Data, events, processes, etc, are non-independent if knowledge of 1 provides some information about the state or value of the other.

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Paired test (non-independent) for rank order data

I have responses from a survey with questions where respondents were asked to rank their top 3 choices from a list of 8 choices. An example of the type of question would be to rank their top 3 methods ...
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0answers
16 views

sum of dependent random variables [closed]

I want to find a function that determine connection between x and y that x and y both of them are determine by a common other factor. in fact x and y are dependent variables. function is like a ...
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0answers
12 views

Testing for dependence of unpaired and unequally-sized samples

I've seen several similar questions, but I haven't been able to find an answer. I have two unpaired samples of unequal size and of equal population variance. One concern is that these samples are ...
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0answers
20 views

Can longitudinal studies ever be treated as having independent observations?

This may be a dumb questions, but for sake of statistical analyses I'm wondering if the data of a longitudinal study can ever pass the assumption of having independent observations? For example, I am ...
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1answer
32 views

distribution of sample variance of correlated observations

It is well known that if we have n i.i.d. observations of a normal random variable, then Cochran's theorem tells us that: $\frac{(n-1)s^2}{\sigma^2} \widetilde{} χ^2_{n-1}$ But what if the samples ...
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1answer
22 views

Extreme Value Distribution of dependent RV

Let $X_1, \dots, X_n$ be random variables with known identical distribution and covariance matrix $C \in \mathbb{R}^{n\times n}$. How can I model / calculate the extreme value distribution: $$ f(w) = ...
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0answers
14 views

combined significance of consecutive observations with variable variance

I'm facing a statistics question for which I could use some input. I have the following data: ordered observations (along 1 axis, genome coordinates) for 200 samples. For each position, the average ...
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0answers
7 views

Test for variance homogeneity and dependent samples

I have the following question regarding statistical tests for an fMRI phantom (i.e., roughly speaking a standardized object (e.g. cylinder filled with gel) used to make inference e.g. on properties of ...
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1answer
177 views

Does using lagged independent variables makes sense?

While it seems quite common to calculate a lagged version of the dependent variable and to use it on the right hand side of a model (e.g., autoregressive models), I have rarely seen that lagged ...
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0answers
32 views

Is the limit of n-wise independent events independent?

Let $(\Omega, \mathscr F, \mathbb P)$ be a probability space. Consider events indexed by $m, n \in \mathbb N$: $ \ \ \ \ \ \ \ \ \ \ \ A_{1,n}, A_{2,n}, A_{3,n} ...$ are n-wise independent. ...
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2answers
572 views

For intuition, what are some real life examples of uncorrelated but dependent random variables?

In explaining why uncorrelated does not imply independent, there are several examples that involve a bunch of random variables, but they all seem so abstract: 1 2 3 4. This answer seems to make ...
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1answer
177 views

Conjecture related to Kolmogorov 0-1 Law (for events)

Let $(\Omega, \mathscr F, \mathbb P)$ be a probability space. Conjecture: Suppose we have events $A_1, A_2, ...$ s.t. $\forall \ A \in \bigcap_n \sigma(A_n, A_{n+1}, ...)$, $P(A) = 0$ or $1$. ...
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55 views

model estimation with feedback loop in variables

I have the following problem regarding fitting of a model where some variables can be biased so that their values are based on knowledge or at good guestimate of $Y$ in the past. In other words: some ...
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1answer
57 views

How do we prove these $\sigma$-algebras are not independent?

Given the sequence $(X_n), n=1,2,... $, of iid exponential random variables with parameter $1$, define: $$ M_n := \max \left\{ X_1, \frac{X_1+X_2}{2}, ...,\frac{X_1+\dots+X_n}{n} \right\} $$ I want ...
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1answer
25 views

testing dependent skewed samples

I must compare two distributions of patent data: namely, they are the number of patent applications of companies before vs after an acquisition. I need to perform an hypothesis test to assess if the ...
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0answers
19 views

multivariate analysis of dependent data

I have some diet data I am analyzing that was collected in different locations at different times (over 3 years). The nature of the sampling resulted in multiple predators at the same location. The ...
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2answers
117 views

Expectation and Conditional Independence

This question is an aside from another question here on CV. We know that the expectation of the product of two independent random variables is the product of expectations, i.e., ...
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1answer
18 views

How to check if there is a dependency of a numeric variable on other numeric variables?

