tttjjj/elt_bench huggingface dataset:
large ... well Z and t converge starting with n=60. Just compare the p-values you get from both tests. The t/Normal distribution assumption does not depend on the distribution of the underlying data. It is based on the assumption, that the sampling distribution of the mean is normal. Even if the variable you are testing is distributed Gamma, that still holds. With n=200 or so it should work fine. Again, all this stuff is based on frequentist statistics.
I read Dr. Harrell's comments. I think there is a disconnect between some of that advice and data mining (large data). 25 iterations that I completed took 4 days and that was under sampling the negative cases substantially.
(-1) Did you look up Naive Bayes on the web before ? Do you understand how classification works ? What do you mean by ""heard that's not the right way to do it" ? Why ? What do you mean by "how can we split ..." ?
Sounds like a case of right censoring: http://en.wikipedia.org/wiki/Censoring_(statistics)
It's too contested what it actually is, and too culturally specific.  "Common sense" is short hand for whatever is the perceived sensible way of doing things in this particular culture (which all too often looks far from sensible to another culture in time and space), so referring to it in a definition ducks the key questions.  It's particularly unhelpful as part of a definition of logic (and so, I would argue, is the concept of a "rational person" in that particular context - particularly as I am guessing your definition of a "rational person" would be a logical person who has common sense!)
I edited my post above (check EDIT2) and posted my code of using draws from each conditional rather than your more efficient decomposition as I wanted some extra practice with the coding. I'm now wondering how I can estimate the 5% quantile of $p(\\psi|\\mathbf{y})$ using these draws psi?
@ttnphns: Totally agreed; just given that the OP asks about Matlab and that the `hald` dataset is part of Matlab's "Sample Data Sets" http://www.mathworks.co.uk/help/stats/_bq9uxn4.html it is an honest mistake by a new user. It is available here: http://www.qsar.org/resource/datasets/hald.htm For practical purposes `ingredients` is a $13\\times4$ full rank matrix of positive integer values.
I believe the Mahalanobis distance effectively *downweights* the large-covariance directions, rather than giving "bigger" weights there.
@nico: I believe you can store anything you want in Zotero, including your own documents. It's not exactly an ELN, but it is free and would make it easy to include (and index) other materials as well.
You can get (a little) more information from the help for the function `plot.acf` under the entries for things with `ci` in their name under **Arguments**, as well as the whole of the **Note** section - [find that help page here](http://stat.ethz.ch/R-manual/R-patched/library/stats/html/plot.acf.html)
If A and B are dependent, then joint distribution of A and B is required to arrive distribution of A+B.
Again, how can I conduct a multivariate regression with several categorical (say, 3) and several continuous (say, 2) dependent variables in SPSS?
3 is just a different representation of 2. 1 is just 2 or 3 applied over a testing set. E in 2 or 1 is the average illustrated in 3. Thus, the comparison reduces to 1 or 2 or 3 and 4 and 5. I am not sure about Y^0 in 4 and 5 !
Then CV is not the website to ask the question. If your model is deterministic, i.e. it assumes that the real world behavior is described without any source of randomness, how do you think statistical concepts could help you?
I learned most of what I know of meta-analysis from this book: Card, Noel A., Little, Todd D..; Applied Meta-analysis for Social Science Research. The book explains the process of meta-analysis and the statistics involved in an intuitive way. Reading Chapters 8-10 should cover your questions.
It's highly regulated area. It's very unlikely you will find that.
Further discussion and references can also be found on p.2 in the article describing G*Power3: http://www.psycho.uni-duesseldorf.de/abteilungen/aap/gpower3/download-and-register/Dokumente/GPower3-BRM-Paper.pdf (pdf)
Baum's book is neither a real introduction to econometrics nor a real introduction to Stata. Somewhat disappointing ...
@drknexus: That's fair, but I mention that it's k-fold and I wanted to provide a visualization of the process to help explain it.
Seems a little silly to post as an answer, but [wordle](http://www.wordle.net/) may give you something useful, or at least interesting to ponder...
