:50.590
2011-05-19T18:10:44.623
2011-01-24T17:13:36.567
557
557
[ "machine-learning", "k-nearest-neighbour" ]
6315
2
null
6312
3
null
The Positive Predictive Influence (PPV) is not a good measure, not only because it confounds both mechanisms (discriminability and response bias), but also because of item base-rates. It is preferable to use the posterior probabilities, like P(signal|"yes"), which account for item base-rates: $P(signal|yes) = \frac{P(s...
null
CC BY-SA 2.5
null
2011-01-17T15:24:33.570
2011-01-17T15:38:40.497
2011-01-17T15:38:40.497
447
447
null
6316
2
null
256
7
null
Boosting employs shrinkage through the learning rate parameter, which, coupled with k-fold cross validation, "out-of-bag" (OOB) predictions or independent test set, determine the number of trees one should keep in the ensemble. We want a model that learns slowly, hence there is a trade-off in terms of the complexity of...
null
CC BY-SA 3.0
null
2011-01-17T15:36:54.080
2015-08-25T12:17:32.040
2015-08-25T12:17:32.040
71672
1390
null
6317
1
6323
null
7
1120
In boosting, each additional tree is fitted to the unexplained variation in the response that is currently un-modelled. If we are using squared-error loss, this amounts to fitting on the residuals from the aggregation of the trees fitted up to this point. I am not clear on whether it is at this point that the shrinkage...
When is the shrinkage applied in Friedman's stochastic gradient boosting machine?
CC BY-SA 2.5
null
2011-01-17T15:44:45.267
2011-01-18T00:42:38.193
2011-01-18T00:42:38.193
null
1390
[ "machine-learning", "boosting" ]
6318
1
null
null
13
972
In response to a growing body of statisticians and researchers that criticize the utility of null-hypothesis testing (NHT) for science as a cumulative endeavour, the American Psychological Association Task Force on Statistical Inference avoided an outright ban on NHT, but instead suggested that researchers report effec...
Do likelihood ratios and Bayesian model comparison provide superior & sufficient alternatives to null-hypothesis testing?
CC BY-SA 2.5
null
2011-01-17T16:07:47.570
2011-01-18T15:31:45.893
2011-01-17T17:45:06.630
364
364
[ "bayesian", "confidence-interval", "effect-size", "inference" ]
6319
2
null
1964
2
null
On Matlab File Exchange, there is a kde function that provides the optimal bandwidth with the assumption that a Gaussian kernel is used: [Kernel Density Estimator](http://www.mathworks.com/matlabcentral/fileexchange/14034-kernel-density-estimator). Even if you don't use Matlab, you can parse through this code for its m...
null
CC BY-SA 3.0
null
2011-01-17T17:18:11.883
2016-04-12T16:53:54.970
2016-04-12T16:53:54.970
22047
559
null
6320
1
null
null
5
1057
I have a very large number of observations. Observations arrive sequentially. Each observation is an $n$-dimensional vector (with $n \ge 100$), is independent from the others and is drawn from the same unknown distribution. Is there an optimal policy to estimate the unknown distribution, given some space bounds on the ...
Estimating probability distribution function of a data stream
CC BY-SA 2.5
null
2011-01-17T18:32:55.550
2011-02-06T01:23:06.167
2011-01-17T18:50:47.337
2116
30
[ "estimation", "multivariable" ]
6321
1
6322
null
9
1145
I have two variables, and I can calculate e.g. the Pearson correlation between them, but I would like to know something analogous to what a t-test would give me (i.e. some notion of how significant the correlation is). Does such a thing exist?
Assessing significance of correlation
CC BY-SA 2.5
null
2011-01-17T19:06:08.327
2011-01-21T10:05:07.917
2011-01-18T00:39:18.570
null
900
[ "correlation", "statistical-significance" ]
6322
2
null
6321
8
null
Yes, you can get a $p$-value for testing the null hypothesis that the Pearson correlation is zero. See [http://en.wikipedia.org/wiki/Pearson%27s_correlation#Inference](http://en.wikipedia.org/wiki/Pearson%27s_correlation#Inference).
null
CC BY-SA 2.5
null
2011-01-17T19:09:49.817
2011-01-17T19:09:49.817
null
null
449
null
6323
2
null
6317
4
null
Using trees, the shrinkage takes place at the update stage of the algorithm, when the new function $f(x)_k$ is created as the function prior step ($f(x)_{k-1}$) + the new decision tree output ($p(x)_k$). This new tree output ($p(x)_k$) is scaled by the learning rate parameter. See for example the implementation in R [G...
