Questions tagged [independence]

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 of Mean and Variance of Discrete Uniform Distributions

In the comments below a post of mine, Glen_b and I were discussing how discrete distributions necessarily have dependent mean and variance. For a normal distribution it makes sense. If I tell you $\...
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Violation of Independence of Observations - Logistic Regression

Apologies if this seems a basic question but I can't find enough detailed information about what exactly constitutes a violation of independent observations. The regression I'm wanting to run is ...
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1answer
35 views

Do i need independence for paired t-test?

I am testing the mean change in IOP of eyes in a glaucoma study. When looking at just the 'Primary Eye', i am using a paired t-test to test the mean change from baseline as this is one eye per patient....
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Arch models: dependence and squared residuals

I would like a mathematical and intuitive answer to those questions: Why a dynamics like arch in the volatility of a time series implies that the time series is dependent (although not autocorrelated)...
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Appropriate statistical test for a repeated measures design with nested nominal variables

Context: Financial Portfolios Sample: time series slices of stock investments. Dependent Variable: stock value change during the slice. Independent Variable: Position change of investor during this ...
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2answers
67 views

Determination of statistically relevant quantitative/qualitative variables

I have a database containing records of several parameters: one is a quantitative parameter $D$ (e.g. average fuel consumption), others are qualtitative parameters $X_1, ..., X_n$ (e.g. make, color, ...
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17 views

Are non-independent samples an issue in within groups designs

I'm currently designing a statistical analysis. Currently opting for a repeated-measures ANOVA with 4 factors. The data I am using a list of time series. These are grouped by where they came from and ...
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1answer
56 views

Quantitatively assess if independent variables are sufficient to determine dependent variable behaviour

I have the matrix of the independent variables X with dimensions n_samples x m_features and a vector ...
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48 views

conditional independence mixed linear models

I'm analyzing an experiment using linear mixed models but am not sure whether my model is appropriate or whether I'm violating the assumption of conditional independence. I've asked a statistician at ...
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1answer
24 views

testing for significance of proportion over time

I'm analyzing a survey over time, last year and this year, and I've been asked to compare the proportion of the two time periods for significance, from the same survey and same question data is ...
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16 views

Rewrite joint probability as product of marginals when all the probabilities are $1$ or $0$

I have a question about the possibility of rewriting a joint probability as the product of the marginals when all the probabilities can only take value $1$ or $0$. I start with introducing some ...
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19 views

How to test if a sequence is iid U(0,1)?

I have a sequence of time-stamped numbers between 0 and 1 inclusive. They are not residuals from fitting any time series model: they are just raw data. I would like to test that they are (a) uniformly ...
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13 views

Treating dependent timepoints as independent

I've been given a data set to work with that includes measurements of the same group of individuals over approximately 6 months (3 measurements total). The problem is that they did not include any ...
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1answer
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Do randomization tests for difference in means assume independent groups?

I performed a randomization test and found that the means of groups A and B are significantly different. I am trying to prove that group B is "special", that there is something interesting going on ...
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1answer
38 views

Is it possible to get non-significant post hoc test in a significant ANOVA test while the unpair t-tests are significant? [duplicate]

I conducted One-Way ANOVA to compare means in 4 groups. The ANOVA was significant, but the post hoc tests were non-significant. Then, I applied unpair t-tests to compare each group to the lowest group....
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Show that $\pmb{\hat{\beta}}$ and $\pmb{\hat{\sigma^2}}$ are independents and $SSRes$ and $SSR$ are independents too

I can't show that $\pmb{\hat{\beta}}$ and $\pmb{\hat{\sigma^2}}$ are independents and that $SSRes$ (residuals) and $SSR$ (regression) are independents too. I need to show this in matrix notation.
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Does $P(X>x, Y>x)= P(X>x)P(Y>y)$ implies independence?

