tttjjj/elt_bench huggingface dataset:
Thank you @rolando2, good to know. I'll set aside any concerns I had about multiple comparisons. I've already plotted each correlation to view them prior to determining the Spearman's rho, and yes, despite what I thought was a fairly high rho of 0.64, the paired points are surprisingly scattered (can't figure out how to stick the graph in here). However, for Spearman's, I thought squaring wasn't 'allowed', and that that was reserved for Pearson's only? (I'm using Spearman's because most of the data do not fit parametric assumptions.)
I've actually had four ;)
It was taken from Mike West's website: http://www.stat.duke.edu/~mw/fineart.html
The way you have described this problem is incredibly confusing. What are you trying to classify and how are the nodes/edges related to this classification? Are the paired relations relations between features or individual datapoints that are all defined by the same features (variables)? Some sample data and desired/anticipated results might be illuminating.
In this run, this is superficially true. But I know (since this data is from simulation) that there is a supply function that $f_t$ tends to with some delay.Thank you!
It is unclear what you are asking: could you be specific about what you mean by the "typical way of doing this" and exactly how it "breaks down"?  And, as a matter of clarifying a possible misinterpretation, is an "upper bound of the error on the mean" intended to be an upper confidence limit for the standard deviation of the sample mean or is it meant as an upper confidence limit for the mean itself?
@qoheleth You are right. Actually, I wrote it that way because I tough steph is interested in the effect of genetic, but your point is important.
As, arguably, a machine learner, I'm here to tell you we maximise the heck out of likelihoods. All the time. Loads of machine learning papers start with "hey look at my likelihood, look how it factorises, watch me maximise". I'd suggest that it's dangerous to claim a fundamental basis of either discipline in terms of inference techniques. It's more about which conference you go to!
I thought that the t-test was for _normally_ distributed data, with unknown standard deviation, and gives you an exact test (or _confidence_ interval), whereas the z-test is for _approximately_ normal distributed data, and gives an approximate test (or confidence interval) -- or is this saying the same thing as your answer but in a different way?
I looks to me like you should only need 3 guesses, one for when each of $H'$, $M'$ and $L'$ is largest.  But, I may simply misunderstand the question.
Group and game type are identical so you can drop one.
@Dilip There *are* estimates of standard deviation, often called "pseudo SDs," that assume approximate normality.  One is the IQR divided by 1.35.  Another is half the difference between the 84th and 16th sample percentiles.  A deeper question lurking here is whether an estimated SD is an appropriate way to measure variation for a strikingly non-normal distribution.  (Another issue is the implicit, but incorrect, assumption that positive values cannot be adequately modeled by normal distributions.)
I don't totally understand it, but in a model I am creating in R, I have something like lm (a ~ b / c - 1) which creates interactions between b and c, and by suppressing the intercept ("- 1" in R), I get more easily-interpretable answers that are essentially the same as if I don't suppress the intercept. Somehow, the interaction makes this possible.
OK, let's compare medians. To resolve ties, use two natural principles: (a) *dominance*: when every value in set X, when ordered, is greater than or equal to corresponding values in Y (when ordered), X is preferred; and otherwise, (b) *consistency*: lower variances are preferred.  (b) implies 2244 > 2335, (a) implies 2335 > 2334, and (b) implies 2334 > 2244 (all have a median of 3).  This partial order is not transitive!  What you're confronting here is a [voting paradox](http://en.wikipedia.org/wiki/Voting_paradox).
Neither good nor bad -- read the [FAQ section about bounties](http://stats.stackexchange.com/faq#bounty).
Ask another way - why use fill if it is not necessary? Imagine you want to add another trend line and things get unnecessarily complicated. I would also separate y-axis' unit (s) and scale.
Thanks that got me on the right way and i was able to solve it!
If this is a homework (or self-study) question, you should add the `self-study` tag. See http://stats.stackexchange.com/tags/self-study/info
I believe equal variance is assumed. At least, they did not report any adjustment.
See http://lme4.r-forge.r-project.org/book/Ch2.pdf for an example of cross classified random effects.
