instruction stringlengths 9 38.7k |
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Background:
I have the following data (an example):
headings = {
:heading1 => { :weight => 25, :views => 0, :conversions => 0}
:heading2 => { :weight => 25, :views => 0, :conversions => 0}
:heading3 => { :weight => 25, :views => 0, :conversions => 0}
:heading4 => { :weight => 25, :v... |
Today I have got a question about binomial/ logistic regression, its based on an analysis that a group in my department have done and were seeking comments upon. I made up the example below to protect their anonymity, but they were keen to see the responses.
Firstly, the analysis began with a simple 1 or 0 binomial re... |
I have trouble figuring out what the range bars in plot.stl exactly mean. I found Gavin's post on this question and read the documentation as well, I understand that they tell the relative magnitude of the decomposed components, but still I am not entirely sure how they work.
E.g.:
data: tiny bar, no scale seasonal: fu... |
Does anyone know how to construct a confidence interval for predicting a new test value given a trained Relevance Vector Machine (rvm) and/or Gaussian Process Regression (gausspr) using the kernlab R package?
More specifically, how do I get:
The standard error/deviation (variance) of a new test point;
The parameters e... |
Sometimes I need to get only the first row of a data set grouped by an identifier, as when retrieving age and gender when there are multiple observations per individual. What's a fast (or the fastest) way to do this in R? I used aggregate() below and suspect there are better ways. Before posting this question I searche... |
I have data relative to image intensity, which range from 0 to 255. For some models I need to run, I must transform this intensity data to a different scale, which must have a certain mean (for example, 1.5) and a certain maximum (for this example, 2). I have found information on how to convert data to a scale based on... |
Given a dataset $D$ and a distance measure, I want to split the dataset into two disjoint subsets $X, Y$ of a specified size (say 80% and 20% of the original size), so that the minimum distance of all pairs $(x, y)$ with $x \in X$ and $y \in Y$ is maximized. I found references to max-margin clustering without the size ... |
If my response variable has 2 levels, 0 and 1, I can use a ROC curve to assess the accuracy of my predictive model. But what if my response variable has 3 levels, -1, 0, and 1? Is there a way to plot "ROC surfaces" in R?
I started trying to code this up myself, but I couldn't figure out how to calculate and plot the ... |
A newbie question here. I am currently performing a nonparametric regression using the np package in R. I have 7 features and using a brute force approach I identified the best 3. But, soon I will have many more than 7 features!
My question is what are the current best methods for feature selection for nonparametric re... |
I need to draw a complex graphics for visual data analysis.
I have 2 variables and a big number of cases (>1000). For example (number is 100 if to make dispersion less "normal"):
x <- rnorm(100,mean=95,sd=50)
y <- rnorm(100,mean=35,sd=20)
d <- data.frame(x=x,y=y)
1) I need to plot raw data with point size, correspondi... |
I'm trying to generate random textual data based on regular expressions. I'd like to be able to do this in R, as I know that R does have regex capabilities. Any leads?
This question has come up before in forums (StackOverflow Post 1, StackOverflow Post 2, etc.), but they always mention solutions based on other programm... |
I will simplify our problem in this way. Say there are 100,000 cases in total to examine. Due to the time limitation, we randomly selected 2,000 of them. Then we found 1,000 of them are invalid, so we have only 1,000 valid cases left. Finally we categorize these 1,000 valid cases into 2 categories, A and B; they have 3... |
QUESTION:
I have binary data on exam questions (correct/incorrect). Some individuals might have had prior access to a subset of questions and their correct answers. I don’t know who, how many, or which. If there were no cheating, suppose I would model the probability of a correct response for item $i$ as $logit((p_i = ... |
The question is pretty much contained in the title. What is the Mahalanobis distance for two distributions of different covariance matrices? What I have found till now assumes the same covariance for both distributions, i.e., something of this sort:
$$\Delta^T \Sigma^{-1} \Delta$$
What if I have two different $\Sigma$s... |
I'm doing a binary classification using SVM classfier, libsvm, where roughly 95% belongs to one class.
The parameters C and gamma are to be set before the actual training takes place.
I followed the tutorial but still can't get any good results.
There is a script that comes with the library that is supposed to help wi... |
I am working on a linear regression with R and there are many 0 values in my predictor variables. How are these handled in R's lm() function? Should I remove this data for more accurate analysis?
