The expected squared deviation of a random variable from its mean; or, the average squared deviation of data about their mean.

learn more… | top users | synonyms

4
votes
3answers
41 views

Interpreting random effect variance in glmer

I'm revising a paper on pollination, where the data are binomially distributed (fruit matures or does not). So I used glmer with one random effect (individual ...
2
votes
1answer
35 views

What is the long run variance?

How is long run variance in the realm of time series analysis defined? I understand it is utilized in the case there is a correlation structure in the data. So our stochastic process would not be a ...
1
vote
0answers
19 views

variance and sample confused

When solving (b), is the variance $$ V\bigg(\frac 1 2 (x_1+x_2)\bigg) = \frac 1 4 V(x_1+x_2) = \frac 1 4 \big(v(x_1)+v(x_2)\big)= \frac 1 2 \sigma^2 $$ or should I divide the variance by the sample ...
3
votes
0answers
26 views

Variance of binomial vs. multinomial distribution in cross-validation

Suppose we have a dataset with $N=100$ observations. We do $K$-fold cross-validation with $K=10$ and $K=100$. In the first case, the classification decisions are sampled (can I say it like this?) ...
0
votes
0answers
29 views

Combining the Standard Deviation for Multiple Populations; Small Data Sets

I have been presented with a very small dataset which describes a material property for a particular cast of stainless steel, in this case fracture toughness. The data is: ...
0
votes
0answers
32 views

Two-way ANOVA: error variance in numerator of F statistic for main effect

Let us consider a balanced two-way ANOVA without replications, having $m$ columns and $n$ rows. If we want to test the column effect, we use the statistic $F(c)=MS(c)/MS(e)$, where $MS(c)$ is the mean ...
4
votes
1answer
214 views

Is the following dataset possible?

"Is it possible to create a data set where $\bar{x}=30.0$, range $R=10$ (meaning the max-min=10), and variance $s^2=40.0$?" I feel sort of dumb asking this question, but I'm not quite sure I'm on the ...
4
votes
1answer
45 views

Question about bias-variance tradeoff

I'm trying to understand the bias-variance tradeoff, the relationship between the bias of the estimator and the bias of the model, and the relationship between the variance of the estimator and the ...
3
votes
1answer
49 views

Variance stabilisation

$Y$ has mean $\mu$ and variance function $V(\mu)$. If $V(\mu) = \alpha.\mu^v$ then $h(y) = y^{(2-v)/2}$ is variance stabilising which means that $Var(h(Y))$ is approximately constant. I tried to ...
0
votes
1answer
32 views

Estimate variance of a function given variances of variables

I'm given the mean and the standard deviation of N random variables $A$, $B$, $C$, $D$... I compute the function $f:=f(A, B, C, D...) = \frac { AB... }{ CD... } $. How can I estimate the variance of ...
0
votes
1answer
45 views

Sample variance from second moment

if I have a sample composed by values lesser than 1 and i want to compute the sample variance with $ \frac{n}{n-1}(\langle x_i^2 \rangle - \langle x_i \rangle^2)$ how can i do? Because the mean of the ...
4
votes
1answer
42 views

Looking for a distribution where: Mean=0, variance is variable, Skew=0 and kurtosis is variable

I am aiming to run simulations in order to estimate the influence of the distribution of $Y$ (independent variable) on a certain binary outcome $X$ (dependent variable). $Y$ must always has a mean of ...
0
votes
0answers
21 views

How would I calculate the t-statistic for this data and then determine if it's significant?

Say we want to test the hypothesis that a control group of cancer patients would report higher mean pain ratings than an experimental group receiving special massage treatments. Group 1: Mean = 78.1 ...
0
votes
0answers
9 views

binomial error calculated with formula

i have uploaded a 2D histogram ,, actually it is filled by dividing two 2Dhistograms with same bins.i want to calculate manually each error which is shown with each value i.e binContent.Please ...
0
votes
0answers
19 views

Expected Value and Variance of a summation of correlated sample means

Let $\gamma_i$ be constants and $f(\gamma_i)$ be normally distributed random variables. More specifically, $f(\gamma_i)$ is the sample mean of the population $\gamma_i$. Now I have a sum of the ...
0
votes
0answers
30 views

Cointegration and variance of time series

If we know that $X_t , Y_t$ are two cointegrated discrete random processes, what can we say about the relationship between variance of the two increments $var(X_{t+h}-X_t)$ , $var(Y_{t+h}-Y_t)$ for a ...
0
votes
1answer
83 views

When is Variance Statistically Significant?

