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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12 views

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 ...
1
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0answers
9 views

Different Correlation/dependecy measures

I'm trying to figure what kind of correlation/depency measure to use on a multivariate data set I'm working on. I've tried the (pearson's)correlation, Kendall's Tau and Spearman's Rho. However, all ...
1
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0answers
39 views

Are these distributions independent?

I'm trying to compare the medians of two non-normal distributions: $A$ and $B$. $A$ is the distribution of completion durations for one type of task $B$ is the distribution of completion durations ...
8
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2answers
534 views

Does non-zero correlation imply dependence?

We know of the fact that zero correlation does not imply independence. I am interested in whether a non-zero correlation implies dependence - i.e. if $\text{Corr}(X,Y)\ne0$ for some random variables ...
3
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1answer
50 views

Variance of random variable for normal distribution

How do I find the variance for $z_n=\prod_{i=1}^n(1-k_i e^{a_i x})$ where $x$ is the random variable with a normal distribution and is the same for all $i$ (which is a subscript for time dependency ...
0
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0answers
10 views

Determining dependancy of observations

I have 12 people, 6 in treatment group and 6 in control group. They gave ratings (1 to 7) to 8 different activities they were performing as a part of the experiment. I looked at another thread here ...
2
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1answer
30 views

How to justify the statistical independence among two sets of continuous multivariate observations

I have two sets of continuous multivariate observations $X=\{x_1, x_2, ..., x_d\}$ and $Y=\{y_1, y_2, ..., y_d\}$. How can I justify if they are statistically independent or not? For simplicity, I ...
4
votes
1answer
69 views

Verifying independence for two Random Variables

Could you please give me some hints for the exercise below? Suppose we toss a coin once and let $p$ be the probability of heads. Let $X$ denote the number of heads and let $Y$ denote the number of ...
2
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0answers
69 views

Analysis for cross-subjects correlation

Suppose that an investigator has collected some longitudinal data from each of the $n$ subjects, and that a correlation coefficient is computed on the data between any pair of subjects, leading to ...
2
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1answer
358 views

Are pupils in a school independent and identically distributed when compared to a national population?

I am interested in the way in which data are analysed in education. In England, pupils' reported test results are compared to national test results using z-tests. These results are then used to judge ...
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0answers
15 views

Testing for independence and strength of association

I am having difficulty at formulating properly a null hypothesis regarding the following setup: Suppose that we are interested in probing a possible association between bundled products sold at ...
4
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3answers
79 views

A critical proof or counterexample regarding independence

Does independence of $X^2$ and $Y^2$ imply independence of $X$ and $Y$?
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0answers
24 views

relation between stochastic independence and functional independence

We know if two variables are functionally independent then there will be stochastic independence as well. Can any one give me an example when the converse is not true i.e. X and Y are independent ...
3
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1answer
598 views

If X and Y are correlated, but Y and Z are independent, is X and Z always independent?

If random variables X and Y are correlated, but Y and Z are iid, is X and Z always independent? I am able to prove they are independent for specific types of structure on X and Y (for example if ...
0
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0answers
24 views

How do you prove that if $ X_t \sim^{iid} (0,1) $, then $ E(X_t^{2}X_{t-j}^{2}) = E(X_t^{2})E(X_{t-j}^{2})$? [duplicate]

Suppose we have a time series $X_t$ s.t. $X_t \sim^{iid} (0,1)$. How do you prove that if $ X_t \sim^{iid} (0,1) $, then $ E(X_t^{2}X_{t-j}^{2}) = E(X_t^{2})E(X_{t-j}^{2})$? Or, I guess, if ...
0
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1answer
41 views

Correlation and dependency of two variables

Lets say I am interested in finding the correlation of the following two metrics. They are aggregations and include the same input A in their formula. Is it possible to talk about correlation of ...
2
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0answers
37 views

How to Test Independence of Poisson Variables?

