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What is the difference between the Shapiro–Wilk test of normality and the Kolmogorov–Smirnov test of normality? When will results from these two methods differ?
If you could go back in time and tell yourself to read a specific book at the beginning of your career as a statistician, which book would it be?
Say I've got a program that monitors a news feed and as I'm monitoring it I'd like to discover when a bunch of stories come out with a particular keyword in the title. Ideally I want to know when there are an unusual number of stories clustered around one another. I'm entirely new to statistical analysis and I'm wonder...
What topics in statistics are most useful/relevant to data mining?
From Wikipedia : Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want...
What are pivot tables, and how can they be helpful in analyzing data?
Possible Duplicate: Testing random variate generation algorithms What's a good way to test a series of numbers to see if they're random (or at least psuedo-random)? Is there a good statistical measure of randomness that can be used to determine how random a set is? More importantly, how can one prove a method of gen...
I have a data set where a series of measurements are being taken each week. In general the data set shows a +/- 1mm change each week with a mean measurement staying at about 0mm. In plotting the data this week it appears that some noticeable movement has occurred at two points and looking back at the data set, it is al...
I usually make my own idiosyncratic choices when preparing plots. However, I wonder if there are any best practices for generating plots. Note: Rob's comment to an answer to this question is very relevant here.
At the moment I use standard deviation of the mean to estimate uncertainty: $$\sigma_\textrm{mean}=\frac{\sigma}{\sqrt{N}}$$ where $N$ is in hundreds and mean is a time series (monthly) mean. I present it then like this: $$O_n\geq \frac{-\log_{10} 0.05}{b}$$ for each element (month) in the (annual) time series. Is this...
There are many ways to measure how similar two probability distributions are. Among methods which are popular (in different circles) are: the Kolmogorov distance: the sup-distance between the distribution functions; the Kantorovich-Rubinstein distance: the maximum difference between the expectations w.r.t. the two di...
What is a good introduction to statistics for a mathematician who is already well-versed in probability? I have two distinct motivations for asking, which may well lead to different suggestions: I'd like to better understand the statistics motivation behind many problems considered by probabilists. I'd like to know h...
Coming from the field of computer vision, I've often used the RANSAC (Random Sample Consensus) method for fitting models to data with lots of outliers. However, I've never seen it used by statisticians, and I've always been under the impression that it wasn't considered a "statistically-sound" method. Why is that so? ...
What book would you recommend for scientists who are not statisticians? Clear delivery is most appreciated. As well as the explanation of the appropriate techniques and methods for typical tasks: time series analysis, presentation and aggregation of large data sets.
Data analysis cartoons can be useful for many reasons: they help communicate; they show that quantitative people have a sense of humor too; they can instigate good teaching moments; and they can help us remember important principles and lessons. This is one of my favorites: As a service to those who value this kind of...
It has been suggested by Angrist and Pischke that Robust (i.e. robust to heteroskedasticity or unequal variances) Standard Errors are reported as a matter of course rather than testing for it. Two questions: What is impact on the standard errors of doing so when there is homoskedasticity? Does anybody actually do this...
We're plotting time-series metrics in the context of network/server operations. The data has a 5-minute sample rate, and consists of things like CPU utilization, error rate, etc. We're adding a horizontal "threshold" line to the graphs, to visually indicate a value threshold above which people should worry/take notice....
I am not an expert of random forest but I clearly understand that the key issue with random forest is the (random) tree generation. Can you explain me how the trees are generated? (i.e. What is the used distribution for tree generation?) Thanks in advance !
Another question about time series from me. I have a dataset which gives daily records of violent incidents in a psychiatric hospital over three years. With the help from my previous question I have been fiddling with it and am a bit happier about it now. The thing I have now is that the daily series is very noisy. It ...
A question previously sought recommendations for textbooks on mathematical statistics Does anyone know of any good online video lectures on mathematical statistics? The closest that I've found are: Machine Learning Econometrics UPDATE: A number of the suggestions mentioned below are good statistics-101 type videos....
I have calculated AIC and AICc to compare two general linear mixed models; The AICs are positive with model 1 having a lower AIC than model 2. However, the values for AICc are both negative (model 1 is still < model 2). Is it valid to use and compare negative AICc values?
