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.

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Show that no two sets in the probability space with $\mathbb{P}(\{k\})=2^{-k!}$ are independent

Let $\mathcal{P}(\mathbb{N})$ denote the power set of $\mathbb{N}$. Show that no two non-trivial sets in the probability space $(\mathbb{N},\mathcal{P}(\mathbb{N}),\mathbb{P})$ with $\mathbb{P}(\{k\})=...
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Testing Dependant Contingency Tables

Suppose we have two treatent groups $A$ and $B$ (of $n$ individuals each), we wish to determine if $A$ is statistically more likely to respond to treatment compared to $B$. We run the simplest ...
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2 votes
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Prove $P(X_1+X_2> 2C) \leq P(X_1>C)$ if $X_1,X_2$ are identical, but dependent?

If $X_1,X_2$ are dependent but identically distributed, it seems obvious that $P(X_1+X_2\geq2C) \leq P(X_1\geq C)=P(X_2\geq C)$. At least if we additionally assume that the joint distribution is ...
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Estimation of standard error in observables generated from time series data

Imagine that I have time series data which are time-correlated, non-scalar, and of unknown, but identical distribution From this time series I have a function that takes an subset of X as input to ...
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2 answers
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How to measure marginal effect of interdependent variables on a binary outcome?

My data represents observations on a possible sequences of events that may lead to a positive outcome (y). Each event (A, B, C, D) is dependent on the previous event; for D to occur C must occur, for ...
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Generating a Gausian data with dependent error

I want to generate a Gaussan simulated data with dependent error through R. I wrote my code, but I'm not 100% sure that I did it right. Would someone be able to check if I did it correctly? I assume ...
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Neural networks robust to Gaussian data with dependent error

I'm generating simulated data that follows a Gaussian distribution with dependent error, and I'm trying to fit a general Neural Network(NN) model to the data. Suppose $\mathbf{Z} = \mathbf{Y} + \...
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2 votes
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The percentile method

a research used the percentile method to find the prevalence in severe group as below: The outcome variable was categorized using percentiles to Mild, Moderate, and Severe in the Symptom Severity ...
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1 answer
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Grouping using percentiles

I did visual binning process in spss and made three cutpoints like in this image: I did check off included I want to know the percentage range or value for each group. If I describe it in this way is ...
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Assess whether distance from competitor affects sales in stores

Suppose I'd like to investigate whether proximity of a competitor store affects sales in my stores. I'm struggling on how to frame the question from a regression perspective. Furthermore, there may be ...
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Assumption of independence of observations and data per year in linear regression

I'm doing a linear regression model with data from 30 cities over 5 years (150 observations). However, by using data from cities over time, am I violating the assumption of independence of ...
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3 categorical variables analysis

apologies if this question is obvious. I am trying to determine what type of analysis I should run for an observational study I am doing. The variables are sleep (sleep deprivation <7 hours or ...
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Infer from Confidence Interval of Two Sample's Mean whether they are different

Background: I have 2x8 conditions. I can visualise the 8 different cases on a continuous line (x-axis) and now want to plot the mean and confidence intervals for the 2 different treatments. The CIs ...
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Repeated measures analysis of Likert-style question

I have a Likert-style survey that includes 2 questions: perceived understanding before an intervention and perceived understanding after the intervention. I would like to use some form of inferential ...
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Making a valid inference from higher level fixed predictors in mixed model

I'm planning a field study in which pollinators will be caught from traps in the canopies of 12 woodlands. Within each woodland ~4 traps will be placed. Traps from different woodlands I consider to be ...
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8 votes
3 answers
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Statistical learning when observations are not iid

As far as I am concerned, statistical/machine learning algorithms always suppose that data are independent and identically distributed ($iid$). My question is: what can we do when this assumption is ...
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Central limit theorem for dependent binary-related variable

Let $Y\sim N(\mu, \sigma^2)$ and given sample size $n$, we have an iid sample $\{Y_1, ..., Y_n\}$. We sample $X$ (size $n$) from Bernoulli with probability $\pi$. Denote $Z_i=X_iY_i$. Then, when $X_i=...
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How to use correlated input data to create a ML model in R

I would like to create a machine learning model with R using, for example, the simple linear regression. For independent observations, I use the command ...
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Statistical test for difference in means for 2 populations of non-i.d.d sample points with known means and standard deviations?

