Events (or random variables) are independent when information on some of them tells you nothing about the probability of occurrence (/ distribution) of the others. Please DO NOT use this tag for independent variable use [predictor] instead.

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Independence test for two small, exhaustive, categorical variables

I've got a categorical variable $var$ and a binary variable $critere$, from a pretty small (n = 300) but exhaustive dataset (i.e., the dataset contains the whole population that I want to study). I ...
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26 views

Does the degree to which events are independent increase as the number of events increase?

I'm considering a problem of independence of events. Specifically, I am considering whether events are more independent the greater the number of events. Two examples might help. Example 1: There ...
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5 views

how to quantify the dependence between two sparse signals?

Hi and thank you for your help. I am happy to provide more context/details. In my research, I have a system that has many sensors X_1..X_N and using this ...
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22 views

Data augmentation techniques for general datasets?

In many machine learning applications, the so called data augmentation methods have allowed building better models. For example, assume a training set of $100$ images of cats and dogs. By rotating, ...
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18 views

When used for feature selection, does the chi-squared test require the features to be nonnegative?

scikit-learn says chi squared test used for feature selection in classification problems and implemented by sklearn.feature_selection.chi2 requires the feature ...
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1answer
37 views

Does rank of observation matrix tell anything useful when applying machine learning?

Suppose I have an observation matrix of size $N \times M$ where $N$ is the number of samples and $M$ is the number of variables. If the rank of the observation matrix is $R<M$, does it tell ...
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30 views

What kind of feature selection can Chi square test be used for?

Here I am asking about what others commonly do to use chi squared test for feature selection wrt outcome in supervised learning. If I understand correctly, do they test the independence between ...
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5 views

How do I account for non-independence in occupancy modeling?

I have conducted a survey to look at why badgers are visiting some gardens but not others. I have data on badger presence / absence and garden features that might influence badger presence in that ...
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59 views

Consequence of violation of independence assumption on estimates of standard errors

from the first chapter , Introduction to Multilevel Analysis , p.5 of the book , it is written that : Standard statistical tests lean heavily on the assumption of independence of the ...
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13 views

Suppose X_1 X_2, …, X_n are n independant variables, is their Covariance matrix sigma diagonal?

Suppose I have n variables X: X_1, X_2, ..., X_n that are independent from each other. Which means that: if i≠j, then Cov(X_i, X_j) = 0 As a consequence, I'm wondering if their Covariance Matrix ...
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23 views

Solving the probability of independent events without the complement

Suppose that virus transmission in 500 acts of intercourse are mutually independent events and that the probability of transmission in any one act is $\frac{1}{500}$. What is the probability of ...
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39 views

Independent RVs theorem: rigorous?

I am reproducing here theorem (#3.30) from "All of Statistics" by Larry Wasserman: Let X and Y have joint pdf $f_{X,Y}$ . Then $X\perp Y$ if and only if $f_{X,Y}(x,y)=f_{X}(x)f_{Y}(y)$ for all ...
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1answer
34 views

Are two variables that are dependent also correlated? / Can two dependent variables not be correlated? [duplicate]

I cannot find the answer to my question anywhere, I hope someone can help. I did a Chi-Square test with several variables to see if they were dependent or independent. The result showed that they ...
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19 views

Data Assumptions for AIC model comparisons

I recently started digging into statistical information criteria, more specifically the Akaike Information Criterion. As the literature I have read so far does not cover this, I was wondering whether ...
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35 views

Are Latin hypercube samples uncorrelated

I understand the basics to Latin hypercube sampling, such as implemented by the algorithm LHSA mentioned in the book Design and Modeling for Computer Experiments. But I'd like to make sure: 1, n ...
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14 views

statistically analyzing independent variables

I am kind of new to statistics. I have 4 independent variables that has been observed from a system in 4 different configurations. At this point, I don't know what are the best statistical functions ...
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3answers
55 views

importance of independence among random variables

I always read random variables as being independent and identically distributed. I understand the concept of being identically distributed, because if different random variables are distributed in ...
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40 views

CDF of sum of 3 independent discrete uniform random variables on {1,2,…,n}

What is an approximate closed formula for this probability, with a derivation: p(k,n) is the probability, that among $n$ PC discs and $k$ errors in sum on them, there will be at least $1$ disc ...
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1answer
31 views

assuming independency between independent variables in multiple regression?

