Questions tagged [variance]
The expected squared deviation of a random variable from its mean; or, the average squared deviation of data about their mean.
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How do you calculate variance for percentages?
I know this seems like a simple questions but I am trying to wrap my head around calculating variance for percentages (e.g. 15%, 16%).
I know that 15% is equivalent to 0.15, but when I try to ...
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7 views
What statistical method deals with a continous predictor characterized by low variance?
I would like to run a study in which my predictor is a continuous variable. I already know that the distribution is normal but most of the points fall close to the center. I think that small ...
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1answer
21 views
How does pooling affect variance?
Suppose you are looking at the prevalence of a certain disease and you can detect this disease in fecal samples. How does having a bunch of pooled fecal samples (i.e., taking a fecal sample from 5 ...
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1answer
14 views
How much will the variance change in this scenario?
Imagine that a firm decides to increase the salary of every single of its employees by 10% of their current salary. The average of the salaries will increase by 10% too. But, how will the variance of ...
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21 views
Explanation for Bessel's correction [duplicate]
In textbooks and online the explanation for Bessel's correction is that the sample points are closer to the sample mean than the population mean.This is true for sampling with replacement as well. So, ...
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28 views
Unbiased estimator for Variance
So basically I have a survey where for each unit 1, ..., N in the population, we flip a fair coin to decide whether this person will be included in the survey or not. Let S be the r.v. denoting the ...
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23 views
Mean and variance of a function of random multivariate vector
Let's assume to have a scalar function $Y=f(X)$, that is function of a multivariate normally-distributed random variable $X\sim\mathcal{N}(\mu, \Sigma)$.
Is there a general way to compute, even in an ...
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48 views
Is the $\sigma$ estimator more efficient than the $\mu$ estimator?
Are my empirical findings correct? How to get the same result analytically?
I studied the efficiency of the mean and standard dev estimators:
$$\mu_n=\sum \frac {x_i} {n}\space\space\space\space\...
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36 views
Don't understand how pseudo-R-squared results for mixed model are even possible (MuMIn in R)
We're using MuMIn in R to look at the delta R-squared when adding a term into a mixed model like this:
...
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How Does Variance Propagate From Likelihood Function To MCMC Posterior?
Suppose we are trying to obtain the posterior distribution of three parameters that influence a discretely observed population. The likelihood function is unfortunately intractable, as it is a mix of ...
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1answer
122 views
How to compute Variability Independent of the Mean (VIM)
Although I find this reading regarding the interpretation of the Coefficent of Variation (CoV) very interesting, I did not found hints regarding the Variability Independent of the Mean (VIM) which is ...
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Moments of truncated Student's $t$-distribution
I performed random sampling on a Student's $t$-distribution. I used SciPy to calibrate my parameters and then truncated my allowable values to the maximum and minimum observation in the data for ...
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Aggregating variance from many variables for Levene's test? [closed]
I am interested in finding out whether the composition of students has become more heterogeneous over time. People vary by several important variables: age, gender, ethnicity etc.
I have large cross-...
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23 views
Fitting environmental variables to an ordination (artificially replicating data?)
I collected five samples of animal tissue from each of 3 different sampling sites (15 samples total). For each sample, I determined bacterial community composition, so I have a standard multivariate ...
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1answer
27 views
Changing only one point of a discrete distribution to maximize variance augmentation
X has a discrete distribution with support $x1, x2, ...$ in $ {]}0,1{[}$. You have the right to change only one of the $xi$ to lead to the highest increase in variance (or, at least, a systematic ...
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18 views
Is there an alternative to Box's M test for data that is not multivariate normally distributed?
My research question is to test whether two groups have a difference in variance-covariance across multiple measures. However, the data do not follow the multivariate normality assumption required for ...
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9 views
How to determine the accuracy and variance in categorical survey data responses?
I've conducted a survey where I have shown citizens images of transect squares placed in a field. For each image of a transect square, I've asked citizens to i) count the number of beetles (a ...
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1answer
36 views
PCA; variance, interpretability, and scaling
I've been going through threads about PCA and the predictive power of various axes, but since I cannot comment, I am opening a new question.
There is a lot of discussion whether PCA components with ...
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22 views
Relation between bias and R-square
I am trying to understand relation between bias and R-squared value in linear regression.
High bias means that the model is underfit. By this I am assuming that the R-square d will be less.
So my ...