Any advice is appreciated. Thanks.
|
In SPSS, I want to compare two clusters of management sciences department faculty members in two universities.
Which test should I use?
Can you explain how to do it in SPSS?
|
I am currently working on a project where I generate random values using low discrepancy / quasi-random point sets, such as Halton and Sobol point sets. These are essentially $d$-dimensional vectors that mimic a $d$-dimensional uniform(0,1) variables, but have a better spread. In theory, they are supposed to help reduc... |
I played around with some unit root testing in R and I am not entirely sure what to make of the k lag parameter. I used the augmented Dickey Fuller test and the Philipps Perron test from the tseries package. Obviously the default $k$ parameter (for the adf.test) depends only on the length of the series. If I choose dif... |
From what I know, using lasso for variable selection handles the problem of correlated inputs. Also, since it is equivalent to Least Angle Regression, it is not slow computationally. However, many people (for example people I know doing bio-statistics) still seem to favour stepwise or stagewise variable selection. Are ... |
I'm working on a problem from "The Elements of Statistical Learning" (prob. 6.8):
Suppose that for continuous response
$Y$ and predictor $X$, we model the
joint density of $X, Y$ using a
multivariate Gaussian kernel
estimator. Note that the kernel in
this case would be the product kernel
$\phi_{\lambda}(X)... |
I am not in statistics field.
I have seen the word "tied data" while reading about Rank Correlation Coefficients.
What is tied data?
What is an example of tied data?
|
I'm not in Statistics field. I conducted the case study and collected the data as shown below
I have data as shown in the table below:
I would like to find correlation coefficient from this two table data(between NOA and HVOC, and between NOA and HVOL). I conducted the case study with the source code.
I measured sof... |
I am running linear regression models and wondering what the conditions are for removing the intercept term.
In comparing results from two different regressions where one has the intercept and the other does not, I notice that the $R^2$ of the function without the intercept is much higher. Are there certain conditions... |
I would like to find the correlation between two variables. It was suggested to me that two variables should be independent; otherwise it is not meaningful statistically to calculate a correlation. For example, variable is x and another is $y$ which won't be calculated from $x$, e.g., $y=ab/c+x$. $a$, $b$, and $c$ are ... |
I am using Sweave and xtable to generate a report.
I would like to add some coloring on a table. But I have not managed to find any way to generate colored tables with xtable.
Is there any other option?
|
Would you please give an intuitive illustration of Newton's Method, when we deal with nonlinear regression?
Basically I understand that if we can use Taylor's theorem to expand the RSS function of parameter beta, we can change it into quadratic form, and minimize RSS w.r.t parameter. Please give me a multivariate exam... |
Starting out with arima models in R, I do not understand why fitted.values (of an AR(2) process for example) are not part of the output like they are in regressions. Did I miss them when running str(result) or did I get something completely wrong?
|
I want to estimate the quantile of some data. The data are so huge that they can not be accommodated in the memory. And data are not static, new data keep coming. Does anyone know any algorithm to monitor the quantiles of the data observed so far with very limited memory and computation? I find P2 algorithm useful, but... |
The New York Times has a long comment on the 'value-added' teacher evaluation system being used to give feedback to New York City educators. The lede is the equation used to calculate the scores - presented without context. The rhetorical strategy appears to be intimidation via math:
The full text of the article is ... |
I have a simple sampling problem, where my inner loop looks like:
v = sample_gamma(k, a)
where sample_gamma samples from the Gamma distribution to form a Dirichlet sample.
It works well, but for some values of k/a, some of the downstream computation underflows.
I adapted it to use log space variables:
v = log(sample_g... |
I have a number of rasters of environmental data (~10) which may be important predictors for modelling species presence and abundance at ~10 different locations.
I would like to know which of the rasters are important in explaining the variance in observed results. Is it appropriate to look for principal components of ... |
Imagine you have a set of four elements (A-D) with some numeric values of a measured property (several observations for each element):
A: 26 25 29 21
B: 24 17 16
C: 32 34 29 19 25 27 28
D: 23 29 26 20 14
I have to detect if there are significant differences on the average levels. So I run a one way ANOVA to determine ... |
Having worked mostly with cross sectional data so far and very very recently browsing, scanning stumbling through a bunch of introductory time series literature I wonder what which role explanatory variables are playing in time series analysis.
