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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How do test that two continuous variables are independent using rank statistics in R? [on hold]

This question a particular case of this question. Suppose we have a sample $(X_i,Y_i),i=1,\ldots,n$ from the joint distribution of $X$ and $Y$. Are there any other function (or package) apart from ...
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0answers
7 views

Logit: using lagged dependent variable

Is it methodologically feasible to include lagged dependent variable in the logit model?
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3answers
58 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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0answers
11 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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0answers
37 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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1answer
440 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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0answers
15 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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21 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
8k 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 ...
7
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1answer
93 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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0answers
16 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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0answers
16 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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17 views

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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0answers
6 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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2answers
43 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
50 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 ...
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1answer
65 views

Asymmetric measure of non-linear dependence/correlation?

I am definitely not a statistician/mathematician so feel free to tell me I'm an idiot if I am. As far as I can tell from my Wikipediaing all of the main measures of dependence are symmetric and ...
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0answers
18 views

Compare two independent samples with one variable

It is assumed that in computer programming courses, students programming in pairs will have better grades than students programming alone (solo-programming). After collecting data about the grades of ...
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1answer
60 views

Examples of marginal independence, conditional dependence

I am interested in finding "real-world" examples of when variables might exhibit marginal independence but are conditionally dependent given some other variable. It seems to me that the converse ...
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0answers
44 views

Is this interaction endogenous or independent?

Imagine a multiple regression of the form $ y = \beta_0 + \beta_1x_1 + \beta_2x_2 + \beta_3x_1 x_2 + u $ Now imagine that $x_1$ is endogenous (in that it is correlated with $u$) but $x_2$ has been ...
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0answers
8 views

Observations independence

I have observed prices of products (phone plans) that appear in the market in each year during 8-year period. When the product is on the market, its price doesn't change. For such products, when price ...
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0answers
18 views

Flow of influence in a v-structure for Probabilistic Graphical Models

I'm not very sure I understand why an observed v-structure have different flow of influence behaviour for a directed and an undirected graph. What is the intuition behind the actual definition for ...
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1answer
134 views

Why is independence required for two- sample proportions z test?

I read in several books as well as in different posts (e.g. here) that independence is required for two-sample proportions z tests. But so far I could not find an explanation why this is the case and ...
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9 views

What is the best way to test if an IV has a stronger effect on the DV than another IV that a subset of the first IV?

I wish to investigate the effect of general international experience of a corporation measured as the number of foreign subsidiaries it own vs. the effect of local experience in a region measured as ...
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0answers
30 views

Does diagnolizing higher-order cross-moment matrices lead to independent variables?

Diagonalizing the covariance matrix transforms multivariate data into uncorrelated variables, but does not make them independent necessarily. Does it follow from this that if I were to diagonalize ...
3
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1answer
151 views

Linear independence vs statistical independence (PCA and ICA)

I'm reading this interesting paper on application of ICA to gene expression data. The authors write: [T]here is no requirement for PCA components to be statistically independent. That is true, ...
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1answer
48 views

Paired samples or independent sample hypothesis test for two time periods

I want to know if employees in an organization are surveyed in 2013 and again in 2014 if the samples from the two time periods are considered related and dependent or independent if they are asked the ...
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1answer
22 views

Reg: MGF and independence

If three random variables X, Y, and Z are pairwise independent, whether U = aZ+bY, V = aY+bX are independent? I tried using MGF technique and arrived (i don't know its correct or not) as U and V are ...
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1answer
26 views

Independence within groups - which test?

I have a table of data with three columns: ...
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2answers
61 views

Can someone explain what it means for an observation, from a group of data, to be independently and identically distributed?

I don't quite understand what the difference is between an observation being independent and it also being identically distributed. Can someone explain please?
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2answers
31 views

Determining unusual binomial results from a sub-population

If I have a population of 1948 students with a success rate of .154 (301 successes) and I break the 1948 students into their respective majors, how to I determine if the sub-population success rate is ...
0
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1answer
30 views

Are identical samples independent?

Are results of two different tests performed on exact same sample independent or dependent? For example, if the same group of rats were injected some drug A, results collected, then long enough time ...
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0answers
19 views

How to determine if these values are different?

