The independence tag has no wiki summary.
2
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1answer
119 views
Jointly stationary random process
If two wide-sense stationary processes $X(t)$ and $Y(t)$ are uncorrelated, then the cross correlation is
$R_{XY}(t_1,t_2) = E\{X(t_1)Y(t_2)\} = E\{X(t_1)\}E\{Y(t_2)\}$,
which will be a constant, ...
1
vote
1answer
668 views
How to cope with multicollinearity and interactions between IVs in generalized linear models?
I have made a generalised linear model with a single response variable (continuous/normally distributed) and 4 explanatory variables (3 of which are factors and the fourth is an integer). I have used ...
1
vote
2answers
149 views
Independence of variables and ANOVA
I performed a test to study the joint effects of hardness and alkalinity (independent variables, IV) on reproduction (number of offspring, dependent variable, DV) of water fleas, but I’m not sure what ...
0
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0answers
433 views
Is the product of two independent random variables independent of a random variable which is not independent of one of the factors?
Let $A$, $B$, $C$ be random variables.
$A$ and $B$ are not independent
$A$ and $C$ are independent.
$B$ and $C$ are independent.
Are $A$ and the product $BC$ independent?
This is, is ...
6
votes
2answers
581 views
Can somebody illustrate how there can be dependence and zero covariance?
Can somebody illustrate, as Greg does, but in more detail, how random variables can be dependent but have zero covariance? Greg, a poster here, gives an example using a circle here.
Can somebody ...
21
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2answers
6k views
What is covariance in plain language?
What is covariance in plain language and how is it linked to the terms dependence, correlation and variance-covariance structure with respect to repeated-measures designs?
4
votes
2answers
820 views
Test for IID sampling
How would you test or check that sampling is IID (Independent and Identically Distributed)? Note that I do not mean Gaussian and Identically Distributed, just IID.
And idea that comes to my mind is ...
1
vote
2answers
302 views
What's the probability of an event happening exactly once after two independent trials?
The problem:
If event $A$ happens with probability $p$, what is the probability $P[K=1]$ that, after two independent trials, $A$ happened exactly once?
Is the answer:
$P[K=1] = p(1-p)$, since ...
1
vote
2answers
150 views
How is the standard definition of independence applied to time-series?
So, [Wikipedia says] that the standard definition of independence is:
$f_{X,Y}(x,y) = f_X(x) f_Y(y)$
How is this applied to timeseries? How do we calculate each side of the equation?
If we're ...
1
vote
1answer
296 views
ANOVA - independence assumption
I have conducted a study in which I have gathered 3 sentences per participant. These sentences were then classified and the words per sentence were counted. I want to test if there are significant ...
1
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1answer
97 views
$\chi^2$ test - correcting for not fully independent sample
I have carried out a study in which I have gathered 3 sentences per participant. These sentences were then classified in 2 ways. I want to test if there are significant interactions between the ...
0
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1answer
761 views
1
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1answer
168 views
How to interpret results of a $\chi^2$ test of independence?
I've run a chi-square test of independence on a two-way table with two categories on the rows and four categories on the columns. My $p$-value is below my chosen $\alpha$, so I may conclude that the ...
2
votes
1answer
489 views
Kendall's tau and independence
Kendall's tau is an association measure between two random variables, say $X$ and $Y$.
If $X$ and $Y$ are independent, then $\tau = 0$. However, $\tau = 0$ does not imply independence because ...
4
votes
1answer
155 views
What is a reasonable independence test for a time series?
Suppose that I have a time series, $x_{1:n}$, and I would like to test whether they are all independent samples from the uniform distribution on $[0,1]$. This is a somewhat basic question, but how do ...
8
votes
6answers
408 views
When two events $A$ and $B$ have no result in common
I and my friends just had a little discussion whether the events are independent or dependent if they have no outcome in common. I thought that they have to be independent. When two events are ...
1
vote
1answer
773 views
How can I perform a chi-square test for independence on signal samples?
Let's say I have two signals $x$ and $y$, sampled $N$ times, i.e.
$$ x = [ x_{1}, x_{2}, ..., x_{N} ] $$
$$ y = [ y_{1}, y_{2}, ..., y_{N} ] $$
I would like to check whether $x$ and $y$ are ...