I have a question related to some results I've generated. We have run N experimental runs across 2 different experimental conditions with M technical replicates for each of the n=1,...,N experiments. (...
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Is this a statistical test ? what is the experimental unit? and how to treat dependency between observations?

I'm trying to understand which statistical test to use and what is my experimental unit? The problem: We have a budget algorithm that moves the budget between 10 different ad campaigns and tries to ...
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Linear regression with non-independent observations

The might be a basic question for some of you, but I am looking for the appropriate method to run a linear regression when observations are not independent. Let's say I have the following data ...
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Example of a parametric family of distributions that always has dependence on among its variables

Inspired by this question, I would like an example of a parametric family of distributions such that there is dependence for all choices of parameters. The family could be infinite or finite, but I ...
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What statistical analysis should I do?in my situation

I have a questionnaire on the experience of teleworking. My independent variables are: gender professional status have you teleworked during the period of confinement. My qualitative dependent ...
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Linear model with one continuous and one categorical predictor: is a significant difference a problem?

I have collected people's reactions to pictures (rating 0-100). The pictures are either greyscale or in colour (categorical predictor) and they vary in resolution (continuous predictor). I want to use ...
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How to test for inequality in the presence of non-independent noise?

I have multiple samples which include a response time of a system. I want to test if no sample is significantly different (primarily the expected value). For two sample testing I'm using the sign test ...
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How to express a likelihood function conditioned on a filtration?

Suppose we have the sequence of discrete dependent variables $\{Y_t\}_{t=1}^n$ and we are interested to express its joint likelihood function conditioned on an entire history of a process $X$, where $...
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Does probability independence have anything to do with functional independence (on general case)?

On normal-linear case I know it holds for example if $cor(X_1,Y)=0$ then $g_{X_1Y}(X_1,Y)=g_{X_1}(X_1)g_{Y}(Y)$, where $g_{(.)}$ is the distribution of (.), and that imples to $\beta_1=0$ on: $Y=\...
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How to find the standard deviation of a ratio?

I have means from two dependent datasets (leg length [A] and arm length [B]). I do not have raw values for these datasets, but do have N, median, 10th/90th percentiles, and standard deviation. I would ...
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How to create the dependent variable for amount of deals?

I have a data base in which each line is a M&A event, with the following informations: (i) target company; (ii) country of target company; (iii) industry of target company; (iv) year of ...
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1 vote
1 answer
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MANOVA: Dependence in dependent variables

In my study, I have two age groups (YA and OA) and 3 scores (A, B, C) are collected from each participant. Here I'm interested in two dependent variables, "RCG" which is calculated by ...
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Analyzing relationships in 5 time series (cointegration)

I don't have a dependent variable in this case. 5 time series correspond to 5 different sections of the same company. I want to analyze the relationships between the sections based on these 5 time ...
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Permutation test on dependent data

Say that I have a sample of observations which are pairs of real numbers $(x_i, y_i)$. Pairs are i.i.d., but $x_i$ and $y_i$ are not independent. I want to test whether the mean of $x$ is equal to the ...
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2 votes
0 answers
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How do I know if my data violate the assumption of independence?

I have data on reaction time (dependent variable, continuous) from participants viewing a visual stimulus that can have 7 different states (-3, -2, -1, 0, 1, 2, 3, independent variable, nominal). I ...
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Estimating Joint Probability of non-i.i.d., dependent, Bernouli trials

A joint probability space of $n$ bernouli trials has $2^n$ parameters (one probability for each configuration of T/F). I want to estimate the distribution using a subset of the necessary knowns. ...
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Multi-level Mixed-effect Modeling of Growth Trajectories: Grand mean-centering or Transformation to Normal for Dependent Variable?