@MattKrause: Thanks for the flowers :-). Poor man's venetian blinds: I think so. But note it does come from traditional calibration/regression settings, where also the number of affordable calibration samples (physical meaning) is low. I'd say it is a very straightforward way of stratifying according to a metric variable, although more sophisticated methods may exist (I don't know any offhand - I'd argue that if this distinction becomes crucial, it is high time to get back to the lab and get more real samples...).
Recommend you read [Morgan and Winship, 2007](http://www.amazon.com/Counterfactuals-Causal-Inference-Principles-Analytical/dp/0521671930).  Chapters 4 and 5 do an explicit compare and contrast of regression and matching for causal effect identification.
@whuber That's because I wasn't analyzing it, I was designing an experiment from those parameters *de novo*.  Clarified in the edit.
+1 for the creative (and insightful) interpretation and explaining the distinction.
How about you give us an example of what your data look like and you show us your graph? As it stands now it's almost impossible to answer your question unless we know SPSS by heart, or unless we try it out on one of our own datasets.
Many t-test applications are overkill. They are needed only when the difference of means is (a) of practical importance and (b) of the same order of magnitude as the standard errors of the means.  Here, your standard errors are around $0.002$ and $0.003$, so if the difference of means is much larger than $0.01$, there's no question it is significant and it won't matter what test you apply. In particular, there would be no point in applying any procedure that takes more than a few seconds of your time and the computer's time total.
What is the subscript $_i$ for?
(+1) I like this one. However, one might need awful amounts of data to get reliable estimates for all $p(x_t|x_{t-1},c)$
APA is widely used, not just in psychology. Essentially, you have to use whatever style the place you are sending this to requires.
No, I think my way of computing the standard error should be correct. As pointed out [here](http://stats.stackexchange.com/questions/15505/converting-standard-error-to-standard-deviation), the standard error is the standard deviation of the sampling distribution of a statistic. My statistic is the mean based on $N$ observations, so I compute the standard deviation of that statistic. Another way to see it: I already consider $\\sqrt{N}$ by computing the mean with $N$, instead of 1, observation.
@GaëlLaurans 

Yes I expect the difference in RT between `Regular` and `Random` to change over time. 
Specifically, both trials will become faster as time progresses, but the decrease in RT for `Random` trials should be a linear decrease based on practice effect, whereas the decrease in RT for `Regular` trials should be steeper because of the learning effect. Answering your second question, I want to test whether the differences in RT are different.

So to answer your third question, there is indeed a difference between types of trials. The difference is in fact the experimental manipulation.
I think the wrinkle is the time invariant variable (3 levels, 2 dummies) which is created using aggregations of the cross-sectional data (states).  So if I run the fixed effects model in Stata the two dummies drop out.  Is the solution to drop the two dummies and just look at the individual states which comprise these two dummies?
Thanks again, RB
Could you add some examples?
@Leo Yeah I imagined that what you suggested and similar approaches were possible, but they all seemed quite ad hoc.  As such, I was wondering if there was a more robust, standard approach to the problem.
[Here](http://stats.stackexchange.com/questions/47222/techniques-for-analyzing-ratios/) might help.
calculating expectations almost always involves integration. Unfortunately there are no universal simple rules how to calculate integrals.
Welcome to the site, @BabOuSunshine. Would you mind giving a precis of the info found in that document? This will help readers decide if it's what they're looking for, & may help in case of linkrot.
In Fig 2b, you see the 3' and 5' UTR predictions for human Miranda were the *worst* performing in terms of their calibration (O/E ratio in the vicinity of ~10%). The authors' point is that the precision of the predictions were weak and the prediction intervals indicate that this estimate may have still been consistent with the expected 3' / 5' UTR Miranda location (or expression... or whatever they're measuring here). When they say 
"slight" they are downplaying the fact that it's actually somewhat big (but not statistically significant... after correcting for multiple comparisons...)
perhaps you can run cronbach's $\\alpha$ on each group? But I wonder what your final intent is, as this is not comparing the control vs intervention group.
Thanks for your comment, Michael. I've edited my answer to reflect that fact.