I heard that multiple regression assumes that the independent variables are correlated somehow. So when we convert the multiple regression into SEM diagram, we see covariance arrows are drawn ...
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1answer
45 views

Are $\hat{\beta}_{\text{ls}}$ and $S^2$ independent if errors are not normally distributed?

When estimating a linear model $$ Y_i = X_i\beta + \varepsilon_i \quad \quad 1\leq i\leq n$$ We have $\hat{\beta}$ the least squares estimation of the slope and the estimation of the variance, $S^2 = ...
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2answers
47 views

Show that $Y_1 X_1 + Y_2 X_2$ $\,{\buildrel d \over =}\,$ $(Y_1^2+Y_2^2)^{1/2}X_1$

I would like verification of my solution to the following problem. QUESTION: Let $X_1, X_2 \,{\buildrel iid \over \sim }\, N(0,1) $ and let $Y_1, Y_2$ be two independent random variables ($X_1, ...
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25 views

Test for independence in 3x2x2 table with small expected cell values

I have three unordered categorical variables. I have made a 3x2x2 table, but I'm uncertain of how to test for independence. The usual manner is a chi-squared statistic, but I think this is ...
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1answer
65 views

What is the demonstration of the variance of the difference of two dependent variables?

I know that the variance of the difference of two independent variables is the sum of variances, and I can prove it. I want to know where the covariance goes in the other case.
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19 views

How to run ANOVA on multiple groups of samples, each composed by different variables

I have a $m$ x $n$ matrix, where the $n$ columns are split into multiple classes. If I had only a $1$ x $n$ vector, I would have used ANOVA to evaluate if all subset of columns had the same ...
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4 views

Chi-square test for independence of categorical variables [duplicate]

I'd like to know about independence of categorical variables. I read an article from https://explorable.com/significance-test-2 H0: “Having breakfast in the morning has no effect on the grades of ...
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Comparing change in lateral root densities between treatments for different genotypes

I have been growing 4 genotypes of the same plant and been recording their lateral root density under both control conditions and a salt treatment. I have calculated the decrease in lateral root ...
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2answers
99 views

Random variables independence

I need to check if $Z$ and $W$ are dependent or not. $X,Y \sim \mathrm{Exp}(2)$ Then I define: $Z=X-Y \ \text{,}\ \ W=X+Y$. Now How I can check that $Z$ and $W$ are dependent or not ? I know ...
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234 views

In linear regression, what does $\beta_1 = 0$ really mean?

If granted omniscience and we know that $\beta_1$ in a multiple linear regression model is truly 0, what does that mean in words (and math notation)? The model is: $Y = \beta_0 + \beta_1X_1 + ...
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69 views

In Berkson's paradox, is $\beta_1 = 0$ or $\ne 0$?

There is "a general phenomenon known as Berkson’s paradox (Berkson, 1946), whereby observations on a common consequence of two independent causes render those causes dependent. For example, the ...
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13 views

shape of distribution and indepencence

I have a sample of observation on which normality tests (Anderson Darling, Shapiro - Wilks, KS,...) would accept the assumption of normality. Nevertheless I know that there is a certain time - ...
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2answers
113 views

Approaches for generating synthetic survey data with dependent answers?

I would like to produce synthetic survey data. At the moment I produce independent answers between questions according to an arbitrary discrete distribution as in this question. I want to generate ...
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19 views

Probability mass function of a r.v $Z$, $Z:=$ the sum of the values of two die

We are told that we are rolling a die twice, where $$X:=\;the\;value\;of\;the\;first\;roll$$ $$Y:=\;the\;value\;of\;the\;second\;roll$$ $$Z:=X+Y$$ We are told to find the moment generating function ...
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is it legitimate to t-test between statistics of a bootsrap?

say I have two samples $x_1$ and $x_2$ and a function which calculates a statistic out of each sample, denotes as $f(x)$. I would like to test the significance of the difference $f(x_1)-f(x_2)$. A ...
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12 views

