tttjjj/elt_bench huggingface dataset:
@Adhesh, all of your last 4 or 5 questions go round in a circle. You seem to have stumbled on something. What might it be? What is the aim of your study, after all? If that is `to see if the relationship between A and B is affected by gender` then the significant interaction showed you that.
There's a Welch-Satterthwaite adjustment for ANOVA, just as with the t-test. Some packages offer it, I believe. I can't say that I recall having used it.
@Procrastinator, when you're playing poker against other players (not the house), you could certainly have the odds in your favor if your skill greatly exceeds their's. The odds could even be so far in your favor so that they negate any 'rake' the site takes from the pot. How do you think professional poker players consistently make money?
@Gerenuk see my edits
@ Anthony Damico,  I have checked *tab [stratum]* and *tab [clusters]*. I also have checked a cross-tabulation of stratum vs cluster. Everything is fine there. Unfortunately due to space limitations, I couldn't include the *tab* outputs here.
A somewhat interesting relevant paper: http://harrisschool.uchicago.edu/sites/default/files/Bilger%20Manning%20-%20Measuring%20overfitting%20and%20mispecification%20in%20nonlinear.pdf
Thank you @Aghila +1 if I had more rep, I think that makes a lot of sense. However, if you could tell If I were to report the 2 means for `z` and  2 slopes for`z` in your `m4` what they would be? So I know I am subrtactingadiing the effect sizes in the correct way.
@MichaelChernick, you've got me, actually. I simply did cor(x,y) in R, which returns a value (and also chooses samples that discriminate between groups, as it turns out). I suppose I should calculate the cosine of the angle between the two vectors? Or use Spearman's rank correlation?
1. Having identified the clusters.. I am working further on the results obtained.  I am not testing the most important predictors of the cluster analysis.
2. As to the Mann Whitney as not being an alternative in comparing means, I followed Field (2009), in a chapter on comparison of means. He is suggesting using Mann Whitney as an alternative when the normal distribution assumption does not hold.  As to your seventh question, yes it is two clusters.
@MattAlbrecht This is exactlly what I was looking for. Thank you so much!
If you run ANOVA with 8 groups and and ordered to perform multiple comparisons on them it will be all 8 groups.
Someone tag this with R
Am also facing the similar problem. Could you please provide the script for Weighted Random Forest and Metric based random forest, if you have?? Looking forward for your reply
You have both types of measurement (from the device & self-reported) on each individual?
Indeed, in my specific problem the number of predictors is large enough for this approach to be rather inconvenient. But more than mere inconvenience, I think treating non-existing cars as missing data is supplying somewhat misleading information to the classifier. 

The bag-of-features approach that I mention below is one idea but I also heard that some SVM kernels can naturally incorporate variable numbers of features. Is this correct?
From your description, it looks like y = -0.1x, so no transformation needed. Or have I misunderstood?
You will probably need to test each question separately by gender. Are the questions independent of each other? Or, could the answers to certain questions influence others? You can look at the correlation between questions separated by gender as well.
+1 Nice explanation (especially that introductory one-sentence summary). The link is interesting. Since it has no archive on the [Wayback machine](https://web.archive.org/web/http://creatorguides.com) it likely is new. Because it so closely parallels my (three-year-old) answer, right down to the choice of red for positive and blue for negative relationships, I suspect it is an (unattributed) derivative of the material on this site.
@Srikant: The tree would likely require far less RAM than caching the entire dictionary to begin with.  Are you really concerned about a few megabytes of RAM, anyway?  BTW, there's only one tree, not many: they are all rooted at the empty word.  Your approach, as I have understood it, requires multiple searches of the dictionary (up to 7! of them) on *every iteration*, making it impracticable as @shabbychef fears.  It would help if you could elaborate on the algorithm you have in mind where you write "see if you can form a word": that hides a lot of important details!
If your cost function increases as you train, your learning rate may be too high. If your cost function increases when you train with a low learning rate, and you aren't doing something like stochastic gradient descent, then you probably have a bug.
