The independence tag has no wiki summary.
21
votes
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?
16
votes
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 ...
16
votes
2answers
316 views
Independence of residuals in a computer-based experiment/simulation?
I conducted a computer-based assessment of different methods of fitting a particular type of model used in the palaeo sciences. I had a large-ish training set and so I randomly (stratified random ...
13
votes
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 ...
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 ...
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 ...
8
votes
1answer
255 views
Does the multivariate Central Limit Theorem (CLT) hold when variables exhibit perfect contemporaneous dependence?
The title sums up my question, but for clarity consider the following simple example. Let $X_i \overset{iid}{\backsim} \mathcal{N}(0, 1)$, $i = 1, ..., n$. Define:
\begin{equation}
S_n = \frac{1}{n} ...
7
votes
2answers
589 views
Statistically significant vs. independent/dependent
What is the difference between having something statistically significant (such as a difference between two samples) and stating if a group of numbers are independent or dependent.
7
votes
2answers
491 views
Factor analysis of dyadic data
An anonymous reader posted the following question on my blog.
Context:
The reader wanted to run a factor analysis on scales from a questionnaire - but the data was from paired husbands and wives.
...
7
votes
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 ...
6
votes
4answers
332 views
Is winning a soccer match independent of previous wins\losses?
$\quad$ I have a friend of mine who is a bit of a gambler ask me this question. He is of poor mathematical background, but has a sense of logic and will probably accept a logical answer in the natural ...
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 ...
6
votes
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 ...
6
votes
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 ...
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 ...
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 ...
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 ...
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 ...
4
votes
1answer
138 views
Summarising significance tests for multiple independent variables
Having recently run an experiment, I have been left with a dataset that I don't quite know how best to handle, I think simply due to the number of independent variables to consider.
Setup
I have ...
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 ...
4
votes
1answer
223 views
How to report results of Fisher's test for larger than 2 by 2 tables
This is probably a very easy question but what is an acceptable phrase for reporting a Fisher's test where the number of rows and the number of columns are both $>2$. An example in R:
...
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 ...
4
votes
2answers
298 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 ...
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 ...
3
votes
1answer
98 views
Level of analysis and assumption of independence in Pearson Chi-square test
I have survey data about injuries occurring to athletes over the span of their careers. Many of the athletes suffered multiple injuries (the most any athlete reported was five and this did not occur ...
3
votes
1answer
87 views
Showing independence
$X_{1}$ and $X_{2}$ are independent, chi-square distributed random variables. I've managed to show that $Z=X_{1}+X_{2}$ is independent of $\frac{X_{1}}{Z}$. How do I conclude then that $Z=X_{1}+X_{2}$ ...
3
votes
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 ...
3
votes
1answer
171 views
I want to know how independent two variables are
I have no formal training in statistics so please correct me if I use the wrong terms as I try to explain my problem.
I have a set of data (less than 80 points) with essentially 1 single outcome (a ...
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 ...
3
votes
1answer
63 views
Optimal approach to independence check
I want to see if a vendor is biased against one type of vehicle compared to another.
I have two categories of vehicles: OWN and T/C.
The vendor sells fuel to these vehicles.
The process is as ...
3
votes
2answers
173 views
What is the difference between using the multiplication rule or using Venn diagram subtraction for probability?
Take two problems:
Andrew is 35, and the probability he will be alive in 10 years is .72. Ellen is 35, for her, .92. Assuming these are independent, what is the probability they both will be alive ...
3
votes
1answer
181 views
Experimentially proving that random variables are independent
I just had a very simple (possibly very dumb) question.
How would I, experimentally prove that two random variables drawn either from the same population or two different populations are independent ...
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.
3
votes
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
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 ...
3
votes
1answer
53 views
Independence of samples
Recently I started doing verification on daily temperature forecasts by different providers. I calculated the absolute forecast errors for each of the providers, and I am planning on performing ANOVA ...
3
votes
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 ...
2
votes
2answers
76 views
Does independence imply conditional independence?
If two or more variables A, B, C, etc. are jointly mutually independent of one another, does this imply that that they are also conditionally independent given some set of conditioning variables X, Y, ...
2
votes
1answer
487 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 ...
2
votes
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 ...
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 ...
2
votes
1answer
40 views
Is there a function to check a set of events/random variables are mutually independent?
Say, 5 random variables A,B,C,D,E which can take values either 0 or 1.
I have the theoretical population chances for the 32 cases of P(A,B,C,D,E). Obviously they add up to 1.
How to check if ...
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 ...
2
votes
1answer
127 views
How to get conditional variance from Schur complement?
Suppose you have vectors X and Y with covariance matrix
$V = \left( \begin{array}{cc}
A & B \\
B^T & C \end{array} \right)$. This Wikipedia article says that $Var(X | Y) = A - BC^{-1}B^T$, ...
2
votes
1answer
123 views
Independence of mutually exclusive dummies in same regression?
I have been wondering about this for a while. When I have mutually exclusive dummies in the same regression, are their coefficients independent?
For example, suppose I have the following:
...
2
votes
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, ...
2
votes
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. ...
2
votes
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? ...
2
votes
1answer
36 views
How to prove independentness of marginal/conditional (?) posterior distributions?
This is a question about exercises 4.2 and 4.3 of Jim Albert’s “Bayesian Comptutation With R” (p. 82). Note that while this might be homework, in my case it is not.
We are to prove that, given two ...
2
votes
1answer
29 views
How does randomization testing for correlating two variables work?
I was going through OpenIntro Statistics[http://www.openintro.org/stat/textbook.php] and came across two case studies in the first chapter
Discrimination against women during promotion - Page 42
...
