Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [non-independent]

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

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

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On the importance of the i.i.d. assumption in statistical learning

In statistical learning, implicitly or explicitly, one always assumes that the training set $\mathcal{D} = \{ \bf {X}, \bf{y} \}$ is composed of $N$ input/response tuples $({\bf{X}}_i,y_i)$ that are independently drawn from the same joint…
Quantuple
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How do I test a nonlinear association?

For plot 1, I can test the association between x and y by doing a simple correlation. For plot 2, where the relationship is nonlinear yet there is a clear relation between x and y, how can I test the association and label its nature?
user1447630
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The meaning of "positive dependency" as a condition to use the usual method for FDR control

Benjamini and Hochberg developed the first (and still most widely used, I think) method for controlling the false discovery rate (FDR). I want to start with a bunch of P values, each for a different comparison, and decide which ones are low enough…
Harvey Motulsky
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Is correlation equivalent to association?

My statistics professor claims that the word "correlation" applies strictly to linear relationships between variates, whereas the word "association" applies broadly to any type of relationship. In other words, he claims the term "non-linear…
Asad Saeeduddin
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Properties of PCA for dependent observations

We usually use PCA as a dimensionality reduction technique for data where cases are assumed to be i.i.d. Question: What are the typical nuances in applying PCA for dependent, non-i.i.d. data? What nice/useful properties of PCA that hold for i.i.d.…
Richard Hardy
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How to add two dependent random variables?

I know, I can't use convolution. I have two random variables A and B and they're dependent. I need Distributive function of A+B
Mesko
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How does one find the mean of a sum of dependent variables?

I know that the mean of the sum of independent variables is the sum of the means of each independent variable. Does this apply to dependent variables as well?
Gh75m
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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 sense. My interpretation: A random variable and its…
BCLC
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What is the long run variance?

How is long run variance in the realm of time series analysis defined? I understand it is utilized in the case there is a correlation structure in the data. So our stochastic process would not be a family of $X_1, X_2 \dots$ i.i.d. random variables…
Monolite
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What is the difference between linearly dependent and linearly correlated?

Please explain what is the difference between if two variables are linearly dependent or linearly correlated. I looked up the wikipedia article but didn't get a proper example. Please explain it with example.
Happy Mittal
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Linear mixed-effects modeling with twin study data

Suppose I have some some response variable $y_{ij}$ that was measured from $j$th sibling in $i$th family. In addition, some behavioral data $x_{ij}$ were collected at the same time from each subject. I'm trying to analyze the situation with the…
bluepole
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Why do mixed effects models resolve dependency?

Say we're interested in how student exam grades are affected by the number of hours that those students study. To explore this relationship, we could run the following linear regression: $$ \text{exam.grades}_i = a + \beta_1 \times…
luciano
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How problematic is it to control for non-independent covariates in an observational (i.e., non-randomized) study?

Miller and Chapman (2001) argue that it is absolutely inappropriate to control for non-independent covariates that are related to both the independent and dependent variables in an observational (non-randomized) study - even though this is routinely…
Patrick
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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.
Ricky
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Is Hurlbert 1984 the best introductory overview to pseudoreplication?

I often find myself explaining (or wanting to explain but not wanting to be boorish) the basics of random sampling and the consequences of pseudoreplication, specifically the limitations and assumptions of the standard statistical methods that are…
Abe
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