The "homework" tag doesn't mean the question is elementary or stupid: it's used for self-study questions that can even include research-level queries. It distinguishes routine, more or less context-free questions (of the sort that might ordinarily grace the math forum) from specific applied questions.
I thought that logistic regression still determines linear coefficients before making classifications. Least squares is usually involved in the cost function of that process, or is probably effected by scaling. That's not the only way to determine those coefficients, but I guess it might depend on he logistic regression algorithm? Damn, now I've got a question.
Neither the x variables nor the raw y-variable are assumed to be be normal. There are things [assumed to be normal](http://en.wikipedia.org/wiki/Panel_data#Analysis_of_panel_data), however (and you probably shouldn't ignore them), but it doesn't sound like you looked at anything that would tell you about them.
@Glen_b I should have mention that I only require how to compute the mean and co-variance I already knew it should be normal.
"*I feed in a list of numbers and it tells me whether or not the numbers are normally distributed*" -- no hypothesis test can tell you if data *is* normally distributed. It can sometimes tell you if it is reasonably clearly not, but failure to reject doesn't say the null is actually true -  it almost certainly isn't (except in some very limited circumstances). ... why do you want to test normality?
@Dimitri We have just developed this enhanced feature within AUTOBOX , a software package that I helped to develop. Our customer a large fast food franchise will not allow us to publish the results as they don't want their competitors to be able to work/plan smarter. I can tell you that the system allows for price/promotion/holidays etc to play a role in both the 96 individual forecasts and the daily forecast. We are using promotional inputs as predictor series. If you want them to demo this for you please contact them at sales@autobox.com
yeah..so almost marrying the answer by mpiktas and mine..you can use factor analysis with method = prin. This would request to use the principal axis method.
@Christopher (I TeXified your question to make it readable.)  You should double-check the distributional form for $Y_i^2$, because it is incorrect: it is not Gaussian, but exponential.  (That is, the argument of exp should be linear in $x$, not $x^2$.)  There also needs to be a factor of $x^{-1/2}$.  Once you fix that, all you need to show is that a sum of Gamma distributions is also Gamma.
Thank you for your kind edit. I do not use LaTex but I have good Mathematics Word Processor like Math Type if you feel I'll post next time with a better typing. True, likelihood functions are changing but why they are changing? And by same issue I tried to mean change of likelihood function, it may be in other probabilistic models also. Parameter I used in literary sense. Any other issue like deeper angle of the question I may be missing please suggest, if there is any.
It is best not to do feature selection in this sense at all. Doing so leads to a lot of problems. If this doesn't make sense / you want to understand why, it may help you to read my answer here: [algorithms for automatic model selection](http://stats.stackexchange.com/a/20856/7290)
@David, no! This is why bayesian modelling is so great. The NAs will be replaced by MCMC simulation samples using the model. Look at the rules I specified in the model (for loop) - this is exactly the markov chain principle, and that's all you have to care about! Don't be bothered with some details like missing values :-). We are in Bayesian world! You don't have to understand how it works at all, but if you want, read something about MCMC sampling or gibbs sampling...
I did try looking into post-pruning but didn't get anywhere in that respect. I couldn't find any examples that even remotely related to my problem.
"Dichotomous" means *dividing into two classifications.* Thus ["likely high value customer"]/[not likely a high value customer] is a dichotomy and so is "yes/no." This is the source of our puzzlement: logistic regression applies directly to these variables. Are you perhaps making a distinction between "dichotomous" and "0/1"? If so, you may actually have a question about ways of numerically encoding classifications for analysis rather than a question about logistic regression *per se*.
Interactions in nonlinear models are messier than in linear models. See [Karaca-Mandic et al. (2012)](http://onlinelibrary.wiley.com/doi/10.1111/j.1475-6773.2011.01314.x/abstract) for an overview. Basically the problem can be boiled down to all terms (not just interactions) have differing effects at different points on the original untransformed probability metric. This naturally makes life difficult for us sometimes.
What do you mean by indices? Combining scores across different dimensions is indeed in my experience the most common thing one does with PCA, and is definitely legit.