What are the variable/feature selection that you prefer for binary classification when there are many more variables/feature than observations in the learning set? The aim here is to discuss what is the feature selection procedure that reduces the best the classification error. We can fix notations for consistency: f...
I am proposing to try and find a trend in some very noisy long term data. The data is basically weekly measurements of something which moved about 5mm over a period of about 8 months. The data is to 1mm accuracey and is very noisy regularly changing +/-1 or 2mm in a week. We only have the data to the nearest mm. We pl...
Sometimes, I just want to do a copy & paste from the output window in SAS. I can highlight text with a mouse-drag, but only SOMETIMES does that get copied to the clipboard. It doesn't matter if I use "CTRL-C" or right click -> copy, or edit -> copy Any other SAS users experience this, and do you know a workaround/optio...
I've heard that when many regression model specifications (say, in OLS) are considered as possibilities for a dataset, this causes multiple comparison problems and the p-values and confidence intervals are no longer reliable. One extreme example of this is stepwise regression. When can I use the data itself to help spe...
What is your preferred method of checking for convergence when using Markov chain Monte Carlo for Bayesian inference, and why?
In the context of machine learning, what is the difference between unsupervised learning supervised learning and semi-supervised learning? And what are some of the main algorithmic approaches to look at?
Debugging MCMC programs is notoriously difficult. The difficulty arises because of several issues some of which are: (a) Cyclic nature of the algorithm We iteratively draw parameters conditional on all other parameters. Thus, if a implementation is not working properly it is difficult to isolate the bug as the issue ca...
As you know, there are two popular types of cross-validation, K-fold and random subsampling (as described in Wikipedia). Nevertheless, I know that some researchers are making and publishing papers where something that is described as a K-fold CV is indeed a random subsampling one, so in practice you never know what is ...
I have two different analytical methods that can measure the concentration of a particular molecule in a matrix (for instance measure the amount of salt in water) The two methods are different, and each has it's own error. What ways exist to show the two methods are equivalent (or not). I'm thinking that plotting the ...
We all know the mantra "correlation does not imply causation" which is drummed into all first year statistics students. There are some nice examples here to illustrate the idea. But sometimes correlation does imply causation. The following example is taking from this Wikipedia page For example, one could run an experi...
In answering this question on discrete and continuous data I glibly asserted that it rarely makes sense to treat categorical data as continuous. On the face of it that seems self-evident, but intuition is often a poor guide for statistics, or at least mine is. So now I'm wondering: is it true? Or are there established ...
In an answer to this question about treating categorical data as continuous, optimal scaling was mentioned. How does this method work and how is it applied?
ANOVA is equivalent to linear regression with the use of suitable dummy variables. The conclusions remain the same irrespective of whether you use ANOVA or linear regression. In light of their equivalence, is there any reason why ANOVA is used instead of linear regression? Note: I am particularly interested in hearing ...
I am trying to get a global perspective on some of the essential ideas in machine learning, and I was wondering if there is a comprehensive treatment of the different notions of loss (squared, log, hinge, proxy, etc.). I was thinking something along the lines of a more comprehensive, formal presentation of John Langfo...
This is a fairly general question: I have typically found that using multiple different models outperforms one model when trying to predict a time series out of sample. Are there any good papers that demonstrate that the combination of models will outperform a single model? Are there any best-practices around combini...
Instrumental variables are becoming increasingly common in applied economics and statistics. For the uninitiated, can we have some non-technical answers to the following questions: What is an instrumental variable? When would one want to employ an instrumental variable? How does one find or choose an instrumental vari...
Difference in differences has long been popular as a non-experimental tool, especially in economics. Can somebody please provide a clear and non-technical answer to the following questions about difference-in-differences. What is a difference-in-difference estimator? Why is a difference-in-difference estimator any use?...
I'm curious if there are graphical techniques particular, or more applicable, to structural equation modeling. I guess this could fall into categories for exploratory tools for covariance analysis or graphical diagnostics for SEM model evaluation. (I'm not really thinking of path/graph diagrams here.)
In "Convolutional deep belief networks for scalable unsupervised learning of hierarchical representations" by Lee et. al.(PDF) Convolutional DBN's are proposed. Also the method is evaluated for image classification. This sounds logical, as there are natural local image features, like small corners and edges etc. In "Un...
