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.

learn more… | top users | synonyms

-2
votes
0answers
21 views

Independence of the products of two independent normal variables with a Rademacher variable [on hold]

Let $X$ and $Y$ be two iid $N(0,1)$ random variables, and let $Z$ be a Rademacher variable i.e. $P(Z=1)=P(Z=-1)=0.5$ distributed independently of $X$ and $Y$. Let $U=XZ$ and $V=YZ$. Are $U$ and $V$ ...
2
votes
2answers
42 views

Show that $Y_1 X_1 + Y_2 X_2$ $\,{\buildrel d \over =}\,$ $(Y_1^2+Y_2^2)^{1/2}X_1$

I would like verification of my solution to the following problem. QUESTION: Let $X_1, X_2 \,{\buildrel iid \over \sim }\, N(0,1) $ and let $Y_1, Y_2$ be two independent random variables ($X_1, ...
2
votes
0answers
19 views

Test for independence in 3x2x2 table with small expected cell values

I have three unordered categorical variables. I have made a 3x2x2 table, but I'm uncertain of how to test for independence. The usual manner is a chi-squared statistic, but I think this is ...
1
vote
1answer
46 views

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.
0
votes
0answers
14 views

How to run ANOVA on multiple groups of samples, each composed by different variables

I have a $m$ x $n$ matrix, where the $n$ columns are split into multiple classes. If I had only a $1$ x $n$ vector, I would have used ANOVA to evaluate if all subset of columns had the same ...
0
votes
0answers
4 views

Chi-square test for independence of categorical variables [duplicate]

I'd like to know about independence of categorical variables. I read an article from https://explorable.com/significance-test-2 H0: “Having breakfast in the morning has no effect on the grades of ...
0
votes
0answers
2 views

Comparing change in lateral root densities between treatments for different genotypes

I have been growing 4 genotypes of the same plant and been recording their lateral root density under both control conditions and a salt treatment. I have calculated the decrease in lateral root ...
2
votes
2answers
94 views

Random variables independence

I need to check if $Z$ and $W$ are dependent or not. $X,Y \sim \mathrm{Exp}(2)$ Then I define: $Z=X-Y \ \text{,}\ \ W=X+Y$. Now How I can check that $Z$ and $W$ are dependent or not ? I know ...
4
votes
3answers
215 views

In linear regression, what does $\beta_1 = 0$ really mean?

If granted omniscience and we know that $\beta_1$ in a multiple linear regression model is truly 0, what does that mean in words (and math notation)? The model is: $Y = \beta_0 + \beta_1X_1 + ...
1
vote
0answers
65 views

In Berkson's paradox, is $\beta_1 = 0$ or $\ne 0$?

There is "a general phenomenon known as Berkson’s paradox (Berkson, 1946), whereby observations on a common consequence of two independent causes render those causes dependent. For example, the ...
2
votes
0answers
12 views

shape of distribution and indepencence

I have a sample of observation on which normality tests (Anderson Darling, Shapiro - Wilks, KS,...) would accept the assumption of normality. Nevertheless I know that there is a certain time - ...
7
votes
2answers
102 views

Approaches for generating synthetic survey data with dependent answers?

I would like to produce synthetic survey data. At the moment I produce independent answers between questions according to an arbitrary discrete distribution as in this question. I want to generate ...
0
votes
0answers
17 views

Probability mass function of a r.v $Z$, $Z:=$ the sum of the values of two die

We are told that we are rolling a die twice, where $$X:=\;the\;value\;of\;the\;first\;roll$$ $$Y:=\;the\;value\;of\;the\;second\;roll$$ $$Z:=X+Y$$ We are told to find the moment generating function ...
3
votes
0answers
33 views

is it legitimate to t-test between statistics of a bootsrap?

say I have two samples $x_1$ and $x_2$ and a function which calculates a statistic out of each sample, denotes as $f(x)$. I would like to test the significance of the difference $f(x_1)-f(x_2)$. A ...
0
votes
0answers
11 views

Factor conditioning variables

Let $A,B,C$ be $3$ random variables. If $p(A,B\mid C) = p(A\mid C) \cdot p(B\mid C)$ holds, then $A$ and $B$ are conditionally independent given $C$. My question is: What are the underlying ...
0
votes
0answers
18 views

