tttjjj/elt_bench huggingface dataset:
A good search keyword is [TOST](http://stats.stackexchange.com/search?q=TOST).
Thank you for respond. I mean, there will be differences p-values between these methods. But for example in SAS, while p=0.04 for X2 , in R p=0.10 for X2, but p-values of other variables are similar, it means when they are significant in SAS, they are also significant in R, or when they are not significant in SAS, they are not significant in R.
@ Robert Smith. I am sorry but I am not familiar with the code. Can you write the equation in mathJax please?
It is a good idea to spell out acronyms and abbreviations.
This seems to have worked, thanks!
What is theta, and what is the distance measured from? What is the goal? What do you mean that the data is not useful?
I have no information on the drop-outs (it's secondary data), but the mode of assessment was face-to-face interviewing so I expect little drop-out. Also the question order was not random. And unfortunately there is no data on timing per question. But I can estimate the question complexity myself. Thanks, and I will have a look at your suggestions.
By 'simulating from a state space model' do you mean simply adding additive independent observation error?
You cannot violate circularity with only two levels of the repeated measure.
I'd be inclined to add in the information you gave on what the variables represent to your question.
@Dmitrij Celov, I've upvoted your answer, since I was intending to write something similar, but please fix the language
+1. Very good explanation. I also think that some "robust" methods are rather ad hoc (truncated means), and that "robust" is tied to a particular aspect of a method and is not a general quality but many people interpret "robust" to mean "I don't have to worry about my data, since my method is robust".
If you have all the $y_i$, surely you also know $n_s$?  ie just by counting the $y$s.
@BYS2: You're quite right, it should of course be 0.0505!
@whuber The OP assumed the distributions had their means and variances known.
xtable has already been rewritten (or perhaps pre-written) as the [latex](http://lib.stat.cmu.edu/S/Harrell/help/Hmisc/html/latex.html) function in the R package Hmisc.  Personally I swear by it for proper looking tables.  I haven't checked whether it has room for the fancy insertion trick described below, though I'd be surprised if not.
@Michael One is torn between competing objectives: closing quickly can *help* the OP by directing them immediately to a solution. Leaving a question open allows it to collect answers which then later will either disappear or will have to be merged with the duplicate, which can create a little confusion (as well as quite a bit more work for the mods :-). Because a closed question is still visible, can still be discussed (as we are doing here), and can easily be reopened, I find it's best to err on the side of closing so that such early answers do not accumulate.
@AdamO what I am talking about is the same data set-up as discrete time hazard models, but the outcome is continuous. I am not modeling failure here. Think of it this way, I know the amount of the account (balance) at time t=3 and i have attributes about the customer at that point in time and I am trying to predict the balance (the stream) at each time t from 4 to 36.
I am not a statistics expert. Could you please explain more about the plotting idea?
"Unreplicated" just means that each person is observed exactly once at each time point, but not twice of more often. So "unreplicated" $\\neq$ "not repeated". For the post-hoc comparisons, [this question](http://stats.stackexchange.com/questions/14078/post-hoc-test-after-anova-with-repeated-measures-using-r) or [this question](http://stats.stackexchange.com/questions/575/post-hocs-for-within-subjects-tests) provide a start.
I have voted to close this question. Unfortunately, data sourcing questions are not generally considered on-topic here. The FAQ and some threads on meta contain more discussion on this.
*Please, vectorize that pesky* `for`. **Ok**. How's this? `x <- matrix(rgamma(prod(dim(a)),a),ncol(a)); x <- x / rowSums(x)`
Alright, well I'm not able to figure out how to run a linear restriction model or, essentially devise an F test based on the stats of each coefficient.  Maybe stats packages know how to do that, but without understanding that I can't really implement it on my own.  If you can give a specific example of the calculation I can just implement it on my own.  Just make up 4 coefficients as measures, a standard error and df for reach, etc, and show me how to set up the test manually.
@user2991243 For the beta distribution the quantile function is, unfortunately, not available in closed-form. However, you can approximate it numerically using  MATLAB.
Thanks a lot @John.
You do not define $e_1$. What is it?