This may seem like a rudimentary question relative to other posts, but how do I determine whether the variance is statistically significant? For example, let's say I have a population of 10000. I ...
0
votes
0answers
11 views

Overlap between 1) regression results and 2) correlation between residualized versions of variables

Scenario: 1) Regress a standardized variable A ("stand. A") on a standardized Variable B "(stand. B"). Since both Variable A and Variable B have a number of potentially confounding influences on ...
0
votes
0answers
19 views

How to compare variability between two variables when using the coefficient of variation is inadvisable?

I have two variables with different means. They both include negative and positive values. How can I compare their variability, given that the coefficient of variation should not be used when I have ...
0
votes
0answers
30 views

Superposition of two renewal processes

Usually, superposition of two independent renewal processes may not lead to a renewal process. However, in my problem, the interval time between two events of the renewal process is more specific ...
1
vote
0answers
25 views

Error of the variance

I have a collection of $(x,y,z)$ data points. I want to compute the mean, $\mu$, and variance, $\sigma^2$, along each axis, as well as the errors on each. I know that the standard error of the mean ...
0
votes
1answer
55 views

Residual variance formulas difference

There is a bi-dimensional table of frequencies: Doing the regression analysis with the fit formula being $\hat y=a+bx^2$, where $\hat y$ is the same as $y^{est}$, the filled table looks like this: ...
3
votes
1answer
71 views

What is the covariance called when it is not divided by N?

I noticed that in signal processing they have this term called cross-covariance. The cross covariance function produces covariances of two functions with different lags. At the center of the vector ...
1
vote
1answer
40 views

How do I show that $-\frac{1}{2}\sum_{i=1}^n(X_i - \bar{X})^{T} \sum^{-1}(X_i - \bar{X})=-\frac{n}{2}trace(\sum^{-1}S)$?

In multivariate statistics the variance $S=\frac{1}{n}\sum_{i=1}^n(X_i - \bar{X})(X_i - \bar{X})^T.$ My lecturer showed me that $-\frac{1}{2}\sum_{i=1}^n(X_i - \bar{X})^{T} \Sigma^{-1}(X_i - ...
2
votes
1answer
172 views

What is Bartlett's theory?

This neuroimaging paper has been cited thousands of times. In it, a method is proposed for computing the correlations among several seed regions and all other brain voxels. Part of this method ...
1
vote
0answers
29 views

Assigning variance in regression

Say we have a linear regression model $$y_t = \mathbf{x}_t'\boldsymbol{\beta} + \epsilon_t, \qquad \epsilon_t \sim \mathcal{N}(0, \sigma^2)$$ Assuming $y_t$, $\boldsymbol{\beta}$, and $\sigma^2$ are ...
2
votes
2answers
107 views

Double integral, monte carlo estimation

Suppose I have pairs of random variables where $X_i$~$U[0,1]$ and $Y_i$~$U[0,1]$ and I want to estimate it $$\theta=\int_{0.5}^{1}\int_0^{0.5}e^{xy}xydxdy$$ but $\theta$ needs to have variance less ...
0
votes
0answers
16 views

Concerns regarding correlation structures and random variance using lme

I’m modeling some variables repeatedly measured over a three months period for a total of 300 individuals. These variables (e.g. activity) were measured at three different time scales: daily (90 ...
-1
votes
0answers
19 views

Logistic Regression with negative signal

I'm trying to build Logistic regression to identify bots. But I found in my dataset that presence of one feature indicate that this is NOT a bot. Unfortunately this feature is not appearing often ...
0
votes
0answers
24 views

Estimate the population variance from a set of weighted means

Proviso: I do not have a lot of experience with statistical theory, so please forgive my occasionally poor choice of notation.$$\\$$ My problem is as follows: I have a set of measurements $X_i, ...
0
votes
0answers
25 views

Median Absolute Deviation vs Standard Deviation

To measure spread we use Variance or Standard Deviation. Variance and hence Standard deviation uses mean to find out the spread. Recently came across the MAD (median absolute deviation). ...
0
votes
1answer
19 views

Unbiased estimator and variance

A random sample of n people are asked whether they are against smoking or not. Suppose x are against smoking. What is the distribution of the random variable X (number of those against smoking). State ...
1
vote
1answer
28 views

What is the meaning of averaging combinations of independent random variables?