Variance of multinomial distribution that is product of 4 Beta random variables

I have a system of 4 binary random variables, $A$, $B$, $C$ and $D$. $A$, $B$ and $C$ are conditionally independent given $D$, and I'll call one set of samples $ABCD$ an event (e.g. $ABCD$ meaning all ...
0
votes
0answers
11 views

Logit: using lagged dependent variable

Is it methodologically feasible to include lagged dependent variable in the logit model?
1
vote
3answers
59 views

Dependent or Independent…a little intuition

I have a time series that describe the power consumption of a building. For every hour of the day I have a measurement (e.g Hour 0 = 2.3 kWh, Hour 1 = 4.2 kWh etc). Do you believe that the ...
0
votes
0answers
13 views

Chi square test of independence with multivariate nominal data

I used a list-type open-ended question to collect responses, in which respondents can list up to 6 items. After coding the items, I have the multivariate nominal data. I want to check if my IV ...
1
vote
0answers
75 views

Independence among intersubject correlations

Suppose that there are some data collected in the form of time series from 3 subjects: $X_1 = (x_{11}, x_{12}, ..., x_{1n})$ $X_2 = (x_{21}, x_{22}, ..., x_{2n})$ $X_3 = (x_{31}, x_{32}, ..., ...
9
votes
1answer
492 views

Are PCA components of multivariate Gaussian data statistically independent?

Are PCA components (in principal component analysis) statistically independent if our data is multivariate normally distributed? If so, how can this be demonstrated/proven? I ask because I saw this ...
0
votes
0answers
17 views

Factorization of probability distribution and its Bayesian Network

My question is if we have a distribution $P$ that can be factorized into cond. distributions, can we model it with Bayesian Networks? I mean, $P(X_1,X_2,...,X_n) = \prod_{i=1}^n P(X_i|Cond(X_i))$ ...
1
vote
0answers
26 views

Does negative binomial regression assume sample independence?

I'm working with a negative binomial multiple regression and I'm wondering about the assumption of spatial independence of samples. White and Bennetts (1996) say that the assumption of spatial ...
34
votes
10answers
9k views

Are your chances of dying in a plane crash reduced if you fly direct?

I recently had a disagreement with a friend about minimizing the chance of dying in a plane due to a crash. This is a rudimentary statistics question. He stated that he prefers to fly direct to a ...
7
votes
1answer
99 views

Plain language meaning of “dependent” and “independent” tests in the multiple comparisons literature?

In both the family-wise error rate (FWER) and false discovery rate (FDR) literature, particular methods of controlling FWER or FDR are said to be appropriate to dependent or independent tests. For ...
0
votes
0answers
18 views

Dealing with independent events and a “given” statement

I'm given a question: Two buddies, plan a squirrel-hunting trip. B has a shot 2x better than A. A's chance of hitting the squirrel is 0.39, they see a squirrel and both shoot at the same time. ...
0
votes
0answers
21 views

joint distribution translated into union of intersection?

Consider the declaration of the intersection property for conditional independence. $$ \left.\begin{align} X \perp\!\!\!\perp A \mid B \\ X \perp\!\!\!\perp B \mid A \end{align}\right\}\text{ and ...
0
votes
0answers
20 views

How to do a test of independence on discrete quantitative observations

When doing A/B tests on websites I typically use Fisher's exact test. Now this works fine when using goals that either are reached or not, but in an e-commerce context it's really more interesting to ...
0
votes
0answers
6 views

FE Model: independence of residual and firm specific component

I'm estimating a fixed effects model and want to consider Petersen's (2009) suggestion: "The components of X (μ and ν) and ε (γ and η) have zero mean, finite variance, and are independent of each ...
4
votes
2answers
50 views

Are cross-validated prediction errors i.i.d?

Say, we test an arbitrary regression or classification procedure on $n$ independent samples with leave-one-out cross-validation. This results in an estimate of the prediction error $e_n$ for each ...
0
votes
1answer
53 views

Graphical dependence in the DAG X->Z<-Y

In Barber's book pp. 40-41 he says that the belief network X->Z<-Y: is "graphically dependent" since: $$p(x,y|z) \propto p(z|x,y)p(x)p(y)$$ I don't understand why graphical dependence follows ...
5
votes
1answer
71 views

Asymmetric measure of non-linear dependence/correlation?