We know, by definition, that two random variables are independent if $$P(X\leq x, Y\leq y)= P(X\leq x)P(Y\leq y).$$ If, insted, I have that $$P(X>x, Y>y)= P(X>x)P(Y>y),$$ does this also ...
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Test correlation/dependence of many variables on one continuous variable

I have 9 individuals, each with 4640 dependant measurements (gene expression data), and one more measurement (percent of blood cells infected). The data frame has the individuals as columns and ...
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1answer
16 views

Independent variables in conditional probability

So I am reading this paper about reasoning(Hall, Ali, Chater, & Oaksford, 2016). Consider this conditionals. ...
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65 views

Why the distribution $Y/\sigma$ does not depend on $\sigma$?

This book describes the scale parameter as below: Suppose $\sigma$ is a scale parameter, in the sense that $p(y|\sigma)=\sigma^{-1}f(y/\sigma)$ for some function $f$, so that the distribution ...
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Understanding influence of correlated predictors on target variable

I am working on a problem where I have a "target" variable $Z$ that I know for sure is influenced by a "predictor" $Y$. I also have a second predictor $X$ that is correlated with $Y$ (about -.3), and ...
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17 views

Is independence of two random variables sufficient to rearrange summations?

Suppose $X$ and $Y$ are two random variables where their sample spaces may or may not intersect. My question is whether there is ever a situation where the following is not true:$$\sum_{(X,Y)}p(x)p(y)(...
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Why does independence matter in Statistics & Why does a MLM change Fixed Effect Coefficients?

I've been trying to get a better grasp of statistics lately, and have been wondering why exactly independent observations matter when building a model? This is a broad question, but I'm curious about ...
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How to compare two samples with not independent observations within each one?

To best of my understanding, both parametric two-sample t-test and non-parametric Mann–Whitney U test assume that observations are independent. I believe that making a permutation test (randomly ...
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1answer
49 views

Why $E$ and $F$ are conditionally independent given $C$ and $D$?

Below is a Directed Acyclic Graph (Fig.a). From this figure, it is said that: $E$ and $F$ are conditionally independent given $C$ and $D$. I am confused about it. Let's assume the causal ...
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1answer
77 views

If $X$ and $Y$ are independent variables from each other, then are $(X,Y)$ and $X$ necessarily independent?

If $X$ and $Y$ are independent variables from each other, then are $(X,Y)$ and $X$ (necessarily) independent? Assume one is trying to analyze the effect of peer education (education from patient to ...
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Why does independence imply zero correlation?

First of all, I'm not asking this: Why does zero correlation not imply independence? This is addressed (rather nicely) here: https://math.stackexchange.com/questions/444408/why-does-zero-correlation-...
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1answer
55 views

$X\perp Y \Leftrightarrow Y\perp r(X)$?

Consider the random variables $Y$ and $X$. Let $\mathcal{X}$ denote the support of $X$. Let $\mathcal{Y}$ denote the support of $Y$. Let $r:\mathcal{X}\rightarrow \mathbb{R}$. I have doubts about the ...
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Co-training independent views

I found a tutorial on co-training that mentions that I need two views for training, which are conditionally independent. Could someone explain to me what this means regarding datasets?
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How to Use Chi-Squared Test for Inference about Three-way independence

If I recall correctly, three random variables X, Y, and Z are three-way independent iff these two statements are met: P(X∩Y∩Z) = P(X)P(Y)P(Z) X, Y, and Z are all pairwise independent of each other. ...
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23 views

I.i.d.-ness of some functions of random variables

I have some doubts on the i.i.d.'ness of some functions of random variables. The framework What I'm describing below is a simplied version of a well known model in economics of demand and supply. ...
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1answer
27 views

Probability of event independent of random variables [closed]

Let {$X_n$} be a sequence of independent random variables and for each $n$, the event $A$ is independent of $X_1$, $X_2$,..., $X_n$. Show that $P(A)$ is $0$ or $1$.
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29 views