Please use capitalisation and punctuation as usual in formal written English. You are not texting friends or relations; you are posting in a public forum and it's not in your interests to make what you say more difficult to read.
The 10% of samples they've picked are the ones that most resemble the population distribution, meaning that the samples were definitely non-normal (in the non-normal conditions, of course)--which is what they're trying to get to (and which is why they've done this). I see your point, but I think saying their methodology is "seriously flawed" might be something of an overstatement.
This is by no means a basic question. Assuming that you know that the t-Test only applies if your data is drawn from a normal distribution (and assuming that it is), the problem at hand is: if you perform the t-test many times, how often do you expect to reject the null hypothesis? 

The answer really depends on your experimental design (i.e., where you measuring the same set of persons?). You can find a discussion of this problem here: http://jalt.org/test/bro_27.htm.
What is the final product supposed to look like? Have you already tried something that doesn't work or takes too long? Where does your "table" above come from?
If it can fit, it can overfit. In terms of RF, think about what happens if your forest doesn't contain enough trees (say your forest is a single tree to make the effect obvious). There are more issues than this one, but this is the most obvious.
I wasn't sure how to add the data set, so I just rewrote my post with a reproducible example. Hope this helps
Witten's page says "sparcl ...for clustering a set of n observations when p variables are available, where p>>n", but here I gather n=800, p=200 ?
This may get better answers on stats.stackexchange.com
Of possible interest: [Feature selection before SVM](http://stats.stackexchange.com/questions/63081/feature-selection-before-svm).
Thank you, what I understood is that the criterion can be changed according to the data.
Have you used two different accounts for question and answer? they will probably be merged. You should edit your original question, instead of providing this 'answer'.
Are there only 2 values, or is there a series of values like the 2nd one or in between the two?
One thing I have learned from working with the exact bootstrap is that the standard normal-theory CI will often work much *better* with small samples even when they are skewed.  The bootstrap comes into its own with large samples: the theory is an asymptotic one, not an exact one.
$\\hat\\phi$ is produced in the glm output. Let me add an example to my answer.
In order to use a Kalman filter you should have the model of your dynamical system (i.e. a system of differential equations) plus the measurements equations. Are they available? Are they linear?
Especially if it's online, you should link to your source for context.
Great solution. I never knew one could sample this way (that is, relying on samples from $Uni(0, k), k>1$ instead of $Uni(0,1)$), but it is obvious in retrospect.
I didn't have your data .... right? So I had to generate a sample from a Pareto IV distribution using rparetoIV. Therefore, the answer is no ... you don't have to generate with these parameters. You just need to create a data frame using your own observations like this : `pdata.new <- data.frame(y =c(obs.1,obs.2, ...., obs.850))`. Then use this new data frame to fit i.e. `fit.new <- vglm(y ~ 1, paretoIV, data = pdata.new, trace = TRUE)`
The ICC = `e(rho)` after `xtreg`
Great, that works - thanks DWin.
The lack of definition of variable in your question causes confusion. Do you mean value? If not, how would a "variable" look like that is a constant? Or do you mean the nth variable to have `range(0-10^1000)`? You have to be more clear.
Many thanks for your answer. Please could you provide a little more explanation. In the table that they have below the example, they have assigned a weight to hallucination as 1 and the actual values for the two patients are also "1", i.e., similar. So as per the rules for binary variables should the value and weight not be considered as "1" instead of "0"? Unless of course 2 means "+" and 1 means"-".
I am not sure if I understand your answer. Is there a reason that the residual degrees of freedom are equal? Any suggestion on an alternative approach to compare the slopes?
+1, A question, though:  If Y were initially continuous (just quite badly behaved), and you converted them to ordinal categories via a rank transform, you could end up with a large number of categories--easily N.  My intuition is troubled by this.  Would ordinal log reg be reliable in such a situation?  Typically, we think of ord reg with situations with a small number of categories (e.g., in surveys, 4) with many observations per category.
Chow test is the most common technique for detecting structural breaks in linear regression. There might be better techniques for panel data, but to start you can just split the data up and estimate the model on each half and see if the coefficients are different.