I have a data set of length $10,000$. Each entry, $e_i$, of my data set is associated with two values, $x_i$ and $y_i$. Let $X$ and $Y$ represent the random variables for which my data set is a ...
3
votes
2answers
96 views

Regression, Independence & Normality of x and y variables (not residuals)

I am trying to predict productivity of inbound process of a warehouse using y-value = productivity in terms of pcs/hr x-value = # pcs and ratio pcs/SKU. (where SKU = stock keeping unit) Basic ...
0
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1answer
37 views

Bayes rule and conditional independence

I have two conditionally independent random variables $A$, $B$ such that $$ P(A,B\mid C) = P(A\mid C)P(B\mid C) . $$ I have to find posterior formula $P(C \mid A,B)$. My result with a ...
2
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1answer
73 views

Hausman test for Independence of Irrelevant Alternatives (IIA), negative value

I get a negative value for the Hausman test for the independence of irrelevant alternatives (IIA) assumption. Now I find contradicting conclusions in the literature: some people say that I should take ...
2
votes
1answer
38 views

Are samples from sliding windows independent samples?

Are samples from sliding windows independent samples? E.g. if I have window size of 90 seconds counting the number of cars on a street and I output the average within the window every second for 30 ...
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0answers
20 views

Clustering on structural variables?

I'm working with land surface models. These models basically take a bunch of meteorological forcing data (downward radiation, wind, rain, humidity, etc), and run it through some ...
4
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2answers
269 views

Independence of a linear and a quadratic form

How can I prove the following lemma? Let $\mathbf{X}^ \prime$ = $ \left[ X_1 , X_2 , \ldots, X_n \right]$ where $ X_1, X_2, \ldots X_n $ are observations of a random sample from a distribution which ...
0
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0answers
53 views

Help with covariance

A deck of 52 cards is shuffled and a bridge hand of 13 cards is dealt out. Let X and Y denote, respectively, the number of aces and the number of spades in the hand. (a) Show that X and Y are ...
0
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1answer
39 views

How do I prove the mutual independence of a set of random variables given another set of mutually independent random variables?

Suppose $X_{1},\,\ldots,\, X_{n}$ and $T_{1},\,\ldots,\, T_{r}$ and two sets of random variables, with each $X_{i}$ being categorical, and each $T_{j}$ being continuous taking on all values in the ...
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2answers
88 views

Proving conditional independence from mutual independence

Suppose I have a Bayesian inference problem where $E$ is the result of a chemistry experiment. The chemistry experiment consists of a controlled sequential digestion of one end of the protein using a ...
2
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1answer
34 views

How to check for independence within a sample

I see sometimes written (see below for examples) that given a random sample from less than 10% of the population then it's reasonable to assume that the data is independent. I wonder why 10% and not ...
0
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0answers
11 views

Checking assumption of dependence in a generalised linear model

I'm wondering if I've violated the assumption of independence in a generalised linear model. The data I've used to make to make the model can be downloaded with this code: ...
0
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0answers
56 views

Are the predictors in an ANOVA assumed to be independent of one another?

I ran an ANOVA with 4 predictors (2 categorical, 2 continuous) and 1 covariate (continuous). Including the covariate did not significantly alter the main effects of the ANOVA when it was run without ...
7
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2answers
327 views

Functions of Independent Random Variables

Is the claim that functions of independent random variables are themselves independent, true? I have seen that result often used implicitly in some proofs, for example in the proof of independence ...
0
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1answer
35 views

What is wrong with this chi squared test of independence?

I'm trying to learn how to run the chi squared test of independence. I've created two fictional variables, Variable 1 and Variable 2, and I want to know if they are correlated. I'm working with the ...
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0answers
23 views

Are these events independent? [duplicate]

We flip a fair coin (independently) three times. Define the following two events: A = "the number of tails is odd" B = "the first coin comes up heads" Are the events A and B independent? I believe ...
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0answers
45 views

What exactly is a higher-order correlation? [closed]

What exactly is a higher-order correlation? Is the term just a catch-all for all dependencies that are not captured by second-order correlations? Or do people mean something more precise than ...
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0answers
44 views

Testing if alcohol consumption and smoking are independent

The question asks to test if smoking status and level of alcohol consumption are independent using the usual five-step procure at alpha $=0.05$: I am having trouble finding expected values. As the ...
3
votes
1answer
467 views

Chi-square test: difference between goodness-of-fit test and test of independence

Concerning the Pearson chi-square test there seems to be a subtle difference between the goodness-of-fit test and the test of independence. What is confusing is that both tests seem to be calculated ...
5
votes
1answer
62 views

Does A independent of B, and B correlated with C imply that C is independent of A?

