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I am seeking recommendations and/or best practices for analyzing non-independent data. In particular, I am curious about non-independent data that does not reflect typical repeated-measures time-based data in which data for the same question(s) or stimuli are collected at different time points. Rather the data collecte...
I was taught to only apply Fisher's Exact Test in contingency tables that were 2x2. Questions: Did Fisher himself ever envision this test to be used in tables larger than 2x2 (I am aware of the tale of him devising the test while trying to guess whether an old woman could tell if milk was added to tea or tea was added...
Student's $t$-test requires the sample standard deviation $s$. However, how do I compute for $s$ when only the sample size and sample average are known? For example, if sample size is $49$ and sample average is $112$, I will then attempt to create a list of $49$ identical samples with values of $112$ each. Expectedly, ...
One of the most important issues in using factor analysis is its interpretation. Factor analysis often uses factor rotation to enhance its interpretation. After a satisfactory rotation, the rotated factor loading matrix L' will have the same ability to represent the correlation matrix and it can be used as the factor l...
I have two implementations of a genetic algorithm which are supposed to behave equivalently. However due to technical restrictions which cannot be resolved their output is not exactly the same, given the same input. Still I'd like to show that there is no significant performance difference. I have 20 runs with the same...
What are the panel's recommendations for books on design of experiments? Ideally, books should be still in print or available electronically, although that may not always be feasible. If you feel moved to add a few words on what's so good about the book that would be great too. Also, aim for one book per answer so that...
I need some help about repeated measurement ANOVA. We are investigating the effect of some intervention on reducing blood stream infection (BSI) rate in some wards. We plan to capture the BSI rate information at a monthly basis, 12 months without intervention first, then 12 months with intervention. We are thinking of ...
How do I test/verify if I can analyze my panel like dataset by simply pooling the individual series? I have a dataset structured as a panel. Now I am wondering if I can simply pool the individual series and estimate it via OLS or if I have to use another estimation technique. (Any R hints and references are highly welc...
How would you describe cross-validation to someone without a data analysis background?
I usually hear about "ordinary least squares". Is that the most widely used algorithm used for linear regression? Are there reasons to use a different one?
Greetings, Currently I'm doing the following in R: require(zoo) data <- read.csv(file="summary.csv",sep=",",head=TRUE) cum = zoo(data$dcomp, as.Date(data$date)) data = zoo(data$compressed, as.Date(data$date)) data <- aggregate(data, identity, tail, 1) cum <- aggregate(cum, identity, sum, 1) days = seq(start(data), en...
Disclaimer: I'm a software engineer, not a statistician, so please forgive any blunt error :-) I have a set of time-series "curves", each measuring the entropy of a given artifact. Now, I'm standing over the following premises (please criticize them as you see fit): In order to approximate the upper bounds of the Kolm...
One way to summarize the comparison of two survival curves is to compute the hazard ratio (HR). There are (at least) two methods to compute this value. Logrank method. As part of the Kaplan-Meier calculations, compute the number of observed events (deaths, usually) in each group ($Oa$, and $Ob$), and the number of ex...
I'm implementing a rating system to be used on my website, and I think the Bayesian average is the best way to go about it. Every item will be rated in six different categories by the users. I don't want items with only one high rating to shoot to the top though, which is why I want to implement a Bayesian system. Here...
For an effect size analysis, I am noticing that there are differences between Cohen's d, Hedges's g and Hedges' g*. Are these three metrics normally very similar? What would be a case where they would produce different results? Also is it a matter of preference which I use or report with?
What tests are available for testing two independent samples for the null hypothesis that they come from populations with the same skew? There is a classical 1-sample test for whether the skew equals a fixed number (the test involves the 6th sample moment!); is there a straightforward translation to a 2-sample test? A...
What do you think about applying machine learning techniques, like Random Forests or penalized regression (with L1 or L2 penalty, or a combination thereof) in small sample clinical studies when the objective is to isolate interesting predictors in a classification context? It is not a question about model selection, no...