What is the preferred method for for conducting post-hocs for within subjects tests? I've seen published work where Tukey's HSD is employed but a review of Keppel and Maxwell & Delaney suggests that the likely violation of sphericity in these designs makes the error term incorrect and this approach problematic. Maxwe...
The AIC and BIC are both methods of assessing model fit penalized for the number of estimated parameters. As I understand it, BIC penalizes models more for free parameters than does AIC. Beyond a preference based on the stringency of the criteria, are there any other reasons to prefer AIC over BIC or vice versa?
I am currently using Viterbi training for an image segmentation problem. I wanted to know what the advantages/disadvantages are of using the Baum-Welch algorithm instead of Viterbi training.
In some papers, for example in "The Geometric Density with Unknown Location Parameter" by Klotz, a Geometric Distribution is called a Geometric Density. For me, this claim looks erroneous, however Klotz is a serious statistician and a professor in the field. My question is, to what extend is it legitimate to call a Geo...
The E-M procedure appears, to the uninitiated, as more or less black magic. Estimate parameters of an HMM (for example) using supervised data. Then decode untagged data, using forward-backward to 'count' events as if the data were tagged, more or less. Why does this make the model better? I do know something about the ...
E-M provides a way to improve the estimation of a generative model with unannotated data. Is there anything out there that works the same way for discriminative models (e.g. perceptrons)? For example, consider averaged perceptron tagger. It would be handy to be able to throw the entire Gigaword through some process of ...
Do you know any good heuristics for finding optimal value of ν in case of ν-SVM classification? In this particular problem I have a radial basis kernel, if it helps.
I am puzzled by something I found using Linear Discriminant Analysis. Here is the problem - I first ran the Discriminant analysis using 20 or so independent variables to predict 5 segments. Among the outputs, I asked for the Predicted Segments, which are the same as the original segments for around 80% of the cases. Th...
In a question elsewhere on this site, several answers mentioned that the AIC is equivalent to leave-one-out (LOO) cross-validation and that the BIC is equivalent to K-fold cross validation. Is there a way to empirically demonstrate this in R such that the techniques involved in LOO and K-fold are made clear and demon...
I have tried to reproduce some research (using PCA) from SPSS in R. In my experience, principal() function from package psych was the only function that came close (or if my memory serves me right, dead on) to match the output. To match the same results as in SPSS, I had to use parameter principal(..., rotate = "varima...
There have been a few questions about statistical textbooks, such as the question Free statistical textbooks. However, I am looking for textbooks that are Open Source, for example, having an Creative Commons license. The reason is that in course material in other domains, you still want to include some text about basic...
I see these terms being used and I keep getting them mixed up. Is there a simple explanation of the differences between them?
In engineering, we usually have Handbooks that pretty much dictate the state of the practice. These books are usually devoid of theory and focus on the applied methodology. Is there a forecasting Handbook out there? that solely focuses on the technique and not the background?
What is an estimator of standard deviation of standard deviation if normality of data can be assumed?
I have a data set of about 3,000 field observations. The data collected is divided into 20 variables (real numbers), 30 boolean variables, and 10 or so look up variables and one "answer" variable We have about 20,000 objects in the field, and i'm trying to produce an "answer" for the 20,000 objects based on the 3,000 ...
Provided a sample size "N" that I plan on using to forecast data. What are some of the ways to subdivide the data so that I use some of it to establish a model, and the remainder data to validate the model? I know there is no black and white answer to this, but it would be interesting to know some "rules of thumb" or ...
Sites like eMarketer offer general survey results about internet usage. Who else has a big set of survey results, or regularly releases them? Preferably marketing research focused. Thanks!
My father is a math enthusiast, but not interested in statistics much. It would be neat to try to illustrate some of the wonderful bits of statistics, and the CLT is a prime candidate. How would you convey the mathematical beauty and impact of the central limit theorem to a non-statistician?
Having just recently started teaching myself Machine Learning and Data Analysis I'm finding myself hitting a brick wall on the need for creating and querying large sets of data. I would like to take data I've been aggregating in my professional and personal life and analyze it but I'm uncertain of the best way to do th...
I bought this book: How to Measure Anything: Finding the Value of Intangibles in Business and Head First Data Analysis: A Learner's Guide to Big Numbers, Statistics, and Good Decisions What other books would you recommend?
I am collecting textual data surrounding press releases, blog posts, reviews, etc of certain companies' products and performance. Specifically, I am looking to see if there are correlations between certain types and/or sources of such "textual" content with market valuations of the companies' stock symbols. Such appare...