Finding distribution and checking independence of transformed normal variables

$X,Y,Z$ are three independent random variables following standard normal distribution. Consider a real function $f$ such that \begin{align}f(x)&=1 , x\geq 0 \\ &= -1, x<0\\ \end{align} Let $...
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1answer
55 views

Identify dependent or independent blocks of time series (clusters)

maybe I am lost in translation but I need your help. Description: Having long time series of two variables I create some blocks (or clusters) with the method of peak over threshold but I need to ...
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1answer
35 views

Independence between sum of $F(X_i)$ and the cumulative distribution function $F$

I am stuck in the following problem. $X_1,\ldots,X_n$ is a random sample from a continuous distribution with Cumulative Distribution Function (CDF) $F$. Prove that the distribution of $T=\sum_{i=1}^m ...
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2answers
29 views

Can independent/dependent events be thought of graphically?

My understanding is that events are subsets of the total outcomes in a sample space. So if two events are mutually exclusive, then they (the sets) do not overlap in the sample space. This can be seen ...
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5 views

Measuring effects of IV (constant) on DV

I have an independent variable (a bias) that is technically a constant. I want to measure the effects of the IV on the DV. How do I do this? I'm using SPSS. Let's say, participants produced A or B ...
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2answers
42 views

Covariance of two normally distributed variables

I saw in a statistic book that "It can be prooved that if two normally distributed variables have covariance = 0, they are independent". How can I start this proof? Can I say that $cov(X,Y) = E(XY) ...
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35 views

Can two random variables be independent in some basis and dependant in other?

If some random variables forming N dimensions are dependant on each other is it possible that in a different coordinate system they'd be independent? For example if (X, Y) are two dependent RVs is it ...
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14 views

Use of a predictor variable for a dependent variable that is directly related to the predictor variable

If I would like to predict a binary variable x, and x is true if y is true and ...
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1answer
17 views

independence of product of independent random variables with one of the variables

Take random variables A and B, which are independent. Is it the case that AB (product) is independent of B?
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13 views

i.i.d. random vectors [duplicate]

If $(X_1,Y_1), (X_2,Y_2)$ are independent random vectors having the same joint distribution function $F$, then is it correct to say: $E(X_1)=E(X_2)$ and $E(Y_1)=E(Y_2)$ (the same for variance); Both, ...
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1answer
11 views

Relationship/independence between 2 binary varibales

I got a dataset in Excel with 2 dichotomous variables: trained (1 or 0), part-time (1 or 0). The question asks if whether there is a relationship between those who have been trained and whether they ...
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19 views

F ratio independence of numerator and denominator

For a particular hypothesis testing problem I have the quantity $F = \frac{\sum_{j=1}^{k} (\overline{X_j})^2}{\sum_{j=1}^{k} \sum_{i=1}^{n} (X_{ji} - \overline{X_j})^2}$ where $X_{ji}$ is the $i^{th}$ ...
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Can I take a random sample of my very large data set to overcome non-independence?

I am trying to run a regression model on a very large time series data set (comparing flow noise to vehicle speed, pitch and dive state). Because my samples are taken about every minute (with some ...
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1answer
49 views

When knowledge of one event tells us nothing about another

I have an example; Say I have two genes on two different locations on two different chromosomes. P(A) = gene is from location 1 P(B) = gene is from location 2 Geneticists believe that knowledge of ...
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56 views

Confused about multilevel analysis and non independence of observations

I'm still struggling with my understanding of multilevel analysis, wondering if it applies or not to my problem. I'v read here the following (where author gives an example of a multilevel model with ...
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27 views

Independence test with priors

Say you are selling a product, and you know from experience that the green version of the product sells better than the blue version. But you have two types of customer A and B, and you want to know ...
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2answers
34 views

What is the difference between having input parameters that are independent/dependent in ML tasks?

This is more of a general question. But, when you feed in inputs into a machine learning algorithm, are the inputs typically dependent or dependent? What are the implications if the inputs are ...