Factor conditioning variables

Let $A,B,C$ be $3$ random variables. If $p(A,B\mid C) = p(A\mid C) \cdot p(B\mid C)$ holds, then $A$ and $B$ are conditionally independent given $C$. My question is: What are the underlying ...
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28 views

Variance of multinomial distribution that is product of 4 Beta random variables

I have a system of 4 binary random variables, $A$, $B$, $C$ and $D$. $A$, $B$ and $C$ are conditionally independent given $D$, and I'll call one set of samples $ABCD$ an event (e.g. $ABCD$ meaning all ...
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30 views

Logit: using lagged dependent variable

Is it methodologically feasible to include lagged dependent variable in the logit model?
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3answers
62 views

Dependent or Independent…a little intuition

I have a time series that describe the power consumption of a building. For every hour of the day I have a measurement (e.g Hour 0 = 2.3 kWh, Hour 1 = 4.2 kWh etc). Do you believe that the ...
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35 views

Chi square test of independence with multivariate nominal data

I used a list-type open-ended question to collect responses, in which respondents can list up to 6 items. After coding the items, I have the multivariate nominal data. I want to check if my IV ...
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80 views

Independence among intersubject correlations

Suppose that there are some data collected in the form of time series from 3 subjects: $X_1 = (x_{11}, x_{12}, ..., x_{1n})$ $X_2 = (x_{21}, x_{22}, ..., x_{2n})$ $X_3 = (x_{31}, x_{32}, ..., ...
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560 views

Are PCA components of multivariate Gaussian data statistically independent?

Are PCA components (in principal component analysis) statistically independent if our data is multivariate normally distributed? If so, how can this be demonstrated/proven? I ask because I saw this ...
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19 views

Factorization of probability distribution and its Bayesian Network

My question is if we have a distribution $P$ that can be factorized into cond. distributions, can we model it with Bayesian Networks? I mean, $P(X_1,X_2,...,X_n) = \prod_{i=1}^n P(X_i|Cond(X_i))$ ...
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33 views

Does negative binomial regression assume sample independence?

I'm working with a negative binomial multiple regression and I'm wondering about the assumption of spatial independence of samples. White and Bennetts (1996) say that the assumption of spatial ...
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10answers
10k views

Are your chances of dying in a plane crash reduced if you fly direct?

I recently had a disagreement with a friend about minimizing the chance of dying in a plane due to a crash. This is a rudimentary statistics question. He stated that he prefers to fly direct to a ...
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1answer
128 views

Plain language meaning of “dependent” and “independent” tests in the multiple comparisons literature?

In both the family-wise error rate (FWER) and false discovery rate (FDR) literature, particular methods of controlling FWER or FDR are said to be appropriate to dependent or independent tests. For ...
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22 views

Dealing with independent events and a “given” statement

I'm given a question: Two buddies, plan a squirrel-hunting trip. B has a shot 2x better than A. A's chance of hitting the squirrel is 0.39, they see a squirrel and both shoot at the same time. ...
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25 views

joint distribution translated into union of intersection?

Consider the declaration of the intersection property for conditional independence. $$ \left.\begin{align} X \perp\!\!\!\perp A \mid B \\ X \perp\!\!\!\perp B \mid A \end{align}\right\}\text{ and ...
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How to do a test of independence on discrete quantitative observations

When doing A/B tests on websites I typically use Fisher's exact test. Now this works fine when using goals that either are reached or not, but in an e-commerce context it's really more interesting to ...
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7 views

FE Model: independence of residual and firm specific component

I'm estimating a fixed effects model and want to consider Petersen's (2009) suggestion: "The components of X (μ and ν) and ε (γ and η) have zero mean, finite variance, and are independent of each ...
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63 views

Are cross-validated prediction errors i.i.d?

Say, we test an arbitrary regression or classification procedure on $n$ independent samples with leave-one-out cross-validation. This results in an estimate of the prediction error $e_n$ for each ...
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1answer
64 views

Graphical dependence in the DAG X->Z<-Y

In Barber's book pp. 40-41 he says that the belief network X->Z<-Y: is "graphically dependent" since: $$p(x,y|z) \propto p(z|x,y)p(x)p(y)$$ I don't understand why graphical dependence follows ...