What's the difference between probability and statistics, and why are they studied together?
What are the main ideas, that is, concepts related to Bayes' theorem? I am not asking for any derivations of complex mathematical notation.
Is there something about statistics that lends itself to this sort of saying, or is it just that people will say anything to support their case, and this includes citing irrelevant or incomplete statistics?
Oversimplifying a bit, I have about a million records that record the entry time and exit time of people in a system spanning about ten years. Every record has an entry time, but not every record has an exit time. The mean time in the system is ~1 year. The missing exit times happen for two reasons: The person has ...
Is anyone aware of good data anonymization software? Or perhaps a package for R that does data anonymization? Obviously not expecting uncrackable anonymization - just want to make it difficult.
I am developing a multi-class perceptron algorithm and was wondering if there are any datasets that could be used to test a multi-class perceptron? - A dataset where the classes are linearly separable and have at least 100 or more instances for training?
I'm doing shopping cart analyses my dataset is set of transaction vectors, with the items the products being bought. When applying k-means on the transactions, I will always get some result. A random matrix would probably also show some clusters. Is there a way to test whether the clustering I find is a significant one...
An hyperspectral image is a multidimensional image with more than 200 spectral bands i.e. an image for which each pixel is a vector of dimension 200 (most often it is a sampled spectral curve that is encoutered in satellite imagery or medical imagery). What are the implemented package (I am especially interested in R ...
What is your favorite statistical quote? This is community wiki, so please one quote per answer.
I was having a look round a few things yesturday and came across Bayesian Search Theory. Thinking about this theory led me to think about a problem I was working on a few years ago regarding geological interpretation. We were looking at the geology at one specific site and it was essentially made up from two different...
I have commonly heard that LME models are more sound in the analysis of accuracy data (i.e., in psychology experiments), in that they can work with binomial and other non-normal distributions that traditional approaches (e.g., ANOVA) can't. What is the mathematical basis of LME models that allow them to incorporate the...
When does data analysis cease to be statistics ? Are the following examples all applications of statistics ?: computer vision, face recognition, compressed sensing, lossy data compression, signal processing.
During every machine learning tutorial you'll find, there is the common "You will need to know x amount of stats before starting this tutorial". As such, using your knowledge of stats, you will learn about machine learning. My question is whether this can be reversed. Can a computer science student learn statistics t...
What is the difference between operations research and statistical analysis?
I've heard that a lot of quantities that occur in nature are normally distributed. This is typically justified using the central limit theorem, which says that when you average a large number of iid random variables, you get a normal distribution. So, for instance, a trait that is determined by the additive effect of a...
I am looking at a scientific paper in which a single measurement is calculated using a logarithmic mean 'triplicate spots were combined to produce one signal by taking the logarithmic mean of reliable spots' Why choose the log-mean? Are the authors making an assumption about the underlying distribution? That it ...
I have data compiled by someone else where score averages have been computed over time- averages range from 0-100. The original scores have negative values in many cases and the average would have been negative also, raw average ranges from -30 to 90. How is this 'normalization' accomplished? Thanks
I'm interested in finding as optimal of a method as I can for determining how many bins I should use in a histogram. My data should range from 30 to 350 objects at most, and in particular I'm trying to apply thresholding (like Otsu's method) where "good" objects, which I should have fewer of and should be more spread o...
I am attempting to calculate the standard error (SE) for the positive predictive value (PPV), negative predictive value (NPV), and diagnostic odds ratio (DOR) that I have obtained using the rates of true positives, false positives, true negatives, and false negatives in a sample. I am able to get 95% CIs but not SE. T...
Lately, there have been numerous questions about normalization What are some of the situations where you never ever ever should normalize your data, and what are the alternatives?
There are a lot of references in the statistic literature to "functional data" (i.e. data that are curves), and in parallel, to "high dimensional data" (i.e. when data are high dimensional vectors). My question is about the difference between the two type of data. When talking about applied statistic methodologies tha...
I am building a web application for used book trading and I am adding a feature to propose other book that would be interesting when they view an offer. Currently the data that I store are the following (they are updated each time someone visit an offer) : ISBN (book of the offer) SessId (a unique id that everyone has ...