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23 views
Relation between Variance of one variable and variance of two independent variable
Is the following statement correct?
If $X$ and $Y$ are independent then $\operatorname{Var}(X)\lt \operatorname{Var}(XY)$ and $\operatorname{Var}(Y)\lt \operatorname{Var}(XY).$
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57 views
Variance of integral of Poisson variables
I have a stochastic quantity (not sure if it is a proper stochastic process), defined as follows:
$$I = \int d x f(x) X(x)$$
$f(x)$ is a positive function of real variable, defined over the integral ...
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1answer
17 views
Error in Derivation for Control Variate Variance?
I'm trying to derive the variance for a control variate estimator, but I seem to be missing a term that allows me to end up with the covariance in the final answer.
Let $f(x)$ be my function and let $...
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15 views
Limiting distribution of sample variance and standard deviation
I have a centered Gaussian sample of $n$ elements $X_i,\,i=1,..,n$, with variance $\sigma^2$. I would like to find the limiting distribution of the sample variance $\sigma_n^2=\frac 1n \sum_{i=1}^n ...
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1answer
54 views
Negative Adjusted $R^2$ in twoway effects within model
I am having serious trouble understanding the results of my Fixed Effects panel regression. I am using two fixed effects (on year and regions) and I get a negative Adjusted R2 (i am using the plm ...
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Is it possible to show that this estimator has minimum variance?
Doing some exercises I stumbled upon this tricky one:
Suppose we have an independent random sample $(X_1, ... , X_n)$ with $X_i \sim Poisson(\lambda)$. Define $\theta = e^{-\lambda}$.
Let $$ \...
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51 views
Mean and variance of a Random Walk with lower boundary
Consider a random walk $S_n$ that starts at $S_0$ and terminates if it hits a lower boundary of $0$.
$$
S_n=\begin{cases}
0, & \text{if } S_{n-1}=0\\
0, & \text{if } S_{n-1}+x_n\le0\\
S_{n-...
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1answer
36 views
Can I predict the variance of a random variable using a machine learning regression model that predicts expected outcomes?
For example, suppose I'm using some machine learning model like gradient boosting that, given some input $x_i$ predicts the expected output $f(x_i) = y_i$.
However, I'm also interested in estimating ...
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20 views
Variance estimator that is optimal under absolute loss
Given a random i.i.d. sample from a population with a finite variance $\sigma^2<\infty$, what estimator of $\sigma^2$ is optimal under absolute loss?
$$
\arg\min_{\hat\sigma^{2}\in F}\mathbb{E}(|\...
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10 views
mixing absolute or relative error with standard deviation for error propagation
I have an equation $$A = \frac{B \cdot C}{D}$$ where I want to know the error of $A$. As the variables are independent, the variance of this should be:
$$\mathrm{Var}(A)=\sqrt{\left(\frac{\partial A}{\...
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Two Factor ANOVA with different sample sizes but similar variances
I gave an educational intervention to Spanish speaking and English speaking students. I gave a pre and post test to these students. Due to certain issues I was not able to identify students with their ...
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2answers
85 views
Is $\hat{\sigma^2}=\hat{\sigma}^2$?
In simple linear regression $$Y_i=b_0+b_1X_i+\varepsilon_i$$ where $$\varepsilon_i\sim N(0, \sigma^2)$$ is it true to say that the estimator for variance and the estimator for SD squared are equal? I ...
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How are $n$ and $Var(\varepsilon)$ affecting to Variance of Estimation of Slope Parameter $\beta_1$ in Simple Linear Regression
Once I have derived the variance of $\hat{\beta_1}$ as:
$\text{Var}(\hat{\beta_1})= \frac{\sigma^2}{\sum(x_i-\overline{x})^2}$
I would like to know how are affecting to this formula:
the size of ...
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23 views
How to Calculate Observed Variance in a Random-Effects Meta-Analysis
I've received a revise and resubmit on a meta-analysis investigating the effects of a positive psychology intervention on depression and anxiety symptoms. I used Hedges' g as the effect size with a ...
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how to pick the daily volatility component in Multiplicative Components GARCH modelling?
Recently I've been drawn to the rather interesting Multiplicative Components GARCH model for intraday volatility modelling, a draft paper written on it can be found here: Chanda, Engle, Sokalska, 2005 ...