I am studying a population of individuals who all begin with a measureable score of interest (ranging from -2 to 2) [call it "old"], then they all undergo a change to a new score (also ranging from -2 to 2) ["new"]. Thus all the variation is in the change (which can be positive or negative), and there are also a variet...
I've been struggling with the following problem with hopefully is an easy one for statisticians (I'm a programmer with some exposure to statistics). I need to summarize the responses to a survey (for management). The survey has 100+ questions, grouped in different areas (with about 5 to 10 questions per area). All answ...
I ran a within subjects repeated measures experiment, where the independent variable had 3 levels. The dependent variable is a measure of correctness and is recorded as either correct / incorrect. Time taken to provide an answer was also recorded. A within subjects repeated measures ANOVA is used to establish whether t...
Standard deck has 52 cards, 26 Red and 26 Black. A run is a maximum contiguous block of cards, which has the same color. Eg. (R,B,R,B,...,R,B) has 52 runs. (R,R,R,...,R,B,B,B,...,B) has 2 runs. What is the expected number of runs in a shuffled deck of cards?
Following to the recent questions we had here. I was hopping to know if anyone had come across or can share R code for performing a custom power analysis based on simulation for a linear model? Later I would obviously like to extend it to more complex models, but lm seems to right place to start.
The question is in the header, but I would extend the context a bit. Next semester I am due to be a teaching assistant (TA) in a course in statistics, where I would need to help sociology students learn to use SPSS. I don't know SPSS, yet, and would like to learn how to use it. I was thinking of taking a simple dataset...
I posted this on mathoverflow, but they sent me here. This question relates to a problem I had at work a while ago, doing a little data mining at a car rental company. Names changed, of course. I'm using Oracle DBMS if it matters. There was a flight of steps out the front of our building. It had a dodgy step on it, on ...
I'm looking to construct a 3-D surface of a part of the brain based on 2-D contours from cross-sectional slices from multiple angles. Once I get this shape, I want to "fit" it to another set of contours via rescaling. I'm aspiring to do this in the context of an MCMC analysis (So as to be able to make inferences, so it...
A question which bothered me for some time, which I don't know how to address: Every day, my weatherman gives a percentage chance of rain (let's assume its calculated to 9000 digits and he has never repeated a number). Every subsequent day, it either rains or does not rain. I have years of data - pct chance vs rain or ...
I would like an advice on a analysis method I am using, to know if it it statistically sound. I have measured two point processes $T^1 = t^1_1, t^1_2, \ldots, t^1_n$ and $T^2 = t^2_1, t^2_2, \ldots, t^2_m$ and I want to determine if the events in $T^1$ are somehow correlated to the events in $T^2$. One of the methods t...
What areas of statistics have been substantially revolutionised in the last 50 years? For example, about 40 years ago, Akaike with colleagues revolutionised the area of statistical model discrimination. About 10 years ago, Hyndman with colleagues revolutionised the area of exponential smoothing. About XX years ago, ......
I have a software benchmark which is quite noisy. I am trying to for the bugs which are causing the noise, and I need to be able to measure it somehow. The benchmark is comprised of a number of subbenchmarks, for example: "3d-cube": 31.56884765625, "3d-morph": 21.89599609375, "3d-raytrace": 51.802978515625, "access-bin...
What are the most significant annual Statistics conferences? Rules: One conference per answer Include a link to the conference
What are the most significant annual Data Mining conferences? Rules: One conference per answer Include a link to the conference
What are the most significant annual Machine Learning conferences? Rules: One conference per answer Include a link to the conference
Gary King made the following statement on Twitter: scale invariance sounds cool but is usually statisticians shirking responsibility & losing power by neglecting subject matter info What is an example of this phenomena, where scale invariance causes a loss of power? Edit: Gary responded: not [statistical] powe...