null
CC BY-SA 2.5
null
2011-01-17T19:35:52.177
2011-01-18T00:42:11.000
2011-01-18T00:42:11.000
null
2040
null
6324
2
null
6312
2
null
This might be an over-simplification, but specificity and sensitivity are measures of performance, and are used when there isn't any objective knowledge of the nature of the signal. I mean your density vs. signalness plot assumes one variable that quantifies signalness. For very high dimensional, or infinite-dimensiona...
null
CC BY-SA 2.5
null
2011-01-17T19:36:23.677
2011-01-18T17:29:07.060
2011-01-18T17:29:07.060
2728
2728
null
6325
2
null
6304
16
null
It's not even a close approximation. For small $n$, the expectation of $T$ equals $\frac{k n}{n-2}$ whereas the expectation of $\chi^2(k)$ equals $k$. When $k$ is small (less than 10, say) histograms of $\log(T)$ and of $\log(\chi^2(k))$ don't even have the same shape, indicating that shifting and rescaling $T$ still...
null
CC BY-SA 4.0
null
2011-01-17T20:28:09.393
2020-01-16T16:09:19.657
2020-06-11T14:32:37.003
-1
919
null
6326
1
6335
null
5
587
I have two treatments A & B. Here are my groups, where X represents the appropriate control for that particular treatment: Group 1: XX Group 2: AX Group 3: XB Group 4: AB The hypothesis is that the treatment B will have an effect, but that that effect will no longer be apparent when combined with treatment A. So, if ru...
Interpreting interactions between two treatments
CC BY-SA 3.0
null
2011-01-18T00:45:45.837
2012-08-03T16:37:10.230
2012-08-03T16:37:10.230
2816
2816
[ "anova" ]
6327
2
null
6312
2
null
You're comparing "What is the probability that a positive test outcome is correct given a known prevalence and test criterion?" with "What is the sensitivity and bias of an unknown system to various signals of this type?" It seems to me that the two both use some similar theory but they really have very different purpo...
null
CC BY-SA 2.5
null
2011-01-18T01:23:18.533
2011-01-18T01:23:18.533
null
null
601
null
6328
2
null
3328
4
null
If you keep the log likelihoods, you can just select the one with the highest value. Also, if your interest is primarily the mode, just doing an optimization to find the point with the highest log likelihood would suffice.
null
CC BY-SA 2.5
null
2011-01-18T01:42:16.450
2011-01-18T01:42:16.450
null
null
1146
null
6329
1
6332
null
8
3682
I've been using the ets() and auto.arima() functions from the [forecast package](http://robjhyndman.com/software/forecast/) to forecast a large number of univariate time series. I've been using the following function to choose between the 2 methods, but I was wondering if CrossValidated had any better (or less naive) ...
Combining auto.arima() and ets() from the forecast package
CC BY-SA 2.5
null
2011-01-18T02:20:54.247
2011-01-19T18:39:32.660
2011-01-19T18:39:32.660
2817
2817
[ "r", "time-series", "forecasting", "exponential-distribution", "arima" ]
6330
1
6348
null
36
69958
I have previously used [forecast pro](http://www.forecastpro.com/) to forecast univariate time series, but am switching my workflow over to R. The forecast package for R contains a lot of useful functions, but one thing it doesn't do is any kind of data transformation before running auto.arima(). In some cases foreca...
When to log transform a time series before fitting an ARIMA model
CC BY-SA 2.5
null
2011-01-18T02:50:01.373
2018-06-19T11:57:38.263
2011-01-19T20:07:15.060
2817
2817
[ "r", "time-series", "data-transformation", "forecasting", "arima" ]
6331
2
null
6326
3
null
If in post hoc testing Group 3's mean was significantly different from all the others' then you've already shown that XB is different from AB. Am I missing something? Your statement about B's effect (and its being lost when combined with A's) would be correct.
null
CC BY-SA 2.5
null
2011-01-18T03:26:40.937
2011-01-18T03:26:40.937
null
null
2669
null
6332
2
null
6329
16
null
The likelihoods from the two model classes, and hence the AIC values, are not comparable due to different initialization assumptions. So your function is not valid. I suggest you try out the two model classes on your series and see which gives the best out-of-sample forecasts.
null
CC BY-SA 2.5
null
2011-01-18T03:35:29.263
2011-01-18T03:35:29.263
null
null
159
null
6333
2
null
6330
41
null
Plot a graph of the data against time. If it looks like the variation increases with the level of the series, take logs. Otherwise model the original data.