I would like to explain a trend instead of de-trending.
Most of what I rea... |
Can we do that? If yes, then what are the conditions which should be met?
|
I am wondering how to generate uniformly distributed points on the surface of the 3-d unit sphere? Also after generating those points, what is the best way to visualize and check whether they are truly uniform on the surface $x^2+y^2+z^2=1$?
|
Suppose $X \sim \mathcal{N}(\mu_x, \sigma^2_x)$ and $Y \sim \mathcal{N}(\mu_y, \sigma^2_y)$
I am interested in $z = \min(\mu_x, \mu_y)$. Is there an unbiased estimator for $z$?
The simple estimator of $\min(\bar{x}, \bar{y})$ where $\bar{x}$ and $\bar{y}$ are sample means of $X$ and $Y$, for example, is biased (though... |
I'm working on a binary classification problem, with about 1000 binary features in total. The problem is that for each datapoint, I only know the values of a small subset of the features (around 10-50), and the features in this subset are pretty much random.
What's a good way to deal with the problem of the missing fea... |
This problem is basically the classic asset selling problem but with imperfect state information.
In the classical problem, we have an asset that we wish to sell, we receive offers w(0) to w(N-1). If we accept the offer at a given period, we can invest that money with a certain rate of interest r > 0. We suppose that... |
I have a general question. What kind of noise is additive, and what about multiplicative noise? How to determine the nature of noise?
Thanks a lot for your help.
|
Suppose we have the following random process. We start with two vectors $a_1=(0)$ and $b_1=(0)$. In going from $i$ to $i+1$, we will a perturbation to $a_i$ and $b_i$. With probability $p$, we perform Case 1, otherwise perform Case 2.
Case 1: We pick an element of $a_i$, say at coordinate $x$ (chosen uniformly at r... |
This is problem 12.10 in "The Elements of Statistical Learning":
Suppose you wish to carry
out a linear discriminant analysis
(two classes) using a vector of
transformations of the input variables
$h(x)$. Since $h(x)$ is
high-dimensional, you will use a
regularized within-class covariance
matrix $W_h + \... |
I am evaluating a scenario's output parameter's dependence on three parameters: A, B and C. For this, I am conducting the following experiments:
Fix A+B, Vary C - Total four sets of (A+B) each having 4 variations of C
Fix B+C, Vary A - Total four sets of (B+C) each having 3 variations of C
Fix C+A, Vary B - Total four... |
Let's say I have a function funToRepeat:
funToRepeat <- function(df){
rows <- nrow(df)
cols <- ncol(df)
err <- runif( rows * cols )
dfNew <- df + as.data.frame( matrix(err, nrow=rows, ncol=cols) )
dfNew
}
I want to operate funToRepeat on dfTest (a toy data set), multiple times, say n.
dfTest <-
s... |
Recurrent neural networks differ from "regular" ones by the fact that they have a "memory" layer. Due to this layer, recurrent NN's are supposed to be useful in time series modelling. However, I'm not sure I understand correctly how to use them.
Let's say I have the following time series (from left to right): [0, 1, 2,... |
I want to discover which genes are expressed in only one of five treatments. This is my pipeline:
ANOVA between the five treatments
Holm multiple testing correction
Tukey for significant genes discovered in step 2
My question is: Should I also correct Tukey p-values for example multiplying the p-value by the number... |
I have a hypothetical experiment where I am comparing scores on some measure at 1 year to scores on the measure at 4 years. I use a non-paired t-test to see if there is a significant difference between the two. Then, I do:
(4 year mean) - (1 year mean)
Now, I want to take that value, a function of two different dist... |
How much data is needed to properly fit a GARCH(1,1) model?
|
Workers in a factory are assembling items built from several parts. For each item they fetch the parts from the warehouse and then assemble the items.
I suppose they need a certain time per item for assembly plus a certain time per part for fetching them.
$D_{order} = n_{items} * D_{fetch} + n_{parts} * D_{assemble}$
I... |
We are measuring conversion rates (% of visitors who bought) on an e-commerce site.
The test apply to a segment of visitors who meet specific criteria (for example people from a certain country).