@user603  See my answer below for cut-and-paste code fragment to read in his data.
Can't these integrals be computed exactly (symbolically)?  That would solve the problem of coping with Monte-Carlo integrations.  Iterated integrals of these inverse logit functions can be expressed in terms of exponentials and polylogarithms.  Barring that, why not use an adaptive quadrature (numerical integration) routine?  For the bisection (or any root-finding) method, you only need to update the integrals, which involves integration over small regions: that ought to be quite accurate and fast.
Are you asking about an explanation of matrix notation?  The reason I ask is that this question doesn't need any mathematical derivation: all your formulas are saying exactly the same things and relating them to one another is just a matter of understanding how matrix notation works.
Could you tell us something about the evidence you have of nonlinear relationships? In many cases a little bit of nonlinearity won't matter.
Wow that is a wonderful one-liner! However, I've just edited my question - I've now mentioned about the weights. I do in fact need 2D weights, of the same shape as the response vector `y`. I'm still new at python, but in the second block of code that you gave, I understand you've used 2D weights?
@abaumann At first view it looks like mixture models are more than I need. I'm surprised there isn't a simple answer to this question. Isn't this a common problem? Covariates can loose their predictive power for certain values, i.e. when they tend to 0. Thus for $\\hat{Y}$ close to 0 we should have larger $\\beta$ confidence intervals.
Ah cool! Sounds like there are some useful paths to explore. So little bit of context - the data arises from a simulation exercise where users are given a budget of say £10 and a menu of prices for different items.

From each 'market' we assume their choice is their optimal bundle and we use a generic utility function = U = alpha(ln(x_1))+beta(ln(x_2)...etc. for k=7 items to compute their relative weights for each item. That is, the solution can be represented by the 7D unit vector; magnitude is irrelevant.

I'm trying to see if men and women differ systematically in their preferences.
Even further, Bayesian hierarchical models rely on this kind of information sharing through the parameters of priors as a way to reduce variance in parameters where there is not a lot of data being used.
(1) Yes, good catch.  I fixed that typo.

(2) We're really looking at *second* derivatives: the increments d[j,i] = h[j,i+1] - h[j,i] act like slopes (and are slopes when times are equally spaced).  I am proposing to distinguish "exponential" from "sublinear" behavior in terms of changes in the slopes.  Whence we want to consider the signs of

d2[j,i] := d[j,i+1] - d[j,i] = (h[j,i+2] - h[j,i+1]) - (h[j,i+1] - h[j,i]) etc.
@whuber I think this is a good advice, but thats my problem: in the journal I want to publish my paper there is no guide for this kind of questions and I don't know an article in this journal, where asymmetric uncertainties are given (it's something like engineering, not statistics).
Can someone explain why this answer was up-voted?
(+1) I think the RHS of the second equation needs some more negative signs though!
Welcome to the site, @nikki0111. Are you thinking of this as a conceptual statistics / psychometrics question, or an R programming assistance question? I'm not sure, but I wonder if it is the latter. If so, this question would be off-topic for CV (see our [help page](http://stats.stackexchange.com/help/on-topic)). It *could* be on-topic on [Stack Overflow](http://stackoverflow.com/), but it would need to have a [reproducible example](http://stackoverflow.com/q/5963269/).
You should be able to double the values of all your angles and use standard circular tests.
The most straightforward way to do this, I think, is by maximizing the (log) likelihood of both samples in a single call to `optim()`. Optimize the likelihood when s1=s2, and then see how much better you do without this constraint. Twice the difference in log-likelihood will have a $\\chi^2_1$ distribution, for large samples, if the values of s are actually identical. (See any text on likelihood ratio tests)
One example: http://stats.stackexchange.com/questions/4768/amoeba-interview-question
Choice #1 is not an improper prior.
I don't see an enormous benefit in simply copying & pasting one of your existing answers, in its entirety, into a new thread. Instead, you might leave a comment to the question w/ a link to where you provided this answer, or make a brief answer w/ some relevant comments & add a link to the answer stating that more information can be found there.