I'm aware of BIC and DIC, but they are not what I'm fundamentally asking for in my question. Note that those information criterions use the likelihood, not the posterior distribution. And, if you read carefully my question, I AM searching for something like an information criterion which includes the posterior distribution (and therefore, the variability of the parameters on each model).
Once you [combine your multiple accounts](http://stats.stackexchange.com/help/merging-accounts), Kelly, you will be able to edit and comment on this post.  (Because you used a different account, you were forced to post your follow-on questions as an answer and I could not preserve all of it when changing it into a comment to the answer.)
Although the question at the end is good, the lead-up to it is questionable, because quite obviously (since $0.573 \\gt 0.50$) these data are consistent with a claim of "more than 50%."  Please rethink what the null and alternative hypotheses ought to be.
It might help if you told us which R package and which function(s) you are using.
I think Glen is right when he says all values in a Confidence Interval are equally likely.  CIs don't tell which value in the CI is closer to the "truth".  Under repeated sampling they will cover the true value with certain probability, but no judgment could be made about the data in hand, or location of "truth" in CI.
@Naji (continued) For a source, [this paper](https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&ved=0CDsQFjAB&url=http%3A%2F%2Fwww.fas.harvard.edu%2F~junliu%2FTechRept%2F96folder%2Fnonpbayes.pdf&ei=MtJeUvepCoP49QTH24G4BA&usg=AFQjCNEosiOI_kGroCnu_PbMMiEINc6XdQ&sig2=oN7LojuVmm7FdrrYyT6uvA&bvm=bv.54176721,d.eWU) has them, but no derivations as far as I know.
@Jonathan: in my case, it is a little bit of both.
Be sure to read the subsection on Adjusted-$R^{2}$, which bears on regression models with more than one predictor: https://en.wikipedia.org/wiki/Coefficient_of_determination#Adjusted_R2
I don't see a question in here, just an attempt to explain the methods with a question mark at the end. I also think you would do a better job with a multivariate regression model. It gets really hard to interpret such post hoc scores in the models you estimate.
`(39+44)/90=92% correct rate` is high for me.
@onestop See http://stats.stackexchange.com/questions/6096/correct-way-to-calibrate-means
I don't want to sound harsh, but I'm not entirely sure what you want. There are lots of ways something could be a poor choice. Typically, we evaluate [estimators](http://en.wikipedia.org/wiki/Estimator) in terms of things like [bias](http://en.wikipedia.org/wiki/Bias_of_an_estimator), [variance](http://en.wikipedia.org/wiki/Variance), [robustness](http://en.wikipedia.org/wiki/Robust_estimator), and [efficiency](http://en.wikipedia.org/wiki/Efficient_estimator). Eg, as you note, the OLS estimator is [BLUE](http://en.wikipedia.org/wiki/Best_Linear_Unbiased_Estimator).
I am going to give it a try by incorporating above equations in R and see how successful I am, since I am not an expert with R yet :)
re: "use logistic regression to estimate x".  Logistic regression is not applicable to estimating income (x).  It is for binary dependent variables only.
Is this for some subject, or for similar self-study from a text or similar? If so, could you please add the `self-study` tag?
@JMS, (+1) especially for the note of caution on scree plots. I would call them "standard", but also "a bad idea" (generally speaking). [Here](http://arxiv.org/abs/0908.2062) is a cautionary tale and also a way to pick the rank more safely, especially if MSE is your metric. This also provides an example, if I recall, where the true rank is the wrong one to pick for minimizing MSE.
@mpiktas, but this is very important for applied statisticians.
Hi whuber, thank you for the response! I am really asking both of those questions. I am trying to get my head round it mathematically and at the same time calculate it in R but am struggling a little.