The people from the segment are divided into 2 groups. Part of them see a banner and the other don't (control group). Usua... |
Here is the dual problem for L2 support vector machine:
$$\max_{\alpha\in\mathbb{R}^{n}} 2\alpha^{T}y-\alpha^{T}\left(K+n\lambda Id_{\mathbb{R}^{n}}\right)\alpha$$
$$\forall i\in\left\{ 1,\ldots,n\right\} ,\,\alpha_{i}y_{i} \geq0$$
However, using the Lagrangian formulation, I get the following. Is there an argument mis... |
I start with a presumably non-stationary time series. By some criterium $k$ I extract $n_k$ pairs of times $(t_{k,i,2},t_{k,i,1})$.
Now I compute the following quantity: $\bar{\tau} = \frac{1}{K} \sum_k \frac{1}{n_k} \sum_i (t_{k,i,2}-t_{k,i,1})$
What I'm looking for is the error of that quantity. I first began by summ... |
I have data that is equivalent to:
shopper_1 = ['beer', 'eggs', 'water',...]
shopper_2 = ['diapers', 'beer',...]
...
I would like to do some analysis on this data set to get a correlation matrix that would have an implication similar to: if you bought x, you are likely to buy y.
Using python (or perhaps anything but M... |
I was wondering if anyone could help me with information about kurtosis (i.e. is there any way to transform your data to reduce it?)
I have a questionnaire dataset with a large number of cases and variables. For a few of my variables, the data shows pretty high kurtosis values (i.e. a leptokurtic distribution) which is... |
Let's say I test how variable Y depends on variable X under different experimental conditions and obtain the following graph:
The dash lines in the graph above represent linear regression for each data series (experimental setup) and the numbers in the legend denote the Pearson correlation of each data series.
I would... |
I have posted a previous question, this is related but I think it is better to start another thread. This time, I am wondering how to generate uniformly distributed points inside the 3-d unit sphere and how to check the distribution visually and statistically too? I don't see the strategies posted there directly transf... |
Precision is defined as:
p = true positives / (true positives + false positives)
What is the value of precision if (true positives + false positives) = 0? Is it just undefined?
Same question for recall:
r = true positives / (true positives + false negatives)
In this case, what is the value of recall if (true positi... |
My second question is about Test Statistics.
The questions and answers are on this PDF: http://www.mediafire.com/?b74e633lxdb49rb
I understand that they work out the join density and I know how to calculate this.
What I really don’t understand is how they figure out the test statistic. They randomly multiply by 1 in so... |
I am writing a program in C# that requires me to use the Ttest formula. I have to effectively interpret the Excel formula:
=TTEST(range1,range2,1,3)
I am using the formula given here
and have interpreted into code as such:
double TStatistic = (mean1 - mean2) / Math.Sqrt((Math.Pow(variance1, 2) /
count1) + (... |
A lecturer wishes to "grade on the curve". The students' marks seem to be normally distributed with mean 70 and standard deviation 8. If the lecturer wants to give 20% A's, what should be the threshold between an A grade and a B grade?
|
I have gazillion documents (your tax return) that I need to check for correctness, but I don't the manpower nor the will power to read through all of it. Even if I do, I can not guarantee the quality and consistency of the proof reading process.
The only thing I can do is to pick a sample collection of document to p... |
Is there an easy way to apply the trend line formula from a chart to any given X value in Excel?
For example, I want to get the Y value for a given X = $2,006.00. I've already taken the formula and retyped it out be:
=-0.000000000008*X^3 - 0.00000001*X^2 + 0.0003*X - 0.0029
I am continually making adjustments to the t... |
I have a bunch of experiments in which I am calculating precision and recall. I want to present a mean precision and recall for these experiments. Should these values be weighted by anything?
|
I use R. Every day. I think in terms of data.frames, the apply() family of functions, object-oriented programming, vectorization, and ggplot2 geoms/aesthetics. I just started working for an organization that primarily uses SAS. I know there's a book about learning R for SAS users, but what are some good resources for R... |
Suppose I'm doing binary classification, and I want to test whether using feature X is significant or not. (For example, I could be building a decision tree, and I want to see whether I should prune feature X or not.)
I believe the standard method is to use a chi-square test on the 2x2 table
X = 0 X = 1... |
Could someone walk me through an example on how to use DLM Kalman filtering in R on a time series. Say I have a these values (quarterly values with yearly seasonality); how would you use DLM to predict the next values? And BTW, do I have enough historical data (what is the minimum)?