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1answer
89 views
Parameter estimation in the linear mixed effects model
In Parameter estimation and inference in the linear mixed effects model, page 1923, the variance
\begin{equation}
\begin{aligned}
\text{var}(\tilde{u} - u) & = \sigma^2G - \text{var}(\tilde{u}) \...
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2answers
92 views
Mean and variance of a non-standard pdf
I have tried to compute the variance and the mean for $\mu=0.5$ of the following PDF using Wolfram cloud but I failed
$$ F(z,\mu,\sigma)=\frac{2 (z-\sigma )^2 \exp \left(-\frac{(z-\sigma )^2
\...
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2answers
108 views
Linear Mixed Effects Model Variances
Consider the following model:
\begin{equation}
Y_i = X_i\beta + Z_ib_i + \varepsilon_i,
\end{equation}
where $b_i \sim N(0, D)$, and $\varepsilon_i \sim N(0, R_i(\gamma))$.
The variance of $Y_i$ ...
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What conclusions can we draw from different correlations between IQ scores between subjects belonging in different groups?
I was reading a presentation where research was quoted according to which children and parents who live together have IQs that are correlated with a correlation coefficient of 0.42 while children and ...
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Why do some people say that an asymptotically unbiased estimator “satisfies a strong law of large numbers”?
If $x\in\mathbb R$, an estimator for $x$ is an integrable random variable $X$. We say that $X$ is unbiased if $\operatorname{Bias}(x,X):=x-\operatorname E[X]=0$.
Now, in the context of Markov chain ...
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1answer
23 views
How to identify periods of high variance in temporal data [closed]
I have a dataset with concentration of a chemical (continuous) as the dependent variable plotted against time (continuous). I expect that certain periods during the year (e.g. summer) will have ...
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25 views
Why do regression estimates provide lower relative error than averaged values?
I am trying to estimate the per-cell protein concentration for some samples. I have performed a series of protein extractions for each of my samples, with each extraction using an increased (and known)...
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Keeping track of the variance of a Metropolis-Hastings estimator
Let $(E,\mathcal E,\lambda)$ and $(E',\mathcal E',\lambda')$ be measure spaces, $p,q$ be probability densities on $(E,\mathcal E,\lambda)$, and $\varphi:E'\to E$ be bijective and $(\mathcal E',\...
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1answer
357 views
Large Numerical difference in variance calculation : Unable to decipher
For the below pdf, I've calculated variance by two methods and observe a large difference (2.1477 vs 2.9100). Wondering why is this difference right at the first decimal? Is it just loss of precision ...
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How to bootstrap a statistic calculed in a meta-analyis?
I have calculated a statistic in a meta-analysis of individual data and I want to bootstrap it to obtain the variance (no analytic expression is available) to make a test.
First, I was naively ...
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1answer
20 views
Variance Estimation for Least Squares with Probability Weights
I'm running a simulation study and finding that the nominal SEs of the estimated coefficients when using weights in lm in R are an underestimate of the simulation SE. I have confirmed that $\hat{\beta}...
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How can I compare the performance of two measurement modalities?
Let's say given some 3D images of the brain, I have two methodologies to measure the brain's volume.
I'll call these two methodologies M1 ...
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33 views
Mean and covariance of Bernouilli
I am given probability distribution here for a multinomial bernoulli:
$p_{x}(x|z=j; \mu^{j}) = \prod^{d}_{i=1}(\mu^{j})^{x_{i}}(1-\mu^{j})^{1-x_{i}}$
where $x_{i}$ takes value 1 or 0, $\mu_{j}$ is ...
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1answer
30 views
$X$ has distribution function $F(x) = e^{-e^{-x}}$. Justify that such a probability measure on $\mathbb{R}$ exists
How can I prove a probability measure exists? If $F(x) \rightarrow 1$ as $n \rightarrow +\infty$, does that mean $F(x)$ does exist? And how should I calculate $\mathbb{E}(F(X))$ and $Var(F(X))$?
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What is the estimate of $\mathrm{Var}\left(\frac{nM}{X}\right)$ where $X$ is hypergeometric?
Consider the classical capture-recapture method, where we are to estimate the number of deer (say) in a sanctuary. So a certain number of deer is captured, tagged and released. Then a random sample is ...
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Question on variance on finding the variance
I have a question on finding the variance of the giving problem:
On an auto collision coverage, there are two classes of policyholders, A and B. 60% of drivers are in class A and 40% in class B. The ...