I'd say IF you plot 3 axes make the plot interactive (e.g. with scatterplot3d), otherwise it's hard to decode. Also 3rd (or 4th or 5th) dimension need not necessarily be color, it can also be shape or size (or even something else like facets or transparent overlaid different geometric objects, if you really want to get fancy).
@mark999 I...just don't like most plots made in ggplot2. Essentially I think the message people have come out with is "ggplot means pretty graphs" when it should have been "thinking actively about how you visualize things means pretty graphs". A busy, unclear plot in ggplot2 isn't any more useful.
@whuber, But Defn 1 doesn't use relative likelihood, only probability under the null.
+1, how does this generalize to where there are more than two values: exp(A_1)/(exp(A_1)+...+exp(A_n))?
the answer hinges crucially on whether or not the mean vector and covariance matrix used to compute the MD have been estimated from the data on which the MD's are computed.
Aren't confusing "date fields" with "features"? If I understand well, you have few text fields that will be converted into features using bag of words. If you have more text fields, you can choose to mix them or have separated bags of words.
Then for the combination, of course it can be extended to more features. You will have more weights to define which might be longer but sometimes, basic values (every weights at 1) just to the trick.
The tests can be useful, but be careful because the p-values will be partly dependent on sample size.
"best" in what sense? Note also that any method based on fitting the tails would require a  moderate-large sample size. If you just want to fit the distribution using MLE, then you can use the command `fitdistr`.
I'm skeptical about this interpretation and also about the conclusion that logistic regression must be used when modelling percentages. Seems to amount to saying "we can't model at the student level, only at the school level." Which, by the way, seems to argue against @GaBorgulya's interpretation, neat as it is. I'd like to hear from other people more experienced than myself.
I am conducting unit root test for the first time.
Is it okay to have a p value =O. 
Also in a different case I am having a p value = 1.0000. Is that alright?
@MichaelChernick: I know your edit was very well-meaning and I appreciate it. However, editing out a potential factual error can drastically change the question meaning and interpretation. My experience is that these errors are often highly correlated with the questioner's actual question and misunderstanding. I believe that may be the case here, hence caution is advised. See also: [Should I edit a factual error?](http://meta.stats.stackexchange.com/questions/1263/should-i-edit-a-factual-error)
Indeed, it makes quite sense that it's accelerating over time with a greater speed than linear one.. I guess I'm going for the cubic fit
This isn't what you want, but my best one-sentence summary is that few deep thinkers on statistical inference have been sure that they knew what Fisher meant by "fiducial", and not a few have suspected that he was obscure largely to hide the extent to which he agreed on fundamentals with others who he had decided to dislike on principle. (By the way, I am a fan of Fisher, on the whole.) More importantly, I don't sense that it _does_ function as generally understood terminology: it's a term widely avoided, except in historical discussions. (I am not a professional statistician, FWIW.)
As I've commented on your previous question, you shouldn't believe SVD when your cov matrix is not positive simidefinite. Because negative eigenvalues (returned by SVD as positive) do matter, still, they can't be interpreted as explaining real variance; rather, they explain the extent to which the data do not converge geometrically in euclidean space. The overal variance (trace of cov. matrix) is split into real, substantial variance (sum of positive eigenvalues) and "imaginary" anti-variance (sum of negative eigenvalues)
@mpiktas - thank you for the comment. I am digging deeper.
We don't often say it, but technically the p-value is only reflecting something about the "probability of getting a test statistic at least as extreme as the one we got in the sample" if the null hypothesis is true, our sample estimate of the population variance is perfectly accurate, and we meet all of the other assumptions of our test.  Throw some confidence intervals around some p-values via bootstrapping and I think you'll see that frequently we aren't all that confident about the hundredths place either.
I don't entirely follow your question. You may find it helpful to read this blog post: [how to ask a statistics question](http://www.statisticalanalysisconsulting.com/how-to-ask-a-statistics-question/). Regarding your question about whether binary responses should be coded as {0,1}, or {1,5}, it will not make any difference--you can try it for yourself & see.