When it comes with analyzing growth trajectories by multi-level mixed-effect modeling, What would be technically appropriate when the dependent variable originally shows a severe positive skewness ...
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65 views

Proportion test for two dependent samples

I'm measuring the proportion of success events for the same group of people before and after an intervention. The two samples are dependent because the same subject are measured. However each sample ...
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Confidence intervals for dependent proportions

I have a strange dataset and I need some help calculating confidence intervals for proportions, with an unorthodox dependence structure. I have been constrained to the following setup, and I have no ...
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1 vote
1 answer
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Suppose $Y\sim N(0,X^2)$, and $X\sim Bernoulli(0.5)$ on $\{1,2\}$, how to prove (or rigorously argue) that $X,Y$ are not independent

Suppose $Y\sim N(0,X^2)$, and $X\sim Bernoulli(0.5)$ on $\{1,2\}$, how to prove (or rigorously argue) that $X$ and $Y$ are not independent? Can I proceed as follows: try to show that there exists $x$ ...
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What test to run to analyse my data [closed]

I am new to stats and unsure what test to use to analyze my data. I am wanting to find out if the number of individuals in each category is significantly different. There are 11 categories A-K. It is ...
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Choose the right analysis method

will appreciate your pieces of advice on the following topic. I have data for each Client ID: Geographical Zone ID Probability of a client being in that Zone Distance from that Zone to the closest ...
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4 votes
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Conditional probability given conditional pdf

Let $X$ and $Y$ be two nonindependent continuous random variables whose support is $[0,1]$. I know $f_{X\mid Y=y}(x)$, i.e., the conditional probability density function of $X$ given the ocurrence of ...
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Alternative to Fisher's exact test when observations are not independent

I have a situation where I was planning to use post-hoc Fisher's exact tests to look for significant differences in the ratios of populations of cell subsets in response to treatments, but I'm ...
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How to add dependency within the outcomes between records in a simulation

For simplicity, consider a Generalized linear model (GLM) for the losses reported to an insurance company for damage to a building. A standard GLM assumes the randomness of the outcomes to be ...
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5 votes
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Does dependency imply an equation?

On regression, we usually think of dependency in terms of an equation relation between variables. For instance, we think that $Y$ "depends" on $X$ If $$E[Y|X] = g(X) + \epsilon \quad \mbox{...
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Standard error of mean for samples from a semi-regular time-series

I am quite a novice in statistics, but am currently facing a problem in my research where I would like to know how much I can trust the mean value from a set of 72 samples. Ideally, the approach would ...
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5 votes
1 answer
181 views

Can we use fractional regression for a dependent variable that is made of continuous numerator and denominator?

I have a dependent variable that is a ratio, which takes values between 0 and 1. Some 30% of values are 1s. The dependent variable measures the distribution of funds and is calculated as amount of ...
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Any advantage of running a multilevel model when the predictor is level 2?

I have data where individuals are nested within families. If I want to predict their daily well-being (depression assessed at a daily level for 10 days) using a baseline measure as a predictor (e.g., ...
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  • 331
1 vote
1 answer
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Comparing two dichotomous variables (non-paired)

I would like to compare two dichotomous variables: pass/fail for a statistics test before statistics class (pre-test) pass/fail for a statistics test after statistics class (post-test) I only have ...
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1 vote
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140 views

Expected value of a product of two dependent random variables

Let me preface this by saying that I'm an engineer, and by no means a mathematician, so please excuse any mathematical "wrong-doing" in my explanation. I have two vectors $V_1$ and $V_2$, ...
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How to calculate the probability of shared categories without replacement?

Given the following distribution of books on a bookshelf: Hardcover Paperback Total Fiction 13 59 72 Nonfiction 15 8 23 Total 28 67 95 Choosing a fiction book first and then a hardcover book ...
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