I doing spatial bayesian data analysis, I am assuming a no-nugget exponential covariance. I have tried a variety of priors for the sills and range parameters (gamma, inverse gamma etc.) , unfortunately the convergence diagonstics are typically horrible. I am wondering how to figure out the poor mixing I observe, is th...
I am interested in running Newman's modularity clustering algorithm on a large graph. If you can point me to a library (or R package, etc) that implements it I would be most grateful.
Suppose instead of maximizing likelihood I maximize some other function g. Like likelihood, this function decomposes over x's (ie, g({x1,x2})=g({x1})g({x2}), and "maximum-g" estimator is consistent. How do I compute asymptotic variance of this estimator? Update 8/24/10: Percy Liang goes through derivation of asymptotic...
If so, what? If not, why not? For a sample on the line, the median minimizes the total absolute deviation. It would seem natural to extend the definition to R2, etc., but I've never seen it. But then, I've been out in left field for a long time.
Despite several attempts at reading about bootstrapping, I seem to always hit a brick wall. I wonder if anyone can give a reasonably non-technical definition of bootstrapping? I know it is not possible in this forum to provide enough detail to enable me to fully understand it, but a gentle push in the right direction w...
What are the most significant annual conferences focusing on quantitative methods in psychology? This could include but is not limited to psychometrics, mathematical psychology, and statistical methods in psychology. Rules: One conference per answer Include a link to the conference
Is there a specific name for normalizing some data so that it has mean=0 and sd=1? Or do I just say "data was normalized to have mean=0 and sd=1"?
(Prompted to some extent by the answers already given by Shane and Srikant, I've rewritten this to try to clarify what I'm getting at, if only to myself.) Suppose we have several similar systems, each with behaviour that approximates a continuous time Markov process. That is, there are some number of discrete states th...
When one wants to compute the correlation of two vectors of a continues variables, one uses pearson (or spearman) correlation. But what should (can) one use for the case of two vectors with 2 (or 3) ordered levels only? Is spearman enough, or does it require another method? I remember coming across someone who once cl...
A (non-statistician) colleague has been encountering meta-analyses in papers he reviews for medical journals and is looking for a good introductory level treatment so he can educate himself. Any recommendations? Favorites? Books, monographs, nontechnical survey articles would all be fine. (Yes, he's familiar with th...
I am doing some Kernel density estimation, with a weighted points set (ie., each sample has a weight which is not necessary one), in N dimensions. Also, these samples are just in a metric space (ie., we can define a distance between them) but nothing else. For example, we cannot determine the mean of the sample points,...
What non-/semiparametric methods to estimate a probability density from a data sample are you using ? (Please do not include more than one method per answer)
What are good statistical journals with quick turnaround (fast review cycle), suitable for short notes in mathematical statistics and preferably with open access. An example is Statistics & Probability Letters, however, that journal only has sponsored open access.
I have a bunch of variables organized into 10 different levels of a grouping factor. I'm doing some ANCOVA on particular variables and also plotting the data using boxplots. I'd like to add 84% confidence intervals to all the groups (since non-overlapping 84% CIs indicate a significant difference at alpha .05 - at leas...
The Question: Are there any good examples of reproducible research using R that are freely available online? Ideal Example: Specifically, ideal examples would provide: The raw data (and ideally meta data explaining the data), All R code including data import, processing, analyses, and output generation, Sweave or some...
Under which conditions should someone consider using multilevel/hierarchical analysis as opposed to more basic/traditional analyses (e.g., ANOVA, OLS regression, etc.)? Are there any situations in which this could be considered mandatory? Are there situations in which using multilevel/hierarchical analysis is inappropr...
Miller and Chapman (2001) argue that it is absolutely inappropriate to control for non-independent covariates that are related to both the independent and dependent variables in an observational (non-randomized) study - even though this is routinely done in the social sciences. How problematic is it to do so? How is th...