I'm getting into the management of multiple independent random variables in determining expectation and variance, but cannot see where averaging of a linear combination of independent random variables ...
1
vote
0answers
20 views
0
votes
0answers
41 views

Using variance in place of standard deviation for z-normalization

I'm implementing a 1-nearest neighbor (with dynamic time warping as the distance measure) classification algorithm on a severely constrained embedded platform with no FPU, so we're doing fixed point ...
1
vote
0answers
32 views

How to explain to laypeople that in a VAR model some variable explaines its own variance?

Background: I observed that people not familiar with vector autoregressive (VAR) models often struggle with the interpretation of a forecast error variance decomposition. I am frequently asked, why a ...
1
vote
2answers
44 views

Variance of the linear transformation of a random variable

I have a problem where the variance I'm calculating does not seem right. I have the following data: ...
0
votes
0answers
16 views

Variance partitioning into trait and method variance using CFA

I am concerned that my data is biased because of common method variance; i.e., the variance shared between the latent factors in my model is only due to the employed survey method (self-reporting ...
1
vote
0answers
12 views

Binary variance? Comparing two sacks of uneven coins or two heterogenous groups of people

I have two sacks of coins. In one sack, the coins are all uniform, each giving a fairly constant 0.5 chance of heads (based on tossing a few of them and also visual inspection). I then estimate the ...
0
votes
0answers
8 views

Do odds ratios have an effect on the variance components (level-2 variance) in multilevel models

I am estimating logistic multilevel models and have a question regarding the variance components (i.e. level-2 variance). I want to report my results as odds ratios and I am wondering if the ...
0
votes
0answers
24 views

The contribution of sub-variables to the overall variance

As part of laboratory quality, we run classic control charts. Within the overall data of these control charts there are results from multiple operators. Can someone please point me in the right ...
0
votes
1answer
28 views

How to statistically calculate speed of mean reversion?

In the image below i have a set of normalised firms earnings, grouped into deciles. As time passes, dispersion decreases and we generally see a mean reversion phenomenon (towards the median value). ...
0
votes
1answer
45 views

Making the most of Standard Deviation and P value — graphing?

I have a question or two in regard to getting the most out of the statistics of my data. By way of background, my qualitative observations of two distinct populations that are uniformly regarded to be ...
0
votes
0answers
9 views

Relative Proportion of Variance for each Factor (ANOVA)

I'd like to calculate how much of the variance is related to each of the input factors. For example (in this case some R-code), if one wants to calculate how much of the "Magic Effect" of a magic ...
1
vote
1answer
24 views

How to derive the standard error of product of two variables with unequal sample sizes?

Say $H$=height, $b$=angle, and $d$=distance; $H=\text{tan}(b)*d$. $b$ has a sample size of $5$ with mean $40.4166$ degrees and variance $3.75E-05$. $d$ has a sample size of $3$ with mean $124.3$ ...
3
votes
0answers
38 views

Prediction Intervals for Incremental OLS regression

I am implementing incremental OLS regression algorithm where the data points arrive one at a time. As the regression parameters are determined by the formula, $(X'X)^{-1} X'y$ and the Sherman-Morrison ...
2
votes
0answers
18 views

When to use Brown-Forsythe Test?

I have been researching the differences between Welch ANOVA and Brown-Forsythe Test. I know that Welch ANOVA is used for more than two groups comparing whether there is statistically meaningful ...
3
votes
1answer
45 views

Variance of a product of Bernoulli with another distribution

This is probably a stupid question, so my apologies if this is too simple. I have a distribution X, now I play the following game: I toss a coin, if it falls on a head, I get nothing, if it falls on ...
0
votes
0answers
28 views

out-of-sample variance calculation using rolling window in R

My objective is to calculate out-of-sample variance of various portfolios. I am currently working on the comparison of the constructed portfolios using ...
1
vote
0answers
39 views

How to simulate data in R given mean, median, and range?

I would like to simulate n numbers (all within the range between a and b, n being an even number) using R, and the mean (u) and median (m) is given. If I use runif then the standard deviation is ...