Assume 3 random variables, $A, B, C$. If $A \perp B$, but $Cov(B,C) \neq 0$, can we say anything about $Cov(A,C)$? I think it can either be 0 or not 0, but it seems like there should be more general ...
0
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1answer
21 views

decomposition of independent random variables

If X and Y are independent random variables such that X = A + B and Y = C + D? Are the pairs (A, C), (B, C), (A, D), (B, D) also independent? By this I mean whether A and C are independent, B and C ...
5
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0answers
99 views

Overlapping sample t-test

I have 10 people working together. They work in group for 6 days. Three days in week 1, three days in week 2. In each day I don't have the full set of people, but a subset of them. In each day I ...
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3answers
85 views

The probability of detecting a defect given defect growth when the two variables are independent

I am dealing with a real world problem and just wanted to check if I am going about this the right way. I have the probabilities that a defect will grow within a particular structure, say ${\rm ...
1
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2answers
66 views

Does randomness imply independence?

By looking at a lag plot, it seems that my dataset is random (no autocorrelation whatsoever). Should this be sufficient to infer independence of observations? As a matter of fact, I know that the ...
0
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1answer
17 views

Cycles in gaussian graphical models

I understand examples where two nodes can be dependent but conditionally independent given their common cause. For instance the common cause is high temperature, and the children nodes are high ...
1
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0answers
64 views

In a linear regression, why is the mean of all $y_i$ equal to 0?

I don't understand why the mean for all $y_i$s must equal $0$. What property/properties does the above assertion rely on? I had thought that the mean of $y_i=E(y_i)$, so: $$ E(y_1)=\alpha $$ $$ ...
1
vote
1answer
76 views

Testing that two models from two different data sets are independent

I have two different sets $(n_1=47$, $n_2=23)$ obtained under different conditions. I fit two different functions $(\text{Fu}_1$, $\text{Fu}_2)$ in MATLAB. $\text{Fu}_1$ was fit using the first data ...
0
votes
1answer
33 views

Independent vs. Dependent Compound Poisson Distributions

I have an issue with a section of some Actuarial lecture notes that I am reading. Here are the snippets from the notes: "Consider a portfolio consisting of $n$ independent policies. The aggregate ...
0
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0answers
25 views

Dependent variables

I am faced with the following problem: In general terms: I have a number dependent measurements in two biological samples and want to test if the difference between the samples is significant. ...
3
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1answer
73 views

What happens in linear regression when observations are not independent in time

Let's consider the example of whether a person's weight is correlated with their height (simple linear regression). What is the difference between running this correlation on the following two data ...
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0answers
16 views

Can mutual independence be defined in terms of conditional distributions?

Suppose there are more than two random variables $X_1, X_2, \dots, X_n$. Can mutual independence between them be defined in terms of conditional distributions? Thanks!
0
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1answer
127 views

$\chi^2$ test of significance vs. goodness of fit

I have 644 companies out of which 154 went bankrupt. I investigate below if the bankruptcy is related to the sector type: ...
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2answers
158 views

Checking Independence for functions in R

Given $$f_{(U_1,U_2)}(u_1,u_2)=\begin{cases} 1/2& -u_1<u_2<u_1 \text{ and } u_1 - 2 < u_2 < 2 - u_1 \text{ and } 0 < u_1 <2\\ 0& \text{otherwise}\end{cases}$$ I found that ...
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0answers
47 views

Chi-square / Fisher test variable independence for an individual

I have a data set of $\approx$100 individuals showing pulse rate before exercise, pulse rate after exercise, sex, smoker status, weight etc. for each individual. I've been asked to select an ...