null
CC BY-SA 2.5
null
2011-01-18T03:41:29.677
2011-01-18T03:41:29.677
null
null
159
null
6334
2
null
6330
1
null
You might want to log-transform series when they are somehow naturally geometric or where the time value of an investment implies that you will be comparing to a minimal risk bond that has a positive return. This will make them more "linearizable", and therefore suitable for a simple differencing recurrence relationshi...
null
CC BY-SA 2.5
null
2011-01-18T03:45:46.210
2011-01-18T03:45:46.210
null
null
2129
null
6335
2
null
6326
6
null
If I understand you correctly, your design is: $\begin{array}{rcccl} ~ & B_{X} & B_{B} & M \\\hline A_{X} & \mu_{11} & \mu_{12} & \mu_{1.} \\ A_{A} & \mu_{21} & \mu_{22} & \mu_{2.} \\\hline M & \mu_{.1} & \mu_{.2} & \mu \end{array}$ The first part of your hypothesis (effect of treatment B within ...
null
CC BY-SA 2.5
null
2011-01-18T11:28:01.773
2011-01-18T11:28:01.773
null
null
1909
null
6336
2
null
6302
3
null
The empirical CDF needs to be treated with care at the end points of the data, and in other places where there is "sparse" data. This is because they tend to make weak structural assumptions about what goes on "in between" each data point. It would also be a good idea to have "dots" for the empirical CDF plot rather ...
null
CC BY-SA 2.5
null
2011-01-18T12:42:18.770
2011-01-18T12:42:18.770
2017-04-13T12:44:54.643
-1
2392
null
6337
1
6338
null
5
890
I have various clinical data on participants in a study. I'm looking at a continuous variable ("A") and a (binary) categorical variable (group) ("O"). I used a Wilcoxon test in R (the data are not normally distributed) to see if "A" is significantly different between the two groups. I got a borderline p-value of 0.054....
Subsets not significantly different but superset is
CC BY-SA 2.5
null
2011-01-18T13:04:50.173
2017-04-03T15:48:27.513
2017-04-03T15:48:27.513
101426
2824
[ "r", "statistical-significance", "nonparametric", "wilcoxon-mann-whitney-test" ]
6338
2
null
6337
7
null
It seems to be a question of [test power](http://en.wikipedia.org/wiki/Statistical_power). If you only look at a subset you have a lot less participants and therefore a lot less power to find an effect of similar size. With a reduced sample size you can only find a much bigger effect. So it is NOT recommended to only l...
null
CC BY-SA 2.5
null
2011-01-18T13:45:26.073
2011-01-18T14:49:41.990
2017-04-13T12:44:28.813
-1
442
null
6339
2
null
6337
6
null
This is not necessarily an issue of statistical power; it could also be an example of [confounding](http://en.wikipedia.org/wiki/Confounding). Example: - One category of $O$ is more common in males but the other is more common in females - The distribution of $A$ differs between males and females - Within e...
null
CC BY-SA 2.5
null
2011-01-18T14:24:30.237
2011-01-18T14:24:30.237
null
null
449
null
6340
2
null
6146
3
null
From the statement of the question, it seems as though you don't require conjugacy per se, rather you would like an analytical solution to your integration. From the form of the distribution, it would appear at first glance that the analytics of most solutions would be rather messy and difficult to interpret. The "an...
null
CC BY-SA 2.5
null
2011-01-18T14:52:28.410
2011-01-18T14:52:28.410
null
null
2392
null
6342
1
6344
null
6
8600
I have continuous data "A", binary categorical data "O", gender/sex and age for several participants in a study. A linear model in R shows no correlation between A and age. I would now like to group A into groups by age and see if there is a difference between the groups. I know about 'hist' and 'split' in R, but the...
Splitting one variable according to bins from another variable
CC BY-SA 2.5
null
2011-01-18T15:01:29.900
2011-01-18T15:31:51.173
2011-01-18T15:07:26.673
919
2824
[ "r", "regression", "histogram" ]
6343
2
null
5542
4
null
A useful way to incorporate data into a prior distribution is the principle of maximum entropy. You basically provide constraints that the prior distribution is to satisfy (e.g. mean, variance, etc.,etc.) and then choose the distribution which is most "spread out" that satisfies these constraints. The distribution gen...
null
CC BY-SA 2.5
null
2011-01-18T15:16:19.887
2011-01-18T15:16:19.887
null
null
2392
null
6344
2
null
6342
5
null
``` > A <- round(rnorm(100, 100, 15), 2) # generate some data > age <- sample(18:65, 100, replace=TRUE) > sex <- factor(sample(0:1, 100, replace=TRUE), labels=c("f", "m")) # 1) bin age into 4 groups of similar size > ageFac <- cut(age, breaks=quantile(age, probs=seq(from=0, to=1, by=0.25)), + inc...