@Dolphi See my updates. For one, you're splitting up test/train the wrong way. Users should be in both the test and train set (otherwise we're not training on any of their ratings).
Thanks,Nick! I understand from your reply that the alternative hypothesis is what matters to my question. But I don't quite understand the following example, in  Fisher's exact test for independence, the count $X_{1,1}$ in the top-left cell has the hypergeometric distribution under independence null hypothesis. I was wondering if it is reasonable to use $|X_{1,1} - \\mu|$ as the test statistic, where $\\mu$ is the mean of the hypergeometric distribution. See my question [here](http://stats.stackexchange.com/q/56773/1005).
I don't know much about what exists for this particular case and haven't tried writing out the equations, but for complex methods, calculating power is often easiest to do by simulation.  Perhaps that would be an option here.
For the reference of future readers, I expand on this geometric answer (with pictures!) in the following thread: http://www.talkstats.com/showthread.php/49357-geometric-argument-for-constraints-on-r_xz-given-r_xy-and-r_yz
Hi Ben: so, if I got you right, it saves me one step of work, right?
Often times the "best" approach is not the most *sophisticated* model but rather the *simplest*. Why don't you start with a regular, run-of-the-mill ordinary least squares regression and then go from there (i.e. use **acf()** to look for autocorrelation, etc.).
Sorry, in your case, it refers to the anova.negbin(), which is doing the likelihood ratio test. (I have changed the answer). So the function is suitable for your negtative binomial model, but the concept is a deviance test rather than a classic anova. (i.e you are not doing a classic anova now)
Yes and no -- this is a different order of magnitude. I would rather say that $M_i^2$ is the scaling parameter for $s_i^2$. Let's say we are measuring $y$ in days. Then $t_i$ is on the scale of years if we have hundreds of observations per cluster, and so $V(t_i)$ must be on the scale of years ^2. $s_i^2$ is only on the scale of days^2, as it is per-observation variance, so $M_i^2$ brings it up to the scale of years^2. Design-based calculations only have the randomization intuition, which may not be particularly relevant here.
Thanks! I have made those changes and it seems to work much better!
Compare the first sentence of [Estimator](http://en.wikipedia.org/wiki/Estimator) vs the first two sentences of [Statistic](http://en.wikipedia.org/wiki/Statistic).
I do not fully understand this answer. I imagine many astronomical datasets (as well as many other small-dimensional datasets) do not come with intrinsically meaningful coordinate systems. Thus your claim that the points are "ordered already" would be invalid in such circumstances. It could be rescued if you were able to show that the KS statistic is *independent of the coordinates used to identify the locations*.  I don't think that's true in two or more dimensions, but I could be mistaken.
+1 for lattice, you're old school homie.
Cross-validation is one option.
Dirk, unfortunately aggregate did not solve my problem, as I want to resample at essentially the same number of points of the original trace. However I found the `reglin` function in `pastecs` that does exactly what I need! http://rgm2.lab.nig.ac.jp/RGM2/R_man-2.9.0/library/pastecs/man/reglin.html
You seem to be mixing up "observation" and "variable"; read the second italicized paragraph, which switches from talking about a "single observation" to describing it as "such a variable".  You might want to clear up the terminology so we are all on the same page as to what refers to what.
Wait. Or rather Weight! Is the question about the number of each types of nuts in the bag (in which case the chi-square will do the job as Macro explains) or about the weights (as the original question seems to imply)?
Have you read the Stata help page for the regression procedure you're using?  Near the bottom of each one is a list of "post-estimation commands"; the `predict` command is usually applicable.  As an option, it will create a variable of residuals.  Calculate its absolute value (use `generate`) and you're all set.
I would second quantile regression, but be careful to not go into the very extreme quantiles. If the larger values are qualitatively different, my suggestion would be to use a finite mixture or latent class model.
Almost the same question is currently being pursued at http://stats.stackexchange.com/questions/19470/violation-of-normality-assumption.
@vulture No worries!  In general, indexing in python starts at 0.  Some other languages (such as R) start at 1.