Are you using PCA or factor analysis? These are two different procedures, but you use both terms. If you do factor analysis, then check out this question, as it contains a good answer: [Are data transformations on non-normal data necessary for an exploratory factor analysis when using the principal axis factoring extraction method?](http://stats.stackexchange.com/questions/34753/are-data-transformations-on-non-normal-data-necessary-for-an-exploratory-factor/)
it's 1v1, two group stages of 4 players, two drop two advance in each stage, after that the remaining 8 players play elimination matches. Top8, top4, finals, winner. Group stages have one game, starting with top8 it's best of 7. Top 8 players always get seeded into the next tournament; the rest of participants must fight for the right to play in additional sub-tournament. I oversimplified a bit but I hope that will give you some idea what I am talking about.
Are you trying to test if the means of 5 conditions differ? What were the t-tests? The KS test is less powerful than the SW test & shouldn't be used if you estimated the means & SDs from your data, rather than knew them a-priori.
Very intriguing!
Fair enough- Lets exchange 'shares' with a more reasonable stocastic system- like inventory- or a more abstract form of resource allocation, and get back to the sequential hypothesis testing issue in this framework. Would like to do a sequential hypothesis testing- for two methods, where each point is modeled with a exponential distribution with different parameters like in GAM's and we have this setting for two methods. aka- sequential hypothesis testing at every point for two methods as data is collected and some form of an online likelihood ratio is measured.
I should have mentioned that I use 28-day "months" for reporting to avoid issues related to number of days in the reporting period.
In line w/ Peter's point (below) re the residuals, but not the outcome, needing to be normally distributed, this: [what-if-residuals-are-normally-distributed-but-y-is-not](http://stats.stackexchange.com/questions/12262/) may be helpful.
After a bit of maths, the class of distributions above all give $p(|\\rho|<1)=\\frac{1}{2}$ so that can't be used as a criterion for making the solution unique.
Yes, I think I can appreciate that any given point on a continuum is equally likely (or rather unlikely) to be the result of a single sample. Maybe that is all there is too it, I am the only thing that gives zero or one, or any integer, special meaning in a continuum. I think I needed some reinforcement to assert that giving zero and one any special meaning in a continuum of chance and that I shouldn't do so as they are all naturally as common.
(1) That's right if you cross out 'and only if'.  Poirot can be sure that there's a murderer on board the Orient Express without being sure who it is. (But I should remove the '*only*' from my answer) (2) Yes.
Without additional assumptions about the joint distribution of $z_1,\\ldots,z_{n-1}$ (namely, that they are multivariate normal), the linear combination may be non-normal.
@powerbar My second answer explains precisely how increased sample size reduces the variance of the estimate.  So you can pick n to be large enough so that the variance is smaller than a value you specify as small enough.  In my first answer I showed that taking n>4/(0.001)$^2$ is a number that can be used for a binomial response variable.  In other cases σ$^2$/n is the variance of the mean.  So requiring it to be less than c means taking n> σ$^2$/c.  like in the case of the binomial if you know an upper bound on σ$^2$ you can use that to get n.
http://stats.stackexchange.com/questions/2715/rules-of-thumb-for-modern-statistics?rq=1
"*I wanted to verify if a normal approximation to these densities gets better as the n increase.*" -- thanks for the clarification. The answer is -- no, the distribution shape is unchanged by dividing by a constant.
Yes this gives a single overall p-value.  If you only look at the individual p-values after finding this overall one significant then that at least gives a protected test.  Are you interested in finding if x1 is significant beyond the contributions of x2?  Or finding which of x1 or x2 (which are correlated and therefore the one that does not cause the outcome will still show significance due to the relation with the other) causes the outcome?  Or some other question?
Thanks for the suggestions. I have never worked with SVM before but I wil get started on that. I have tried to look at both sets useful and not_useful questions to see if there is any pattern but it looks very random to me. Im still playing around with different features to see if it can improve the classifier.
Thank you very much. I find the concept very interesting, but it took me a little while to get the idea, and am not fully comfortable with it.
So what you suggest is that I stack the two datasets together and code an indicator variable that works like a moderator, if I understood your question. So as coefficients for the regression I would use $ind_0\\,\\times\\,X_i$ + $ind_1\\,\\times\\,X_i'$ using as $X_i$ and $X_i'$ from control and study, respectively.