1
vote
1answer
515 views
How can I calculate central moments of a joint pdf?
Let's say I have two signals $x_1$ and $x_2$, each having $N$ samples, i.e.:
$$ x_1 = \{ x_{11}, x_{12}, ..., x_{1N} \} $$
$$ x_2 = \{ x_{21}, x_{22}, ..., x_{2N} \} $$
The signals are both ...
4
votes
2answers
300 views
How to calculate threshold level for mutual information scores?
Im quite new to the world of statistics, and only just finished work on my first (successful) attempt to calculate mutual information scores.
Now lets say that for the column pairs AB, BC, CD and DE ...
2
votes
1answer
141 views
When will PCA be equivalent to ICA?
$X = AS$ where $A$ is my mixing matrix and each column of $S$ represents my sources. $X$ is the data I observe.
If the columns of $S$ are independent and Gaussian, will the components of PCA be ...
2
votes
2answers
443 views
Conditional independence isn't guaranteed when specifying the marginal distributions?
It was mentioned very briefly in a lecture related to graphical models that two random variables $X_3$ and $X_4$ are both dependent on $X_2$. But even when conditioned on $X_2$, the two variables ...
4
votes
1answer
218 views
Manually transforming two dependent variables according to their correlation matrix in R?
I have two continuous variables, X and Y, that are correlated - they are not independent. To correct for non-independence, I have a known correlation structure, a matrix S.
If one calls ...
1
vote
1answer
108 views
Balance between randomization, interspersion and even initial conditions of experimental units
We are setting up a manipulative experiment in forest where we will test the effect of management on a number of health indicators.
We have 1 factor, 3 levels, 3 plots each replicated 3 times; ...
2
votes
1answer
304 views
Do the properties of Pearson's chi-squared test for independence hold true for continuous PDFs?
In probabilist statistics, the properties of a discrete Pearson's chi-squared test hold that:
\begin{aligned}
\chi^2 = \sum_{i=1}^{r} \sum_{j=1}^{c} {(O_{i,j} - E_{i,j})^2 \over E_{i,j}}
...
4
votes
1answer
420 views
Are real and imaginary components of frequency element of fft correlated?
I want to use model-based clustering to classify 1,225 time series (24 periods each). I have decomposed these time series using the fast Fourier transform and selected the harmonics that explain at ...
3
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1answer
359 views
Which are the most effective methods for selecting independent variables?
Some clustering algorithms require independence of variables but (especially working with real data) variables are often highly correlated.
I have been suggested to apply a Principal Component ...
3
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0answers
120 views
Testing for the existence of dependencies in time series
What methods exist to test for the existence of any sort of dependence in a time series? This is in contrast to something like auto-correlation, which tests for a particular type of dependency. Is ...
3
votes
1answer
59 views
Number of independent samples for weighted samples?
I am taking random samples from one distribution, $f(x)$, but trying to get information about another distribution, $g(x)$. I have a weighting function, $w(x)=Cg(x)/f(x)$, to correct for this. The ...
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0answers
148 views
Test statistic and null rejection of independence in normalized redundancy, as implemented and automated in Python
I currently have an output function that roughly follows a $\chi^2$ distribution for random data with one degree of freedom. As a cursory analysis that has since proven mathematically unrigorous, this ...
0
votes
3answers
356 views
Are the products of dependent and independent random variables independent?
Let A, B, C, and D be four random variables such that A and B are independent, and C and D are dependent. It is unknown whether A and C are independent nor whether B and D are independent. Let E and F ...
5
votes
1answer
527 views
Question about independence assumption for ANOVA, t-test, and non-parametric tests
I'm a novice in statistics and I have some confusion about the assumption of independence for statistical tests.
I searched the Internet and some information says that for the t-test, the ...
2
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0answers
66 views
How to analyse this simulation
So, here's the situation:
I have some simulation results, from a simulation driven by two parameters. One of these parameters has two settings, the other has four each was replicated ten times for a ...
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5answers
3k views
Covariance and independence?
I read from my textbook that $\text{cov}(X,Y)=0$ does not guarantee X and Y are independent. But if they are independent, their covariance must be 0. I could not think of any proper example yet; could ...