I need to check if a numeric variable $y$ depends on a set of other numeric variables $(x_1, x_2, ..., x_n)$. I do not know anything about the form of possible dependency (I do not even know if it ...
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0answers
21 views

Estimation of the mean when data points are not independent

When we estimate the mean with 95% confidence, this formula is used: $\hat{\mu}=\overline{\mu}\pm1.95\times\frac{\overline{\sigma}}{\sqrt{N}}$, where $\overline{\mu}$ is the sample mean, ...
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21 views

How to prove dependency?

I am a beginner. I have two variables X and Y. How can I prove that the values of Y are dependent on the values of X? I can show whether the relationship is weak or strong using Pearson's ...
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1answer
26 views

Hosmer Lemeshow for correlated data

Is it OK to use HL to judge the goodness-of-fit of a Logistic Regression when the data is a time series correlated from one period to another? I know that HL assumes independence of events, but I ...
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0answers
9 views

Calculating the error on a variable, given the error on a dependant variable

I have a variable which is given by the equation: M = M(a) * (N/20) Now if M(a) has an error of let's say 10%, how do I ...
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0answers
26 views

Comparing non-independent discrete distributions of animals

My team made some experiments how animals choose their location in different environmental conditions (to check the hypothesis of ideal free distribution). The animals were placed in the experimental ...
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0answers
30 views

Comparing R-squared across regression equations with a dependent sample

I was able to find information on how to compare R-squared values across regression equations with independent samples by creating confidence intervals around the estimates. However, the sample used ...
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1answer
34 views

Can a joint second moment exist if the joint distribution cannot be derived?

I am struggling with writing down a relationship between two variables and I am happy for each and every comment that points out, how I can overcome this problem: Let $x\sim N(\mu,\Sigma), x ...
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1answer
21 views

Correlation of exam notes, the students school and their technological knowledge

I have a set of data about some students and I want to check if their success in exams is determined by their level of technological knowledge, or their school. So, I have a table with those values ...
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17 views

Analyzing dependency in multiple quantitative and qualitative variables

I'm analizing a tiny dataset with data about 30 consumers. I have columns representing gender (QL), age (QN), nationality (QL), technological knowledge (QN), achieved operations (QL), and so on. QL ...
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3answers
782 views

If two events are not mutually exclusive, does that mean they're independent?

Suppose we have two events, $A$ and $B$. I want to find out if $A$ and $B^c$ are which one of mutually exclusive or independent. I have figured out that they are not mutually exclusive.. does that ...
2
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2answers
134 views

Dependent identically distributed random variables

If $X_1$ and $X_2$ are dependent identically distributed, can we show that $Pr(X_1>X_2) = Pr(X_2>X_1)$? For i.i.d, it is obvious, but what if they are dependent?
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0answers
7 views

Comparing dependent anonymous samples

I have data collected each year from 2010-2015. In this data I have demographic information and a self-reported score on a 5 pt Likert scale. The surveys were anonymous but I know that many of the ...
2
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1answer
28 views

KDD 15 paper: scoring bigrams

I am by no mean into Statistics nor NLP. And I am reading the following paper, trying to learn something new: ...
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0answers
9 views

finding multiple proportion CIs when one proportion is dependent on the previous

Is using a normal proportion CI appropriate when a sample from a population has multiple attributes (each attribute represented by a boolean) and these attributes depend on the previous (attributes ...
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22 views

How to use Pearson Chi squarred test on several vaiables

In R I have 2 datasets: group1 and group2. For group 1 I have 10 ...
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37 views