But your question was not answerable as it stood, since it relied on a false premise. The only correct response was to address the mistake and hope the question was edited to ask something else. Indeed, given your response to Aaron's explanation of your misunderstanding, it would have been dangerous to respond to your question (assuming anyone was able to guess your intent) until the problem was clear.
It was indeed the source of the difference. I talked a bit with one of the statsmodels devs, and I think the updated version (I can't remember version numbers, by now!) behaves as R does---i.e., it calculates the correct R^2, given the model.
@Student T I am talking about t-score to find estimated standard error when we don't have true population parameters (standard deviation and population mean).
There is no universal method for all functions, so the more you can say about your function and its domain of definition, the stronger the answers will be. (At one extreme, when the log-likelihood is convex and is defined over a convex region, any local maximum will be a global maximum; at another extreme, almost nothing can be said about discontinuous functions or even continuous functions with non-compact domains.) For functions that are sufficiently smooth, plotting is usually worthwhile, as exemplified by the discussion at http://stats.stackexchange.com/a/7629.
I think what John has shown very nicely here is that LDA for two class uses a single line to separate the classes.  But in the example good classification requires two lines which is done in a three class problem.
(+1) good and a very fundamental point.
I'm pretty sure I just reformulated the math to something equivalent, but feel free to revert if I missed something.
I doubt he 'heard' you, Subhash, you have to use "@chl" in order for him to be notified. However, you should be able to fix your accounts without his help; try reading [I lost my password; how do I reset it?](http://stats.stackexchange.com/help/reset-password) & [I accidentally created two accounts; how do I merge them?](http://stats.stackexchange.com/help/merging-accounts).
I believe Tom Reilly is suggesting to provide a more precise description of your data, or a snapshot thereof, in order to get more insights of its peculiarities.
Related: http://stats.stackexchange.com/questions/6538
Please clarify the question. What you show as ":data" are just numbers, without an indication of which ones come from different samples -- or, for that matter, whether some of them are the "another numbers" you refer to. It'd also help if you showed more concretely what those other measurements are. It's all pretty nebulous as stated.
It is impossible to tell with the information given. Are other variables involved in the stock return model besides GDP growth? What are the range and distribution of GDP growth values? Does the stock return model accommodate a random component in its explanatory variable(s) or not?  What are the estimated coefficients in the stock return model?
"Error terms" is in the plural: they are a realization of one *multivariate* random variable, if you like. If you don't like that point of view, then you must view them as being realizations of multiple separate random variables (which might or might not have any properties in common).
"we can have 0% confidence in rejecting the null hypothesis" ... this is not the meaning of either an attained significance level or a p-value. Please avoid this construction.
I am afraid that this is such a simple idea (yet *not* trivial) that it might have been rediscovered many times, most likely even without being explicitly highlighted -- thus you are rather looking for the first work which introduces the term "Naive Bayes".
+1 Thanks for the link to Penney's game; more sleepless nights :)
It would probably be better to write $\\sigma \\lt 0.0763$ or  $0.0764$ rather than using percentages
It's right in that case, so perhaps you're on the right track; let's make sure you're vizualizing it correctly. What does the likelihood curve look like for that example (in general, descriptive terms)?
@Shusheng I re-read your post in case I was missing something. I would recommend you use the MLE, but not the normal approximation for its CI. You should use a parametric bootstrap for the the CI by fitting a normal to the data (using estimates of mean and variance) and then calculating the upper and lower percentiles of the estimators' bootstrap distribution.
@Macro, I shall check this out. Cheers.
Check out the `glmmLasso` package.
@pmgjones You're welcome.
An interesting change occurs between the beginning and end of your question, Emily. Initially you refer to a "[not] significant effect." That means you could not *estimate* the effect with *sufficient reliability* given the data you have. At the end, though, you appear to use "effect" in the sense of the *true* effect, not its measurement. The two differ in an important sense: the former is your estimate, the latter is real (but unknown). If we now reread your question, understanding the last "effect" in the *first* sense, it may clarify the situation.