I am running LOESS regression models in R, and I want to compare the outputs of 12 different models with varying sample sizes. I can describe the actual models in more details if it helps with answering the question. Here are the sample sizes: Fastballs vs RHH 2008-09: 2002 Fastballs vs LHH 2008-09: 2209 Fastballs vs...
Although I was trained as an engineer, I find that I'm becoming more interested in data mining. Right now I'm trying to investigate the field further. In particular, I would like to understand the different categories of software tools that exist and which tools are notable in each category and why. (Note that I didn...
I am looking through articles citing an article I'm reading - and I wish to judge how much that citing article is "important" or "good" by itself. one way of knowing would be if I had known how "distinguished" that journal was. Which leads me to my question: What measures are there (and where can I find them) for a jo...
Let $X_1$, $X_2, \dots, X_n$ be identically distributed random variables with given mean, and let $N$ be a random variable with $N \ge 0$ that is independent of $X_1$, $X_2, \dots, X_n$. If $Y=X_1+X_2+...X_n$; how do we find $\mathrm{E}(Y|N=n)$? With $D$ being the domain of $y$, I know the conditional expectation is de...
Assume: A previous study looking at the relationship between $X$ and $Y$ obtained a correlation of $r = 0.50$ using a sample of $n = 100$. The raw data is not available. The current study also looking at the relationship between $X$ and $Y$ obtained a correlation of $r = 0.45$ with $n = 50$. How would you do the foll...
This is a very basic questions however I have not been able to find an answer. When you plot your regular bar plot with your standard errors of the means for comparison do you plot the standard errors and means from the raw data ? Or do you plot the ones predicted by the model you are fitting. Thank you in advance for ...
What learning material would you suggest for a CS person / novice statistician / novice mathematician to get into predictive analytics?
If $X_i\sim\Gamma(\alpha_i,\beta_i)$ for $1\leq i\leq n$, let $Y = \sum_{i=1}^n c_iX_i$ where $c_i$ are positive real numbers. Assume all the parameters $\alpha_i$'s and $\beta_i$'s are all known, what is $Y$'s distribution ?
Suppose I have a black box that generates data following a normal distribution with mean m and standard deviation s. Suppose, however, that whenever it outputs a value < 0 it does not record anything (can't even tell that it's outputted such a value). We have a truncated gaussian distribution without a spike. How can I...
I came across this nice tutorial: A Handbook of Statistical Analyses Using R. Chapter 13. Principal Component Analysis: The Olympic Heptathlon on how to do PCA in R language. I don't understand the interpretation of Figure 13.3: So I am plotting first eigenvector vs the second eigenvector. What does that mean? Suppose...
It seems that MLE (via EM) is widely used in machine learning / statistics to learn the parameters of a mixture of Gaussians. I'm assuming we're given random samples from the mixture. My question is: Are there any proven quantitative bounds on the error in terms of the number of samples (and perhaps the parameters of ...
When lecturing statistics, it can be useful to incorporate the occasional short video. My first thoughts included: Animations and visualisations of statistical concepts Stories regarding the application of a particular technique Humorous videos that have relevance to a statistical idea Interviews with a statistician...
Is there a numerically stable way to calculate values of a beta distribution for large integer alpha, beta (e.g. alpha,beta > 1000000)? Actually, I only need a 99% confidence interval around the mode, if that somehow makes the problem easier. Add: I'm sorry, my question wasn't as clearly stated as I thought it was. Wha...
I am currently finishing a paper and stumbled upon this question from yesterday which led me to pose the same question to myself. Is it better to provide my graph with the actual standard error from the data or the one estimated from my ANOVA? As the question from yesterday was rather unspecific and mine is pretty spec...
It isn't clear to me how to calculate cointegration with irregular time series (ideally using the Johansen test with VECM). My initial thought would be to regularize the series and interpolate missing values, although that may bias the estimation. Is there any literature on this subject?