2
votes
1answer
1k views
Comparing relative frequencies between two groups
If i have the relative proportion for two sample.
For example :
group 1:
Male: 50%
Female: 25%
children: 25%
group 2:
Male: 50%
Female: 20%
children: 30%
How can I measure the % of ...
0
votes
1answer
877 views
Reporting $\chi^2$ test results in APA format
I'm trying to report the results of my chi-square test for independence in APA format but these results don't resemble the examples I've seen especially the 4 digits before the period in the ...
2
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1answer
174 views
An inconsistency between the concept of “subindependence” and the chi-square test for independence?
Two random variables are defined as subindependent if their covariance is zero--in other words, if they are uncorrelated. The latter link notes that "not all uncorrelated variables are independent. ...
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0answers
187 views
Is there a covariance MLE which takes into account independence relationships?
In the extreme case where all of the components of an $M$-variate observation are pairwise independent from each other, a multivariate normal distribution can be decomposed into the product of $M$ ...
4
votes
1answer
295 views
Assessing independence of observations using intraclass correlation when some groups have small group sample sizes
Context
I was talking to a researcher in the following situation.
Participants (n = 500) were sampled from schools.
Participants came from around 50 different schools.
The number of participants ...
5
votes
1answer
88 views
Should the group decisions be independent in Wilcoxon rank sum test?
In case you want to compare the average income of a group of male employees against the average income of a group of female employees, the observations are clearly independent.
Now, I have a network ...
2
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3answers
597 views
These two variables are almost uncorrelated. What else can I say?
I have two variables for some districts in the UK:
Number of crimes per habitant
Median yearly income
Here's what it looks like:
I would like to determine if there is a dependence between the ...
10
votes
2answers
444 views
Has anyone solved PTLOS exercise 4.1?
This an exercise given in Probability Theory: The Logic of Science by Edwin Jaynes, 2003. There is a partial solution here. I have worked out a more general partial solution, and was wondering if ...
3
votes
1answer
95 views
Given pdf of $I$ and $R$ (both $I$ and $R$ are independent RV's), how to find pdf of $W =I^2\cdot R$?
The title defines the question. May be the concept would do...like how to go about it? Thanks.
6
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2answers
548 views
Assessing multicollinearity of dichotomous predictor variables
I'm working on a project where we observe behaviour on a task (eg. response time) and model this behaviour as a function of several experimentally manipulated variables as well as several observed ...
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0answers
250 views
Do two variables need to be independent in order to obtain a correlation?
I would like to find the correlation between two variables. It was suggested to me that two variables should be independent; otherwise it is not meaningful statistically to calculate a correlation. ...
3
votes
1answer
169 views
Assessing conditional independence of genes in Trans-eQTL cluster
I've identified a Single Nucleotide Polymorphism (SNP) that is associated with a variable of interest (lets just call it height) using a Genome Wide Association Study (GWAS). The SNP can be of the ...
2
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2answers
334 views
The probability for two people to provide identical answers on survey questions
Here is the problem: A survey contains 7 binary questions (Yes/No responses). If two people are answering the survey, what is the probability for their answers on 4 or more of the questions to match? ...
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5answers
213 views
Does this quantity related to independence have a name?
Obviously events A and B are independent iff Pr$(A\cap B)$ = Pr$(A)$Pr$(B)$. Let's define a related quantity Q:
$Q\equiv\frac{\mathrm{Pr}(A\cap B)}{\mathrm{Pr}(A)\mathrm{Pr}(B)}$
So A and B are ...
6
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3answers
589 views
Testing paired frequencies for independence
I hope this isn't either far too basic or redundant. I have been looking around for guidance but so far I am still uncertain of how to proceed.
My data consists of counts of a particular structure ...
3
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1answer
617 views
Confidence interval based on time series
I have a timeseries of data which was gathered by driving a car around randomly.
One data point was gathered every minute and each data point is either "Yes" or "No". Yes = temperature is above a ...
7
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1answer
474 views
Any ideas about how to analyze survival data with pseudo-replication (dependent data)?
I am a student, working with a team on a large-scale ecological experiment. We want to analyze survival data which has been derived from an experimental design with some pseudo-replication. This ...