I am definitely not a statistician/mathematician so feel free to tell me I'm an idiot if I am. As far as I can tell from my Wikipediaing all of the main measures of dependence are symmetric and ...
0
votes
0answers
18 views

Compare two independent samples with one variable

It is assumed that in computer programming courses, students programming in pairs will have better grades than students programming alone (solo-programming). After collecting data about the grades of ...
3
votes
1answer
81 views

Examples of marginal independence, conditional dependence

I am interested in finding "real-world" examples of when variables might exhibit marginal independence but are conditionally dependent given some other variable. It seems to me that the converse ...
1
vote
0answers
47 views

Is this interaction endogenous or independent?

Imagine a multiple regression of the form $ y = \beta_0 + \beta_1x_1 + \beta_2x_2 + \beta_3x_1 x_2 + u $ Now imagine that $x_1$ is endogenous (in that it is correlated with $u$) but $x_2$ has been ...
0
votes
0answers
8 views

Observations independence

I have observed prices of products (phone plans) that appear in the market in each year during 8-year period. When the product is on the market, its price doesn't change. For such products, when price ...
1
vote
0answers
23 views

Flow of influence in a v-structure for Probabilistic Graphical Models

I'm not very sure I understand why an observed v-structure have different flow of influence behaviour for a directed and an undirected graph. What is the intuition behind the actual definition for ...
2
votes
1answer
154 views

Why is independence required for two- sample proportions z test?

I read in several books as well as in different posts (e.g. here) that independence is required for two-sample proportions z tests. But so far I could not find an explanation why this is the case and ...
0
votes
0answers
9 views

What is the best way to test if an IV has a stronger effect on the DV than another IV that a subset of the first IV?

I wish to investigate the effect of general international experience of a corporation measured as the number of foreign subsidiaries it own vs. the effect of local experience in a region measured as ...
3
votes
0answers
31 views

Does diagnolizing higher-order cross-moment matrices lead to independent variables?

Diagonalizing the covariance matrix transforms multivariate data into uncorrelated variables, but does not make them independent necessarily. Does it follow from this that if I were to diagonalize ...
3
votes
1answer
171 views

Linear independence vs statistical independence (PCA and ICA)

I'm reading this interesting paper on application of ICA to gene expression data. The authors write: [T]here is no requirement for PCA components to be statistically independent. That is true, ...
3
votes
1answer
51 views

Paired samples or independent sample hypothesis test for two time periods

I want to know if employees in an organization are surveyed in 2013 and again in 2014 if the samples from the two time periods are considered related and dependent or independent if they are asked the ...
0
votes
1answer
22 views

Reg: MGF and independence

If three random variables X, Y, and Z are pairwise independent, whether U = aZ+bY, V = aY+bX are independent? I tried using MGF technique and arrived (i don't know its correct or not) as U and V are ...
0
votes
1answer
27 views

Independence within groups - which test?

I have a table of data with three columns: ...
3
votes
2answers
62 views

Can someone explain what it means for an observation, from a group of data, to be independently and identically distributed?

I don't quite understand what the difference is between an observation being independent and it also being identically distributed. Can someone explain please?
1
vote
2answers
35 views

Determining unusual binomial results from a sub-population

If I have a population of 1948 students with a success rate of .154 (301 successes) and I break the 1948 students into their respective majors, how to I determine if the sub-population success rate is ...
0
votes
1answer
30 views

Are identical samples independent?

Are results of two different tests performed on exact same sample independent or dependent? For example, if the same group of rats were injected some drug A, results collected, then long enough time ...
1
vote
0answers
19 views

How to determine if these values are different?

I don't have much stats background (I am a programmer) but want to learn more. I have five long columns of numbers that represent conversion rates (ex. how many successes vs. how many attempts) for 5 ...
5
votes
1answer
145 views

Conditional independence iff joint factorizes

I have proven that: $X⊥Y|Z\ {\rm iff}\ p(x,y|z)=p(x|z)p(y|z)$ for all $x,y,z$ such that $p(z)>0$. The next question is to prove an alternative definition: $X⊥Y|Z$ iff there exist functions $g$ ...
1
vote
2answers
63 views

Transform two correlated random variable to independent variables without knowing correlation

I am thinking about this interesting question which arises in the following realistic setting. For example, in one medical experiment one drug and one placebo are applied to two randomized groups of ...