89 2009Q1
82 2009Q2
89 2009Q3... |
I'm building a logistic regression, and two of my variables are categorical with three levels each. (Say one variable is male, female, or unknown, and the other is single, married, or unknown.)
How many dummy variables am I supposed to make? Do I make 4 in total (2 for each of the categorical variables, e.g., a male va... |
I'm doing some work on modelling transition matrices, and for this I need a measure of discrepancy or lack of fit: that is, if I have a matrix $T$ and a target matrix $T_0$, I want to be able to calculate how far $T$ is from $T_0$. Would anyone be able to provide pointers on what measure I should be using?
I've seen so... |
How can I measure linear correlation of non-normally distributed variables?
Pearson coefficient is not valid for non-normally distributed data, and Spearman's rho does not capture linear correlation.
Thank you
|
I have the following data of 2 diseases from 5 areas. I want to see if there is any relationship between the 2 diseases.
Incidence Rates of 2 diseases (cases per million per year)
Areas Disease 1 Disease 2
1 4.653 0.751
2 6.910 1.121
3 4.957 0.745
... |
How do I know when to choose between Spearman's $\rho$ and Pearson's $r$? My variable includes satisfaction and the scores were interpreted using the sum of the scores. However, these scores could also be ranked.
|
If I want to achieve a margin-of-error of <= 5 % for a representative population sample, how large a sample do I need when: The interviewees are picked from X regions and from Y age groups? That is, how many samples from each age group & region?
I know how many people live in each region and how they are distributed in... |
Let say we have only one sample in which we are interested only on one statistics c of this sample. This is usually true in practice when we usually have only one data set. So, most probably the usual estimating method like MLE cant be applied.
And let say we want to estimate 2 parameters (i.e. a & b) of a certain dist... |
I am running ivprobit in Stata to look at the determinants of enrolment in health insurance (cbhi). I have several exogenous regressors and one endogenous regressor (consumption). I am using wealthindex as an intrumental variable for consumption. However, when I run the ivprobit model all my exogenous regressors appear... |
Revised Version
Situation:
We have a sample of size $r$. Then, we count how many out of these $r$ to be "success".
Let $X=$ the no. of the "successes" and say $X$ follow Poisson dist.
Goal: To test whether $X$ is really Poisson using Dispersion Test with test statistics given by
$D=\frac{\sum_{i=1}^{n}(X_{i}-\overline... |
I am trying to study hidden conditional random fields but I still have some fundamental questions about those methods. I would be immensely grateful if someone could provide some clarification over the notation used on most papers about the topic.
In several papers the most common form of the the HCRF model is given as... |
I'm working on a project where we observe behaviour on a task (eg. response time) and model this behaviour as a function of several experimentally manipulated variables as well as several observed variable (participant sex, participant IQ, responses on a follow-up questionnaire). I don't have concerns about multicollin... |
Why doesn't recall take into account true negatives? In experiments where true negatives are just as important as true positives, is their a comparable metric that does take it into account?
|
I have a dataset that's nominally 16-dimensional. I have about 100 samples in one case and about 20,000 in another. Based on various exploratory analyses I've conducted using PCA and heat maps, I'm convinced that the true dimensionality (i.e. the number of dimensions needed to capture most of the "signal") is around ... |
How do I establish the +/- in terms of a set of mean ages. My mean age is 27.2. The ages are 20 23 24 43 22 26 18 32 18 41 22 20 26 46 21 27 19 19 39 40 19 39 18 38 24 24 23 30.
Thank you.
|
I have a linear string of unit length, and I randomly sample two locations a and b from Uniform(0, 1). Then I cut the string at these two locations to get a sub-string. What is the distribution for the size of the sub-string (i.e. |a-b|)? Otherwise, I want to at least know the mean and variance.
|
Asking this for a colleague:
They have two groups of people with various characteristics and to address the issue of comparability of outcomes they would like to reference a paper or book that discusses the concept and problems of common support.
|
Background
One of the most commonly used weak prior on variance is the inverse-gamma with parameters $\alpha =0.001, \beta=0.001$ (Gelman 2006).