Going from your second to your third line you have made multiple errors. I think this question should probably carry the `self-study` tag (see its [tag-wiki info](http://stats.stackexchange.com/tags/self-study/info))
The "trick" is to reduce the mixed model to a simple model by taking for observations the subjects means in your case and the groups means in the other question. I don't know what you should do but I claimed that the sampling distribution of your Bayesian model is not the same as the one of the frequentist model.
+1 - good to have discussion of the numerical solution of the median.
thanks for trying to understand what i have in my mind and answer my questions.
Adam and @IrishStat, I have removed your exchange of comments because they do not advance the solution to the original question.  If I may paraphrase (and read into) Adam's comment, now deleted, it seemed to suggest that although a good response to this question might indeed discuss "transfer functions" and "ARMAX models," it would need to *explain* what these things are, *why* they might be appropriate here, and *how* to apply them.  Without such explanations, many readers might be impressed but not enlightened.  Let's work to *improve,* rather than attack, each other's replies.
One point: t-tests use the t distribution not the Z distribution
That plane is a [linear discriminant](http://en.wikipedia.org/wiki/Linear_discriminant_analysis). There are other forms of classification. [e.g.1](http://en.wikipedia.org/wiki/Quadratic_classifier), [e.g.2](http://en.wikipedia.org/wiki/Kernel_Fisher_discriminant_analysis)
What model is `betareg` actually implementing?  What are its assumptions and why is it reasonable to suppose they apply to these data?
The problem is that you are generating different numbers in the numerator and denonimator for $Gamma(\\alpha,\\theta)$, try using the same values and it will work. For example, `a<-rgamma(m,1,1)`, `b<-rgamma(m,1,1)`, `c<-a/(a+b)` and then calculate `quantile(c,1:9/10)`.
On your first biplot, the data cloud is round dispite that according to you data PC1 must be much stronger than PC2. This makes me to think that the PC scores on the biplot are standardized (to st. dev. 1). Check if this is true. The loading points (red arrows) are likely to be loadings, as they should. The `results$rotation` figures you present are clearly the _eigenvector values_, **not** the _loadings_. Please be aware that the `R` PCA package you use misuses the word "loadings", incorrectly calling eigenvectors "loadings".
The main task here is to derive the distribution of the maximum. Here's a hint: If $M=\\max \\{X_1, ..., X_n\\}$, then $$ P(M \\leq x) = P(X_1 \\leq x, ..., X_n \\leq x) $$ If the $X$s are independent, as they seem to be here, this calculation is straightforward. Then, you have two independent realizations, $M_A, M_B$ and you can calculate $P(M_A > M_B)$. BTW, in this example, it's intuitive that the probability of A winning quickly goes to zero as $n$ increases since their maximums become increasingly likely to both be six, in which case B wins.
Thank you all for the useful answers.
Related: http://stats.stackexchange.com/questions/35276/svm-overfitting-curse-of-dimensionality
.... last thing, what you wrote ARCH-LM were you referring to http://rss.acs.unt.edu/Rdoc/library/vars/html/arch.html?
The answer depends on whether you want the terminology of null hypothesis to be explicit and on what you call theory. In a broad sense, Arbuthnott and Daniel Bernoulli both used similar ideas roughly two centuries before Karl Pearson. http://www.amazon.co.uk/History-Probability-Statistics-Wiley/dp/0471471291 is good.
Thank you very much for the example!!
It is important to note that DW statistic reported most likely ignores the structure of data. I.e. it treats all data as long time series, instead of 86 different time series. So the usual OLS interpretation of DW statistic is not helpful here.
"We often try to construct the model such that our error term is normally distributed" - to be precise, I think you are referring to the residuals $y-X\\hat\\beta$. These are _estimates_ of the error terms in the same way that $X\\hat\\beta$ is an estimate of $\\mathbb{E}(y)=X\\beta$. We'd like the residuals to look normal because that's what we assumed about the error terms to begin with. We "invent" the error term by specifying a model, not fitting it.
0.012 not 0.12 you missed a decimal