I don't have much stats background (I am a programmer) but want to learn more. I have five long columns of numbers that represent conversion rates (ex. how many successes vs. how many attempts) for 5 ...
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1answer
136 views

Conditional independence iff joint factorizes

I have proven that: $X⊥Y|Z\ {\rm iff}\ p(x,y|z)=p(x|z)p(y|z)$ for all $x,y,z$ such that $p(z)>0$. The next question is to prove an alternative definition: $X⊥Y|Z$ iff there exist functions $g$ ...
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2answers
57 views

Transform two correlated random variable to independent variables without knowing correlation

I am thinking about this interesting question which arises in the following realistic setting. For example, in one medical experiment one drug and one placebo are applied to two randomized groups of ...
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1answer
67 views

Assume (x,y) are drawn from independent & identical distribution when y=f(x)

Sometimes we say the following: $X$ is some training data given by $X:=\{(x_1,y_1),...,(x_l,y_l)\}\subset R^d \text{x}R$. Assume that the training data had been drawn from independent and identical ...
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1answer
56 views

Indepent variables and these functions [closed]

Random variables $x_1, x_2,...,x_n$ are independent. Then I want to show whether these functions $$y_1=f_1(x) \\ y_2=f_2(x) \\ ... \\ y_n=f_n(x)$$ are independent or not . How to prove this?
3
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0answers
65 views

joint distribution, probability, calculating probabilities under false independent assumption, when the random variables are actually dependent

Suppose I have random variables $X,Y,Z$ and I would like to compute the probability that random variable $X$ is smaller than $Y$ and $Z$: $$ \pi_X \overset{def}{=} Pr(X < Y, X < Z) = \int Pr(x ...
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1answer
48 views

Is there a difference between degrees of freedom and independent variables? [duplicate]

They seem to represent the same idea as far as I can tell - can they be used interchangeably?
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2answers
59 views

Derive the LLN for a certain sequence

I have a sequence of dependent random variables $X_1, X_2...X_n$. Each RV is correlated with two other RVs and uncorrelated with the others.The ones that are correlated satisfy the condition ...
2
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0answers
17 views

Is there a test of pair-wise independence for a sequence of non-identical Bernoulli random variables?

Given a sequence of $n$ instances of Bernoulli random variables $x_1,\ldots,x_n$, I am interested in testing whether $x_i$ is independent of $x_{i-1}$ for $i=2,\ldots,n$ (i.e. ...
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0answers
18 views

Probability that difference between demand for two skills in a population sample is due to chance

I am trying to measure the demand for two skills in group of companies that are hiring software developers. One skill might be e.g. Java and the other e.g. C++. If out of 100 companies, 30 report they ...
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1answer
46 views

Example for uncorrelated, not independent , but with same distribution functions random variables

I am looking for an example of two random variables X and Y on $\Omega=\{-2,-1,0,1,2\}$ with the following properties: a) X and Y have the same distribution b) X and Y are uncorrelated c) X and Y ...
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0answers
53 views

Will something terrible happen if my data points aren't independent?

Suppose I run a bunch of experiments, and get a bunch of datapoints, but several of the datapoints were derived from the same experiment. (In the extreme case, I just repeat the same datapoint 10 ...
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2answers
138 views

How to prove dependence of random variables

I need to solve the following problem. Let $X$ be a normal random variable with mean $\mu$ and standard deviation $\sigma$ and let $I$, independent of $X$, be such that $\mathbb{P}(I = 2) = ...
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0answers
67 views

What to use when chi-square independence assumption is violated

I'm trying to describe the characteristics of the sexual partners of each participant. There are multiple partners per participant. All of the variables in my analysis are categorical, so originally I ...
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41 views

Mean independence and full independence

What is an example of two random variables x and u that are NOT fully independent but such that E(u|x) = 0? Many thanks!
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2answers
149 views

Characteristic function problem

Suppose $X_1$ and $X_2$ are independent random variables and suppose also that $X_1$ and $X_1-X_2$ are independent. Show that $$\mathbb{P}_{X_1}[X_1=c]=1$$ for some constant $c$. What I get so ...
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0answers
53 views

Conditional independence: conditioning on an empty set of random variables

Is $X \perp\!\!\!\perp Y$ a conditional independence, arguing that the independence is conditioned on an empty set of random variables? If so, does that mean that an unconditional independence is ...
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1answer
19 views

Why do Fisher & $\chi^2$ tests show dependence for simulated Markov chain in nonadjacent observations?

I'm trying to understand Fisher's exact test and the $\chi^2$ test of independence. Suppose I've got a Markov Chain of first order with the following TPM: $M = \begin{pmatrix} 0.3 & 0.7 \\ 0.99 ...