@Ho1 Applied Time Series Analysis For Managerial Forecasting by NELSON ; Holden-Day 1973 pp162-165 discusses this in detail ... with a diverse opinion
The *theoretical* solution is to use a randomized test. However, *practically*, many find that somewhat unpalatable.
...and, in the case of fixed $X$, then this essentially becomes a hypothesis-testing problem. :)
I don't see any other answers here, which is a pity, since the question is interesting. I will like to take another thinking on the matter. Can you please clarify/verify the data series which comprise your sample?
Hi! Thanks for the hint! I am trying to predict the prices for different objects based on the properties they have (e.g. size, location etc.) independent of the time the sale took place, so it's no time series.
@AlecosPapadopoulos You have sent the reference - I would like to award the bounty to you. Can you somehow make it an answer?
What are you actually trying to do? What is your research question or hypothesis?
my question is related when we are describes properties in general, where no concern of data.
It's not like I have the answers to crosscheck them with what I get, so that's why I put it here. You are the teachers :)
@Mancel Don't indent your formulaes; otherwise, they will be rendered as verbatim (`<pre>...</pre>` in HTML). See [here](http://stats.stackexchange.com/editing-help) for further information on Markdown formatting.
I migrated this question because many very like it have been addressed here on CV.  See what you can learn from a [search](http://stats.stackexchange.com/search?q=[multiple-comparisons]+benjamini), for instance.
I flagged for migration.
+1 @JeromyAnglim - a thorough perspective throwing light on the various aspects of the problem. Kudos!
SPSS will create the dummy variable for you. If you add the interaction it will also create appropriate codes. However, I am not an `SPSS` expert, so I can't provide details. Perhaps someone else here can.
Based on these data, if some statistical test showed that material A and material B were different, would you believe it?
Great counter-example as to when the standard deviation is not the best way to think of fluctuation sizes.
I ended up calculating the slope for linear regression of the two timeline; once done so I compared the two slopes with a t-test and obtained my result
How can I narrow down priors of variances while I'm using Wishart Dist.? The `cov[1:2,1:2]` is an identity matrix and I set df of Wishart Dist. as 2 because of the dimensions of `th`. I completely agree with you about trickiness of BUGS models.
Thank you!! This was really helpful.
The probability you will observe a red ball on the next draw is always the same: it equals the proportion of red balls.  Are you perhaps asking how to update an *estimate* of that probability?  If so, you are either performing a Bayesian analysis (whose answer depends on your prior probability distribution for the proportion in the urn) or a non-Bayesian analysis (which, depending on its form, can yield a "fuzzy" probability or a "p-box" or a host of other non-probabilistic representations of your uncertainty). In any case, this question is unanswerable without more information.
"Power" has a very definitive meaning in statistics. Like many statistical terms, it is also an ordinary word so it is easy to get mixed up and apply non-rigorous definitions when in fact "power" in statistics is rigorously defined.
related: http://stats.stackexchange.com/questions/4258/can-i-semi-automate-mcmc-convergence-diagnostics-to-set-the-burn-in-length
Can you define what you mean by precision and recall? Usually accuracy, sensitivity (per class) and predictivity (per class) are calculated from the confusion matrix.
A chat room has been created for comments to this question at http://chat.stackexchange.com/rooms/3720/discussion-between-manst-and-michael-chernick.  I have deleted all (50!) comments and locked this post to prevent further abuse of the commenting mechanism.
@Glen - There are many things to think about other than statistical significance.  See [this](http://stats.stackexchange.com/questions/10510/what-are-good-references-containing-arguments-against-null-hypothesis-significanc/10511#10511). Better to examine your overall model fit (plot your residuals against your predictions for each model you fit), your theory, and your motivations for modeling.
If this is for homework or a class assignment please add the `self-study` tag. If it is for anything else, I suggest hiring a statistician.
Welcome to the site, @IvanDiaz. It might help if you stated what language the `tmle` package is for, perhaps a link to more info, & where to get it.