null
CC BY-SA 2.5
null
2011-01-18T15:24:02.170
2011-01-18T15:31:51.173
2011-01-18T15:31:51.173
1909
1909
null
6345
2
null
6318
4
null
The main advantages of a Bayesian approach, at least to me as a researcher in Psychology are: 1) lets you accumulate evidence in favor of the null 2) circumvents the theoretical and practical problems of sequential testing 3) is not vulnerable to reject a null just because of a huge N (see previous point) 4) is better ...
null
CC BY-SA 2.5
null
2011-01-18T15:31:45.893
2011-01-18T15:31:45.893
null
null
447
null
6347
1
null
null
3
862
PCA based filtering is used to identify and eliminate noise in data. This would basically involve computing the PCs and using the top k PCs to denoise the data. What if I know for sure that only the extremely small values in my matrix are noise? Now, a value may be small w.r.t the entire matrix but not small w.r.t a pa...
PCA Based Filtering but only filter out small values
CC BY-SA 2.5
null
2011-01-18T16:19:49.377
2011-01-28T00:18:46.790
null
null
2806
[ "pca" ]
6348
2
null
6330
23
null
Some caveats before to proceed. As I often suggest to my students, use `auto.arima()` things only as a first approximation to your final result or if you want to have parsimonious model when you check that your rival theory-based model do better. Data You have clearly to start from the description of time series data y...
null
CC BY-SA 2.5
null
2011-01-18T18:43:46.330
2011-01-19T09:49:07.870
2011-01-19T09:49:07.870
2645
2645
null
6350
1
6351
null
59
245584
The [Wikipedia page on ANOVA lists three assumptions](http://en.wikipedia.org/wiki/Anova#Assumptions_of_ANOVA), namely: - Independence of cases – this is an assumption of the model that simplifies the statistical analysis. - Normality – the distributions of the residuals are normal. - Equality (or "homogeneity") of ...
ANOVA assumption normality/normal distribution of residuals
CC BY-SA 2.5
null
2011-01-18T19:07:59.347
2021-07-05T18:41:58.707
2021-07-05T18:41:58.707
11887
144
[ "anova", "residuals", "normality-assumption", "assumptions", "faq" ]
6351
2
null
6350
43
null
Let's assume this is a [fixed effects](http://en.wikipedia.org/wiki/Analysis_of_variance#Fixed-effects_models_.28Model_1.29) model. (The advice doesn't really change for random-effects models, it just gets a little more complicated.) First let us distinguish the "residuals" from the "errors:" the former are the differ...
null
CC BY-SA 4.0
null
2011-01-18T19:45:40.100
2020-09-29T21:09:34.100
2020-09-29T21:09:34.100
919
919
null
6352
2
null
6350
5
null
In the one-way case with $p$ groups of size $n_{j}$: $F = \frac{SS_{b} / df_{b}}{SS_{w} / df_{w}}$ where $SS_{b} = \sum_{j=1}^{p}{n_{j} (M - M_{j}})^{2}$ and $SS_{w} = \sum_{j=1}^{p}\sum_{i=1}^{n_{j}}{(y_{ij} - M_{j})^{2}}$ $F$ follows an $F$-distribution if $SS_{b} / df_{b}$ and $SS_{w} / df_{w}$ are independent, $\ch...
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CC BY-SA 2.5
null
2011-01-18T20:01:21.290
2011-01-19T09:43:20.550
2011-01-19T09:43:20.550
1909
1909
null
6353
1
null
null
12
53475
It looks like you can use coding for one categorical variable, but I have two categorical and one continuous predictor variable. Can i use multiple regression for this in SPSS and if so how? thanks!
Can I use multiple regression when I have mixed categorical and continuous predictors?
CC BY-SA 2.5
null
2011-01-18T20:04:35.030
2016-03-17T08:02:16.877
2011-01-19T00:38:17.517
null
null
[ "regression", "spss", "categorical-data", "continuous-data" ]
6354
1
null
null
3
867
Most methods for [symbolic data analyis](http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0470090162.html) are currently implemented in the SODAS software. Are there any R packages for symbolic data except clamix and clusterSim?
R package for symbolic data analysis
CC BY-SA 2.5
null
2011-01-18T20:46:44.443
2011-01-21T18:46:58.413
null
null
2831
[ "r", "clustering" ]