I guess using the fitted variogram, the params that I get like exponential model, sill, nugget and range. I can use the exact model to generate a correlation function. They are basically same if I am correct. However, sill in case of correlogram will be like 0. However in variogram it will be like 1
+1: i do the same. But then you have to spoil it saying  that in the real world it was only used at the very beginning and google's success was more about its ability to scale  (i.e. engineering) than math ideas.
I'd argue that the intercept is not an **odds ratio** but rather the average **odds** and only the coefficients ($\\beta$'s) are **odds-ratios**. The $\\text{(Intercept)}$ gives you the average odds (after exponentiating) and when you add the log-odds ratio of e.g. $\\text{period1}$ to the log odds of $\\text{(Intercept)}$ and exponentiate this sum then you have the **odds** for $\\text{period1}$. I think that it is important to really keep **odds-ratios** and **odds** apart. The former is a ratio between odds the latter are the odds of success vs. failure (in a binomial model).
Stationarity is a "non-parametric" concept, it does not depend on any specific distribution. Random walks are non-stationary whatever distribution their building block white noise (what you call the "error") follows - and their first difference is stationary likewise.
We had a follow up to the 1991 paper here: http://www.ncbi.nlm.nih.gov/pubmed/19266502
The $p$-value is always related to a hypothesis test. What is the null hypothesis ?
Doesn't SO have a SAS section? I thought SE was for theory.
alpha correction definitely makes the list for "ritualistic substitutes for thought" in statistics. If good theory & hypotheses are guiding one's statistical testing, then alpha correction is unnecessary for reasons @John says. Without theory & hypotheses -- if one is just fishing in the data -- alpha correction *doesn't* help to make the inferences one is drawing any less fishy (a point that is consistently ignored in the booming fMRI-study industry: http://prefrontal.org/files/posters/Bennett-Salmon-2009.pdf)
+1. But not least fact is that the numerator is the same. This implies that both coefficients are just different ways to standardize the raw regression coefficient _b_.
It is more appropriate to use SS, not MS.
There are also many posts on this site dealing with the definiton of confidence intervals and a recent one in particular on teaching about confidence intervals to graduate students in statistics. So if the OP doesn't know the details about how to generate confidence intervals, therre are plenty of places to find out here as wellas in wikipedia.
Actually, it's more related to law of large numbers than central limit theorem.
@Kasper I understand.  I just thought that was the clearest illustration I could give of my problem/question.  Hope it doesn't keep you from answering (if you can).
As you can tell from @Glen_b's comment, we are sympathetic.  But what is needed to re-open the question is an edit to the question itself that clearly differentiates it from the apparent duplicates.  Do you think you could identify a little more specifically what your problem is?  I think most would-be answerers would struggle trying to respond to the query concerning "how everything fits together," especially because CIs have been described in such detail at so many different levels throughout this site.
Try looking at the Chinese restaurant process representations of them.  For me, at least, those representations provide a lot of intuition.
If I understand your question, it is something like this: I know how to conduct a paired *t* test on *A*. But I want to perform this test on *B*. But *B* is sometimes meaningless. **What is the standard way to do this?** I won't speak for the rest of your audience, but I have no idea what statistical question you are asking. :) Standard way to *do what?* Can you expand a little bit?
Whatever probabilistic assumptions there exist *results* for. I do not have any assumptions except "the data is not uniform". I added the "nearest neighbor search" 1 hour ago already.
@Gavin Simpson. Actually, the problem with my example is that most of the time is taken in the apply part to compute the maximum. I agree with you that a c-based vectorized function like `rowMean` is going to be hard to beat via a general-purpose R tool like `*apply`. However, you seem to suggest that it is faster to sum 10000 numbers *twice* via `rowMean` and `rowSum` rather than only once and use R's builtin division operator. I know R has some efficiency issues (_e.g._ the recent discovery of the curly braces vs. parenthesis issue), but that seems crazy.
Thanks Trey.  It looks like there's no support for Tweedie, but they do have some discussion of Poisson and Gamma distributions.
@user59419 : Yes, x1 is the data behind the red histogram on the image you posted, x2 is the data behind the blue histogram (or the other way around).
I'm confused how the example you give is a "data-visualization" at all, do you perhaps have a screen shot where the values very between the spokes?