Besides taking differences, what are other techniques for making a non-stationary time series, stationary? Ordinarily one refers to a series as "integrated of order p" if it can be made stationary through a lag operator $(1-L)^P X_t$.
There seems to be a large body of applied research where distribution q is picked to minimize KL(q,p) where p is empirical distribution. Are there theoretical reasons to prefer this estimator? For instance, a theoretical reason to prefer MLE for estimating mean of a one-dimensional Gaussian with mean between -1 and 1 b...
I am modelling a nested mixed-effects model with just the intercept in the random part, of the form: fit4<-lme(fixed = Stdquad~factor(LayoutN)+factor(nCHIPS.fixed), random = ~1|Class.Ordered/student) When trying to check the assumption on the independent, identically distributed (iid) random effects in SPlus using ran...
I'm looking for correlations between the answers to different questions in a survey ("umm, let's see if answers to question 11 correlate with those of question 78"). All answers are categorical (most of them range from "very unhappy" to "very happy"), but a few have a different set of answers. Most of them can be consi...
X is uniform random variable in [0,1] and Y=1-X. How do I calculate the distribution function F(X,Y)? I can see that Y is also uniformly distributed and can draw the intervals. But I am unable to compute the distribution function when x+y>1 & x,y in [0,1]. How do I compute it for this specific case?
The waiting times for poisson distribution is an exponential distribution with parameter lambda. But I don't understand it. Poisson models the number of arrivals per unit of time for example. How is this related to exponential distribution? Lets say probability of k arrivals in a unit of time is P(k) (modeled by poisso...
I've implemented the Marsaglia polar method to generate random numbers that are normally distributed. Unfortunately the code as shown on this website returns numbers that are not within the range [0, 1). Code: double x1, y1, w; do { x1 = 2.0 * ranf() - 1.0; y1 = 2.0 * ranf() - 1.0; ...
Is there any free desktop software for treemapping? Every one I've found appears to have a commercial license. Many Eyes is free and has treemapping features but what I'm really looking for is downloadable desktop software. Thanks in advance.
Thank you for reading. I am trying to get sphericity values for a purely within subject design. I have been unable to use ezANOVA, or Anova(). Anova works if I add a between subject factor, but I have been unable to get sphericity for a purely within subject design. Any advice? I already read the R newsletter, fox chap...
I have a web service, which returns a dataset, and I would like to query it from the [R] statistical package. I'd like to know how (or if) this can be done and also how to load the first datatable, of this dataset, into memory. Thanks! EDIT: It is an XML web service
For the selection of predictors in multivariate linear regression with $p$ suitable predictors, what methods are available to find an 'optimal' subset of the predictors without explicitly testing all $2^p$ subsets? In 'Applied Survival Analysis,' Hosmer & Lemeshow make reference to Kuk's method, but I cannot find the o...
As someone who needs statistical knowledge but is not a formally trained statistician, I'd find it helpful to have a flowchart (or some kind of decision tree) to help me choose the correct approach to solve a particular problem (eg. "do you need this and know that and that and consider data to be normally distributed? ...
Some guys told me that it's appropriate to use Wald-Wolfowitz Runs Test as a normality test (like Shapiro-Wilk's or Kolmogorov-Smirnov...). Do you think this is good way to test normality assumptions?
I am using ridge regression on highly multicollinear data. Using OLS I get large standard errors on the coefficients due to the multicollinearity. I know ridge regression is a way to deal with this problem, but in all the implementations of ridge regression that I've looked at, there are no standard errors reported for...
In particular, I am referring to the Pearson product-moment correlation coefficient.
Consider the following exponential expansion form: $$ \exp\left[\sum_{k=1}^\infty \gamma_k x^k\right] = \sum_{j=0}^\infty\delta_j x^j $$ where $\gamma_k$'s are known, and $\delta_0=1$, $$\delta_{j+1} = \frac{1}{j+1}\sum_{i=1}^{j+1}i\gamma_i\delta_{j+1-i}$$ Does anyone know how to prove it?
for eg. if I have a class variable credit scoring with two classes good and bad, where #(good) = 700 and #(bad)= 300. I do not want to shorten my data. which technique I should use? I was using SVM but it is giving all bad as good in predictions.