My main issue would be how you avoid giving them just enough knowledge/tools/status to make them dangerous? You know, the "I got a good R-squared, so this must cause that" kind of thing, which can be misleadingly persuasive to those who don't even know what R-squared means.
"The classifier is an ensemble model (such as random forests), it likely refers to a bagging approach". I'm not following your explanation here. How are they bootstrapping *the model* exactly? Or are they simulating data from this prediction model in some way?
I would strongly suggest not to use this approach, especially because specific functions for variable selection exist, such as the `stepAIC` function in the MASS package. See [the Quick-R page on multiple regression](http://www.statmethods.net/stats/regression.html) for examples.
It would help to clarify what you mean by "could be used". And perhaps clarify any specific case that you may be interested in.
So you're recommending the following interval $(\\hat{\\theta}-\\hat{t}^{(1-\\alpha)}\\cdot \\hat{se},\\hat{\\theta}-\\hat{t}^{(\\alpha)}\\cdot \\hat{se})$. Is that right?
AWESOME! thank you so much!
Adhesh, I am pleased to see you are learning from the questions you have asked here.  The initial set (several dozen of them, as I recall) appeared to focus *entirely* on the computational ritual of hypothesis tests to compare correlation coefficients.  You might enjoy reviewing those early questions and the reactions to them, to see how far you have come.
(+1) whuber. Profitable bookmaking is an accounting problem rather than a statistical problem.
@MattBagg This is actually data from physics.SE so let's assume it is people who understand data and can make sense of visualizations of data. The goal is to show interesting trends of the data across all decades.
My answer apply to any conceivable kind of test or experimental design. It's the idea of looking at the *observed* effect size and concluding that you had low power to detect that particular effect size that is wrong. You can however look at the effect size, notice that it could be practically significant and conclude that your study was insufficient to rule out such an effect. No need for any power analysis for that.
The vignette is deceptively simple; in practice I couldn't figure out how to apply to new data. So I wrote my own code, linked below.
Do you know the source for that Tukey quote? I see it on Wikipedia, but it is unsourced.
I don't think that the LearnR blog has any time series references...
Based on your comments, it seems the longitudinal data is a set of multiple time series data collected from different subjects?
Hot deck imputes based on categorical or discretized background variables only. "Deck" is the pool of donors which are similar with the recipient by some categorical background characteristics. From those donors you select one randomly.
Does it seem better now? I have seen even more general questions asking for a broad comparison between L1 and L2. I practically ask for a comparison between L2 and stepwise LogReg applicable to my case.
(+1) Your comment is almost exactly what I was about to write!
If you are using average-linkage, then that would be $0.25(d(9,8)+d(9,10)+d(11,8)+d(11,10))$, where $d(a,b)$ is the distance (correlation distance) between instances $a$ and $b$.
sparse data matrixes
Calculate the CIs for all 3 and look at them. Though, is it possible you're interested more in something like a regression coefficient than the correlation coefficient?
@CSgillepsie:> thanks for the pointer, but i'm not sure it's the same problem: the way i understand the question you pointed to, all the processes are spawned by mclapply. Here it's a bit different: on each of the machines, all the processes are spawned by mclapply, but this is not the case *across* machines.
+1 Thanks. Seems alright. When I read the Wikipedia article, I seem to have missed the fact that Boltzmann theorem applies for all closed intervals. I had assumed it applied only to variables going from $-\\infty$ to $\\infty$.
(+1) That is an excellent answer and addresses nearly all the main points that one would wish to know. It is fortuitous for the OP that you've specifically addressed his concern, as well. There is *one* point that has appeared here repeatedly that may, or may not, come up in the DSP community. Several times here, I have seen people make the statement to the effect that *because the mean and variance are constant in time*, the process is wide-sense stationary. While the converse is true, the one stated is not; ignoring the invariance of the autocorrelation seems to be a common misunderstanding.
You should probably flag the question with the 'self-study' tag and explain your attempts at answering for better results.
Stepwise regression has been widely discredited.  What about your situation makes you think it works correctly?