Do you know some other inequalities? Do you know the definition of convergence in probability?
this question is not really about implementation, but the theory behind it
That's an excellent recommendation (+1).  The special value of the graphic that has been posted--even though it does not reveal the distribution--is that it shows the inter-arrival times are not stationary.  This suggests that the requested univariate analysis of their distribution will be uninformative or downright misleading.
Been digesting this a bit and figuring how to apply the mutual information formula. It has me on the track of creating contingency tables, which has helped clarify things, I think. I appreciate the help, and will "check" back as I get it implemented.
"*I thought that "time to event" random variable follows a geometric distribution.*" -- you have overgeneralized. Some 'number of trials to event A' variables have a geometric distribution, but many other distributions occur (e.g. 'number of trials to the second success in Bernoulli trials' is not geometric, but negative binomial). When you seek several of the same event in a row you generally don't have a geometric.
Although, it did do a better job of predicting defaulters.
We are grouping our stores into blocks/bins by their click-through rates (CTR). That way we can look at the distribution of stores based on a "small" amount of BINS instead of 10,000 stores. This way it will be easier to compare distribution. So thinking of the data like a histogram, the BINS on the X axis will be groups of stores with a similar CTR. The Y axis will be counts of visitors in those BINS.
@rje42, they are extremely large due to the range in the sample. However, region data is not standardized. It is simply 0 or 1.
Keep in mind that while the H0 is specific the H1 is very vague.  The alternate is essentially, what's left when H0 is gone.  When I say you can't prove the H1 consider how convoluted the logic really is here.  The statistic you calculate is the probability of the data *if* the H0 is true.  If you decide that's too low to believe H0 you then discard H0.  But wait, now you have a statistic that means nothing because you've decided H0 is true and you're left with little to stand on to argue *for* anything.
They'll probably just be parameters (constants) that need to be estimated from the data, and then the estimates of the constants are used to project the curve past the red line.
Okay in what sense? Your question is too vague. Statistics is not some priesthood where we can either declare your actions as anathema or as sanctioned - and even less so without context - it depends on what you're trying to achieve and what characteristics of the resulting analysis are important. Such data-dependent actions can certainly have *consequences*, but if those consequences don't matter to you, you may well regard the result as 'okay'. On the other hand, such a choice may impact your results in ways that matter to you deeply. How could we tell? You don't give anything to go on.
This question does not need the CLT, nor does it require any approximations or asymptotics: it has an exact answer.
Given your explanation, I don't think the part $if(y<fx)$ is wrong. But if your intention is to implement rejection sampling (which appears to be the case), then you need some more work. Can you clarify why you think that part is wrong?
(+1) There seems to be some additional information on this thread: http://forums.spss.co.in/forum_posts.asp?TID=193 (can't check myself).
@jjepsuomi yeah, I saw it after posting it, so I deleted it again, but thanks! Youre welcome.
Doesn't `MatchIt` integrate well with `Amelia II` to do multiple imputation?
Your interval is generated assuming $\\hat \\theta$ is normally distributed. In this situation it's not remotely normal, so the interval isn't useful. Read about [binomial intervals](http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval)
You've captured the trend over time. So if that is your goal, the analysis is good. (the trend here appears to be linear) If you wanted to provide predictions then you'd need to capture some of the cyclical nature of data. You can sometimes do that with dummies, but I don't see a clear pre-specified way to build them. Unless this cycle is well known/described? Given that you'd likely need some time series methodology, smoother or ARIMA. That is fairly painful. So depends on your goals, for many/most this may well be fine.
@Xi'an: I am not claiming one needs to mention the Bayesian perspective, but rather that I find it transparent to do so. This gives a bit of an expansion on why I think that http://stats.stackexchange.com/questions/7455/the-connection-between-bayesian-statistics-and-generative-modeling/40524#40524 But as David Cox once said transparency is in the mind of the beholder.
@Procrastinator: when $\\mu$ is known (as is the case here), the estimator proposed in the answers is unbiased. The $n-1$-estimator is unbiased when $\\mu$ is estimated.