I'm looking for an R package for estimating the coefficients of logit models with individual fixed-effect (individual intercept) using Chamberlain's 1980 estimator. It is often known as Chamberlain's fixed-effect logit estimator. It's a classic estimator when dealing with binary outcome panel data (at least in econom...
I'm investgating the repeatability of an experimental process (actually measuring lift in a wind tunnel), which can be measured using a single number, Q. However, I only have limited access to the tunnel so the number of experiments that I can run is restricted. If I have 5 experiments with the tunnel in one configurat...
When performing linear regression, it is often useful to do a transformation such as log-transformation for the dependent variable to achieve better normal distribution conformation. Often it is also useful to inspect beta's from the regression to better assess the effect size/real relevance of the results. This raises...
I have to compare pairs of audio strems as 1d time series. Looking at the aligned trajectories I need to either cluster them together or assume they arise from independent generators. I remember hearing of Dirichlet processes being applied. Could try to defined a hidden Markov model on the structure, not sure yet how...
A particle filter and Kalman filter are both recursive Bayesian estimators. I often encounter Kalman filters in my field, but very rarely see the usage of a particle filter. When would one be used over the other?
In other words, instead of having a two class problem I am dealing with 4 classes and still would like to assess performance using AUC.
(I know it is not quite appropriate to quote it as "part 2", but since the question has been dormant for quite a while, I hope by doing this will rise peoples' attention again, you may have a look of part I here.) I have come across an article online talking about the case similar to mine, that most of the time the cas...
The kernel trick is used in several machine learning models (e.g. SVM). It was first introduced in the "Theoretical foundations of the potential function method in pattern recognition learning" paper in 1964. The wikipedia definition says that it is a method for using a linear classifier algorithm to solve a non...
I am trying to compute the standard error of the sample spectral risk measure, which is used as a metric for portfolio risk. Briefly, a sample spectral risk measure is defined as $q = \sum_i w_i x_{(i)}$, where $x_{(i)}$ are the sample order statistics, and $w_i$ is a sequence of monotonically non-increasing non-negat...
Say some previous findings identified a curvilinear effect of X on Y, (specifically that X had a positive effect on Y, and that X^2 had a negative effect). You want to see if the same holds for your entirely different sample (although everything else between studies, constructs/measures, are exactly the same). Neither ...
I'm interested in learning how to create the type of visualizations you see at http://flowingdata.com and informationisbeautiful. EDIT: Meaning, visualizations that are interesting in of themselves -- kinda like the NY Times graphics, as opposed to a quick something for a report. What kinds of tools are used to create ...
How to obtain a variable (attribute) importance using SVM?
I'm interested in getting some books about multivariate analysis, and need your recommendations. Free books are always welcome, but if you know about some great non-free MVA book, please, state it.
I need help explaining, and citing basic statistics texts, papers or other references, why it is generally incorrect to use the margin of error (MOE) statistic reported in polling to naively declare a statistical tie. An example: Candidate A leads Candidate B in a poll, $39 - 31$ percent, $4.5 \%$ margin-of-error for $...
I have a great prediction yet I am unsure how to uncover how the results were generated?
Let's say I have a dataset with 1000 observations in 10 variables, "A" through "J." I have 1000 responses/measures for each of the first 8 variables, through "H," but only the first 500 observations for "I" are not missing, and only the last 500 observations for "J" are not missing -- there are no observations for whic...
If given probability of $A$ is $a$ and probability of $B$ is $b$, how do I find min/max probability of intersection? Max value of intersection would be $\min(a,b)$, how do I find the min?
What is the difference between a feed-forward and recurrent neural network? Why would you use one over the other? Do other network topologies exist?