I have R-scripts for reading large amounts of csv data from different files and then perform machine learning tasks such as svm for classification. Are there any libraries for making use of multiple cores on the server for R. or What is most suitable way to achieve that?
I've heard that AIC can be used to choose among several models (which regressor to use). But i would like to understand formally what it is in a kind of "advanced undergraduated" level, which I think would be something formal but with intuition arising from the formula. And is it possible to implement AIC in stata wit...
I am creating multiple logistic regression models using lrm from Harrell's Design package in R. One model I would like to make is the model with no predictors. For example, I want to predict a constant c such that: logit(Y) ~ c I know I how to compute c (divide the number of "1"s by the total), what I would like is...
I have $N$ paired observations ($X_i$, $Y_i$) drawn from a common unknown distribution, which has finite first and second moments, and is symmetric around the mean. Let $\sigma_X$ the standard deviation of $X$ (unconditional on $Y$), and $\sigma_Y$ the same for Y. I would like to test the hypothesis $H_0$: $\sigma_X ...
I'm working on regression models in STATISTICA application and I need to know what is Fisher-Snedecor distribution for and how to analyze my regression model in this distribution. What the significance level means? What is v1 and v2? I need an explanation and little tutorial on real data.
Google Website Optimizer (GWO) is a tool provided by Google to do A/B and MVT experiments on websites. This has been an unanswered question for a long time so I thought I'd ask it here and see if I can get any help. Here is some documentation (clues) that Google has published about the statistics used: All about stati...
The coefficient on a logged explanatory variable when the dependent variable also is in log form is an elasticity (or the percentage change in the dependent variable if the explanatory variable changes by one percent). Suppose I estimate a regression without logging the dependent variable but I use a log link in a Gen...
Does anyone know of a variation of Fisher's Exact Test which takes weights into account? For instance sampling weights. So instead of the usual 2x2 cross table, every data point has a "mass" or "size" value weighing the point. Example data: A B weight N N 1 N N 3 Y N 1 Y N 2 N Y 6 N Y 7 Y Y 1 Y Y 2 Y Y 3 Y Y 4 Fisher'...
Sorry for the verbose background to this question: Occasionally in investigations of animal behaviour, an experimenter is interested in the amount of time that a subject spends in different, pre-defined zones in a test apparatus. I've often seen this sort of data analyzed using ANOVA; however, I have never been entirel...
Say I want to estimate a large number of parameters, and I want to penalize some of them because I believe they should have little effect compared to the others. How do I decide what penalization scheme to use? When is ridge regression more appropriate? When should I use lasso?
I created a quick fun Excel Spreadsheet tonight to try and predict which video games I'll enjoy if I buy them. I'm wondering if this quick example makes sense from a Logistic Regression perspective and if I am computing all of the values correctly. Unfortunately, if I did everything correctly I doubt I have much to loo...
Given a list of p-values generated from independent tests, sorted in ascending order, one can use the Benjamini-Hochberg procedure for multiple testing correction. For each p-value, the Benjamini-Hochberg procedure allows you to calculate the False Discovery Rate (FDR) for each of the p-values. That is, at each "positi...
I realize this is pedantic and trite, but as a researcher in a field outside of statistics, with limited formal education in statistics, I always wonder if I'm writing "p-value" correctly. Specifically: Is the "p" supposed to be capitalized? Is the "p" supposed to be italicized? (Or in mathematical font, in TeX?) Is t...
Has anyone gone through some papers using Vector Error Correction Models in causality applications with more than one cointegration vectors, say two. I guess there will be more than one ECM terms. How to assess the endogeneity of the left hand variables if t-stats on different ECM coefficients yield different (conflic...
My question is about cross validation when there are many more variables than observations. To fix ideas, I propose to restrict to the classification framework in very high dimension (more features than observation). Problem: Assume that for each variable $i=1,\dots,p$ you have a measure of importance $T[i]$ than exact...
Here's something I've wondered about for a while, but haven't been able to discover the correct terminology. Say you have a relatively complicated density function that you suspect might have a close approximation as a sum of (properly weighted) simpler density functions. Have such things been studied? I'm particularly...
Possible Duplicate: How to understand degrees of freedom? I was at a talk a few months back where the speaker used the term 'degrees of freedom'. She briefly said something along the lines of it meaning the number of values used to form a statistic that are free to vary. What does this mean? I'm specifically looking...

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