Expected value with respect to what probability distribution?  ML is usually applied in non-Bayesian analyses where (a) the data are given (and fixed) and (b) the parameters are treated as (unknown) constants: there are no random variables at all.
Mr. Glen, The graph we need is not smooth. We thus need to find the gradient at a given point and later need to sum up. We are searching for a tool for
You lost me at the second paragraph: there cannot exist a single way of re-expressing the values that will make all these random variables Normal unless all the $\\mu_i$ are equal or they were all Normal to begin with.  Perhaps it would help if you could explain why you are looking for such a transformation.
Aha. Because my friend claims that the average monthly family income in a certain country is for example 5000 euro. He argues as follows. The average family size is 4. First we compute the average income per person, and multiply this number by 4. This gives the average income per family.
Is there a particular field in which you want to apply your statistics knowledge (other than "Statistics", of course)? Because you might want to consider that as a tiebreaker. Or, compare the professors teaching the courses--it won't matter how useful the course "should" be if you're stuck with a lousy lecturer (conversely, a *great* professor is worth their weight in gold!).
"Can I add them after I add ship presence and perform the Likelihood Ration test to the additional terms to see if these reduce the deviation?" Yes. That's ok. As for the dependent variable: The integer seconds would be acceptable, if we assumed the time variable in continuous measurement had Weibull distribution. Which is not unexpected.
Even though you link to the help page, I'd probably put a `library(ggplot2)` before qplot as that code will not run in a fresh R session w/o loading the appropriate package.
That really depends on the distribution of the $X$'s. In general,  ${\\rm E}[S_0(t)^{\\exp(\\beta X)}]\\neq S_0(t)^{\\exp(\\beta{\\rm E}[X])}$, which seems to be what you are thinking.
@Michelle, good point. I edited the answer to make the general pattern clear.
I don't think a "ggplot" tag will be very useful here (maybe mods would have a different opinion).
@Nick_Cox, Thanks for your answer, which is very clear to me.
Could not find anything regarding publication bias in the mentioned packages for diagnostic accuracy: mada, HSROC, metamisc, bamdit...
@curious_cat homework tag is [deprecated](http://meta.stackexchange.com/q/147100/182549) on SO, no need for it here either
Can you demonstrate exactly how you plan to use the vectors that you wrote to test contrasts, i.e. the actual code?
@bravetang8: (1) you are right: optimistically biased measures are not a good idea: not for internal optimization because the optimization cannot distinguish between different models which all seem to be perfect. Not for external optimization because in many applications it is better to have a conservative estimate of the performance than an overoptimistic one. But it is good to know whether the internal optimization suffers of the internal estimate being overoptimistic, or whether this is not a problem here.
@QuantIbex. Great, thank you. This answer is definitely useful. I'll upvote when I get the 15 reputation threshold required for this !
@dassouki: No problem!
no longer available ;(
Adjusted R Squared (R2) is within about 0.03 of R2 in all cases (so above 0.837 in all examples). Really helpful to know about things like AIB and BIC, and I'm sure I can probably work these into my Excel sheet. Also really helpful comment about p-values. I've tried re-working things where the p-value is less than 0.2 and it seems like it should fit (e.g. "big chances" appearing initially significant and then not - and then when included again in the 3rd image it became significant again). I've recorded the p-values of all variables that I have dropped out so may start re-including some.
There is no need to sign posts here -- your signature is appended automatically.
I did think over picking a metric. I came down to Jaccard Coefficient and Hamming Distance among which I feel Jaccard might suit my needs.
The trouble with OLS is that it assumes the errors are independent, and, if data are clustered, that assumption is violated.
@Fixee: Hopefully no one is still using LCGs for uniform pseudorandom variate generation. Also, I suspect that [CORDIC](http://en.wikipedia.org/wiki/CORDIC) is more likely used for $\\sin$ and $\\cos$ than Taylor series in most implementations, though there are some C library implementations that use Taylor series. The $\\log$ function may be the biggest stinker among these, but I seem to recall seeing some CORDIC-like implementations of these as well. I know that $\\exp$ can be done with *very* low-order rational approximations after an appropriate deflation of the input.