However, this distribution has a 90%CI of approximately $[3\times10^{19},\infty]$.
library(pscl)
sapply(c(0.05, 0.95), function(x) qigamma(x, 0.001, 0.001))
[1] 3.362941e+19 ... |
I am currently reading a paper concerning voting location and voting preference in the 2000 and 2004 election. In it, there is a chart which displays logistic regression coefficients. From courses years back and a little reading up, I understand logistic regression to be a way of describing the relationship between mu... |
In R I can perform a Breusch–Pagan test for heteroscedasticity using the ncvTest function of the car package. A Breusch–Pagan test is a type of chi squared test.
How do I interpret these results:
> require(car)
> set.seed(100)
> x1 = runif(100, -1, 1)
> x2 = runif(100, -1, 1)
> ncvTest(lm(x1 ~ x2))
Non-constant Varian... |
According to this document: The estimated logarithm of the hazard ratio is approximately normally distributed with variance (1/d1) + (1/d2), where d1 and d2 are the numbers of events in the two treatment groups.
Do you have a reference for this statement? Or at least can you say me which estimator is used?
|
Our small team was having a discussion and got stuck. Does anyone know whether Cox regression has an underlying Poisson distribution. We had a debate that maybe Cox regression with constant time at risk will have similarities with Poisson regression with a robust variance. Any ideas?
|
I am trying to sample from a Gamma distribution in JAGS
gd[i] ~ dgamma(k,r)
where k and r are have priors such that they are positive. However I get the following error when I compile the model:
Error in node gd[9]
Unobserved node inconsistent with unobserved parents at initialization
Any ideas?
EDIT: BACKGROUND
W... |
I want to calculate the hat matrix directly in R for a logit model. According to Long (1997) the hat matrix for logit models is defined as:
$$H = VX(X'VX)^{-1} X'V$$
X is the vector of independent variables, and V is a diagonal matrix with $\sqrt{\pi(1-\pi)}$ on the diagonal.
I use the optim function to maximize the l... |
I have two variables and 1000 cases. How can I statistically find representative cases from total of 1000, based on statistical properties of both variables and correlation between them. Perhaps something based on T-test and 95% (or 99%) interval but for both variables? I would like to know which statistical method can... |
I am a software designer by trade and I am working on a project for a client, and I would like to make sure that my analysis is statistically sound.
Consider the following: We have n advertisements (n < 10), and we simply want to know which ad performs the best. Our ad server will randomly serve one of these ads. Su... |
I read from a textbook that Gauss-Newton regression is also called 'artificial regression'. Please give me an example, how does it work? And what's the relation with Newton's method? Thank you.
|
I am running a large OLS regression where all the independent variables (around 400) are dummy variables. If all are included, there is perfect multicollinearity (the dummy variable trap), so I have to omit one of the variables before running the regression.
My first question is, which variable should be omitted? I hav... |
I have a boxplot output in R using ggplot2:
p <- ggplot(data, aes(y = age, x = group))
p <- p + geom_boxplot()
p <- p + scale_x_discrete(name= "Group",)
p <- p + scale_y_continuous(name= "Age")
p
I need to add horisontal lines like on common boxplot (and to change vertical line style if possible):
boxplot(age~group,d... |
Is there an analytic form for the Hellinger distance between von Mises distributions?
|
If, for example, I have 0011 as a set of known bits $x$, how do I determine the probability that a sequence of randomly generated bits is equal to $x$?
Thanks for the help! I'm sure this is a dumb question, but probability has always been my weakness (which my algorithms class is highlighting!).
EDIT: This is what I sh... |
I solve Rubik's cubes as a hobby. I record the time it took me to solve the cube using some software, and so now I have data from thousands of solves. The data is basically a long list of numbers representing the time each sequential solve took (e.g. 22.11, 20.66, 21.00, 18.74, ...)
The time it takes me to solve the ... |
Does any body know of a Java implementation of McNemar's Test?
|
I have almost the same question as:
How can I efficiently model the sum of Bernoulli random variables?
But:
(1) The number of random variables for summation is ~ N=20 (case 1) or N=90 (case 2).
(2) $p_i$ ~ 0.13 (case 1)
(3) The precision of the model based on Poisson law is not enough.
(4) We need that our approx would... |
Apologies for the rudimentary question, I am new to this form of analysis and have a very limited understanding of the principles so far.
I was just wondering if many of the parametric assumptions for multivariate/univariate tests apply for Cluster analysis? Many of the sources of information I have read regarding clus... |
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