Quantile aggregation for a sum of dependent variables

I am currently working with a sum of dependent variables following complex laws. For these laws I have a vector of means, $\mu$ and a linear correlation matrix $\Sigma = \rho_{i,j})_{i=1..n,j=1..n}$. ...
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23 views

Clustering variables by dependence

Let consider a set of $p$ variables. I have a sample of size $n$ of these. I would like to determine groups of variables that depends on one another. My current idea is to use distance correlation as ...
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0answers
23 views

how to perform casuality test on data that are not timeseries

I have 2 arrays of variables: A = [x1,x2,x3,...,xn]; and B = [y1,y2,y3,...,yn]; They are not 2 time series, i.e. their ...
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1answer
25 views

Column1 = Temp_F and Column2 = Temp_C — are these linearly dependent?

If $X$ is a matrix of size $m$ x $2$, where the first column is a range of Celsius values and the second column is their corresponding Fahrenheit values, would the columns be considered linearly ...
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14 views

Interaction within my dependant variable

So my regression model is ideal within my scenario of evaluating CSR disclosure and assurance, as both seperately are significant using OLS and logistic regression. The key issue is I want to have an ...
2
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0answers
9 views

Violation of independence to be in multiple groups?

Ideally, I'd like to run an ANOVA across a variable regarding group membership on a continuous outcome variable. The problem is that each individual can be in multiple groups, which I believe violates ...
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0answers
35 views

Analytical Formula for Exceedance Correlation of Multivariate Normal Distribution and others

I understand that the Exceedance Correlation concept. Knowing that the multivariate normal distribution has asymptotic independence on the tail, lower and lower exceedance correlation approaching to 0 ...
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1answer
14 views

Sort of repeated measure (that will be constant with one switch)

I cannot be specific about the data because it is proprietary. However, suppose we have data for a large number of customers for about 150 consecutive days. On each day, each customer can decide to ...
3
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2answers
79 views

Probability of a run of events from past data

I would like to calculate the probability that there will be a car crash at a certain crossroad for three days in a row. I would like to compute that based on the data I have about the crashes in the ...
3
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1answer
150 views

statistics of airline crashes

Ive been going back and forth with a friend of mine on the issue of airline crash statistics. The concept of "independent variables" seems to be the biggest disagreement between us, so I was hoping to ...
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0answers
17 views

Testing whether two samples come from the same population without assuming independence?

I'm doing some analysis of frequency data coming from the Sun. I want to test the null hypothesis of two different signals coming from the Sun having the same frequency. I measured both of these ...
0
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1answer
31 views

Looking for something similar to a three way anova analysis for non-independent response samples

I have devised an experiment that consists of measuring how quickly a person can complete a set of tasks. I have three variables that I wish to investigate whether or not they affect the performance ...
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0answers
57 views

Testing cross-sectional dependence and serial correlation for Panel Data

Nature of the data is a balanced panel of non-overlapping 5-year data of 7 countries from 1980 to 2010. I have read that the Breusch-Pagan test and the Wooldridge test is not well applied for a ...
0
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0answers
23 views

Non-independent variables (covariates) in survival analysis

I want to perform survival analysis, and compare at which of 3 spatial scales habitat variables affect the most nest survival. I thought to perform analysis separately for each spatial scale and ...
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1answer
72 views

Ordinal Dependent Variable and Ordinal Independent Variable. Which test to perform analysis with?

I have a question regarding Ordinal data. I have measured 'Attitude towards a product' using Likert scale and I have measured 'Purchase Intentions to buy the product' also using Likert scale. Now I ...
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1answer
67 views

Probability distribution for a binomial proportion 'derived' from serially dependent data

Consider the following type of data: This is data from a single-case experiment: an experiment in which one entity (i.e. one person) is observed repeatedly over time (cf. measurement times 1 to ...
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2answers
42 views

Hypothesis test for mutually exclusive samples from a single population?

Let's say I gave 100,000 people a survey on their favorite fruit, where they can bubble in "Apple" or "Pear" (but not both). They can also leave it blank. The results are 90,000 people left it blank, ...