Thank you for the answer. I've been reading about multilevel models, but I came across rosner's generalization of the matched t-test; I think that it is just what I was looking for.
(contd.)  This is the information that we're interested in, since we want to see if the leader seesaws. `sum` would just sum all 1's and -1's, which would give you the final result after _all_ 20,000 viewers have been accounted for (i.e. the last element of the `cumsum` vector).
You might find these [recent slides from the ETH by Florian Herzog](http://www.idsc.ethz.ch/Courses/stochasticsystems/Probability.pdf) to be helpful: they cover all this material (and much more) starting from first principles in a very clear manner.
What are the variables and what are you trying to do?
@whuber, you are way too smart, no offense. Most people would compute skewness as the moment of data, not through a parametric assumption as you just did. Now, if I said "Suppose you are fitting a Pearson distribution by method of moments" -- would this argument be relevant, then?
More information is needed.  To check for a *uniform* distribution one would ordinarily check *all values,* not just those near a particular value.  The interval you request doesn't exist because it cannot answer questions about uniformity.  It would be better to state in plain non-statistical terms what data you have obtained and what you're trying to accomplish.
@Glen_b thanks for your input.  The more I investigate the more I think this has to be done in R or MATLAB because of the time variation.
Your reasoning is good.  Actually, one would expect instability to occur when two or more eigenvalues are nearly coincident, for then although the eigenvalues are determined, the eigenvectors are not, and therefore neither are the loadings.  For numerical reasons, there is also instability in eigenvalues (and eigenvectors) that are very small in size compared to the maximum eigenvalue.
Have you seen [this comment](http://stats.stackexchange.com/questions/9664/what-are-examples-where-a-naive-bootstrap-fails#comment70554_9678) to an answer in this thread?  Incidentally, that comment links to an Amazon page for Chernick's book; the reader reviews are enlightening.
@Kirsty, to be fair, not the unit roots have such a history, but weak convergence. Central limit theorem on which most of the econometrics is based is weak convergence of sequences of random vectors. Functional central limit theorem involves convergence of sequences of functions in nice spaces. Empirical processes generalise the notions of central limit theorem and law of large numbers to sequences (nets if you know what it is) of a very general random objects.
I think the part where you want to put a 1 in the columns for left and right when it's on both sides makes sense (with a column for interaction if you think there may be interaction). On the other hand I'm not sure why you're having numerical problems with the other approach you mentioned, since it's effectively the same as three dummies for three separate categories. Either way you end up with three columns which should pick up three effects (though parameterized differently), so if you had problems with one you may have them each way. On your second part, I have to agree with Frank Harrell.
The definition you quote suggests the second is a subset of the first, but as they've actually defined them there (I'd swap about some parts of those definitions to the other term!) - and usually in practice - they seem to be used interchangeably. Nonparametric in this sense basically means 'infinite-parametric' while distribution-free methods are ones whose implementation and properties like null distributions don't depend on the distributional shape. Some books do make a distinction between the two; if I think of a reference I'll come back and add it.
I replied to you and @onestop in an answer to my own question.
Maybe I don't understand the term bivariate, I assumed it means 2 variables. I have the name variable, the bind variable and the miRNA bool.
I am sorry I didn't see your question before. Something to consider: How do you work out the null-distribution of the test statistic in that case? Can you do it now?
Thanks for the input.  I ran the model, did not notice any change on the fixed effects, but the variance and std.dev of the wave random effect were 0.  Should I drop the wave random effect?
Yes, assumptions are needed--but you appear to have made some additional unstated assumptions that could confuse the unwary. One of them is that these data are cumulative totals. What, for example, would happen with annual mean temperatures?  Would you propose dividing them all by four?  Even in an area where temperatures never vary (a "uniform rate")? :-)
Something is going wrong w/ the site's markup / HTML for code formatting. I don't know what it is, but we'll see if we can figure it out.