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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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 ...
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16 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 ...
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33 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: ...
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10 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 ...
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8 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 ...
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7 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 ...
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14 views

Variance Calculaton from a linear regression coefficient [on hold]

I need assistance with this variance calculation for a regression coefficient. If the linear model is $y=Bx^2$, the estimator of $B$ is $\hat{B}=\frac{\sum_i y_i x_i^2}{\sum_i x_i^4}$ Can you please ...
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20 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 ...
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24 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). ...
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42 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 ...
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7 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 ...
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1answer
17 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 $124.3$ ...
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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, ...
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15 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 ...
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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 ...
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21 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 ...
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33 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 ...
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12 views

Variance matrix for model errors

I am having trouble with understanding how can I write out the variance matrix for model residuals. I have a very simple data with 6 observations: ...
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1answer
38 views

Visualise variance partitioning

I'm interested in visualising variance partitioning in the context of linear models. Say you run an linear regression that predicts peoples weight based on their height and age. How can you visualise ...
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34 views

one way anova in R

I have only just started using R in my first year at university and I am completely stuck. I have done an anova test as the data is normally distributed and parametric. However, this is my result. I'm ...
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34 views

Why are these formulas for the variance equal?

I am trying to understand why the simple bootstrap procedure does not work, but for now I would like to know why we can we write $s^2_n = \frac{1}{n} \sum^n_{i = 1} X^2_i - (\bar{X}_n)^2$ ? This is ...
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1answer
110 views

Variance reduction technique in Monte Carlo integration

I have some trouble understanding the variance reduction method called "Antithetic variables": Suppose that the integrand is $g(x)=x^2$ and the reference density $f(x)=e^{-x}I_{[0,\infty]}$ is ...
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1answer
29 views

Powering a study to show differences in variance, e.g. in R?

I'm hoping to do a study to calculate whether 1 method of measurement is more variable than another in a subgroup of patients. I assume this will be done with an F-test, from some reading? However, ...
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26 views

How to obtain variance of a random variable that depends on a hypergeometric variable?

I have been given the following problem: In an assembly line production of industrial robots, gearbox assemblies can be installed in two minute each if holes have been properly drilled in the ...
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1answer
40 views

How can one resolve an apparent paradox regarding the uncertainty of the product of two measured quantities?

Suppose one has three quantities $X$, $X_1$ and $X_2$, such that $X = X_1X_2$. Since percentages uncertainties of products just add up we have: $$\frac{\delta X}{X} = \frac{\delta X_1}{X_1} + ...
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What can be inferred from “covariance matrix of residuals” and “correlation matrix of residuals” after VAR?

I have this VAR: summary(VAR(V6CADModelSt45obs1D.df[,c(5,3,2,6,1,4)], p=5, type="none", ic="SC")) The following is the result of this VAR: ...
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32 views

Is this the correct way to calculate the mean and variance of $(X-n)/(2n)$ where $X$ follows a Chi-squared distribution with $n$ degrees of freedom?

Let $X_n$ follow a Chi-squared distribution with $n$ degrees of freedom. I would like to study the variance and mean of $$\lim\limits_{n \rightarrow \infty} Y_n := \frac{(X_n-n)}{(2n)}$$ I would also ...
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40 views

Homogeneity of variance is violated for z-scores but not for raw data?

Is this a normal thing to happen or have I done something wrong in SPSS? I am using a Levene's test.
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18 views

Variance component model for longitudinal data

I have a dataset with fixed and random effects, sampled over time (body phenotypes under fixed stimulations). Generally speaking, I'd like to construct a variance component/ partitioning model to ...
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1answer
15 views

Two random vars, finite mean and variance, represent Var(Y) with conditional expectations

This was asked as an self-assessment question, that I was quite embarrased by, as I had no idea how to start it... Consider two random variables X and Y that are allowed to be correlated and whose ...
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36 views

Variance of a function of the sample variance

I'm looking for the sampling standard deviation of $\hat\sigma^\gamma$, where $\hat\sigma$ is a sample standard deviation. For simplicity, lets do the sample variance of the sample variance and take ...
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24 views

Estimating the variance of a sum of predictions

I have $N$ plots that were used to estimate a relationship between three predictor variables, $X_1$, $X_2$, $X_3$, and an outcome, $Y$, using a generalized linear (lognormal) model. The resulting ...
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27 views

Additivity and linear combination of chi-squared distributed variables

I am trying to get a better understanding of the Satterthwaite pooled degrees of freedom estimation, which led to understanding the general problem of pooling variances. My confusion, in short, is ...
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26 views

Justification for variable reduction by removing predictors with near zero variance

I have a large number of variables that I'm trying to reduce, and I've stumbled on Kuhn's (2008) suggestion that I eliminate variables with zero or near-zero variance. This makes sense to me, it's ...
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48 views

Variance of the maximum likelihood estimator of Rayleigh Distribution

I want to calculate the variance of the maximum likelihood estimator of a Rayleigh distribution using $N$ observations. The density probability function of this distribution is : $$ f(\sigma,y_i) = ...
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1answer
40 views

PCA/MFA for (graphical) dimension reduction: what to do with very small explained variance?

I ran a Multiple Factor Analysis on a data set with 3,924 rows and 96 columns, of which six are (unordered) categorical, with 12-14 categories in each, and the rest are numeric, mean-centered and ...
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23 views

What sample size is needed to estimate the population mean, with unknown variance?

I want to know what's the sample size needed to estimate the population mean, with unknown variance? I'm filling up a database that stores the values of wifi-accespoints' strength level at certain ...
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21 views

Linear form arising in expected value of empirical variance of non-independent variables

Consider a normal vector $Y \sim \mathcal N(\mu, V)$ with $\mu \in\mathbb R^n$ and $V\in\mathbb R^{n\times n}$. I am interested in the expected value of $$ {1\over n-1} \left( Y'Y - {1\over n} ...
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42 views

How to compare means, variances and standard deviations of durations for statistical significance

I am trying to compare multiple mean values, variance and standard deviation values for statistical significance. For example I have the following data: Data 1 Mean: 0.01304 Sample ...
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28 views

What role does the sampling fraction play in the simple random sample variance formula?

Consider a survey where the population being estimated is finite. Using a simple random sample, you draw $n<N$ data. The sampling fraction is $f=\frac{n}{N}$. The variance will be ...
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1answer
72 views

Intelligently selecting outliers

I'm trying to remove what might be considered "unreasonable" data by evaluating the percent error in the mean and square root of the variance. Here's the setup: Let's say I have three bids on a ...
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14 views

How to determine proportion of variance explained in factor analysis

How can I determine proportion of variation explained by 2 factors obtained in output of following code of factor analysis using pacakge "rela" in R: ...
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57 views

How can increasing the dimension increase the variance without increasing the bias in kNN?

My question is about understanding Figure 2.8 in The Elements of Statistical Learning (2nd edition). The topic of the section is how increasing dimension influence the bias/variance. I can roughly ...
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1answer
23 views

variance in test accuracy will increase as we increase the number of test examples؟

I see this statement on 1 that say a True statement on Machine Learning Context. The variance in test accuracy will increase as we increase the number of test examples. my challenge is why ...
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16 views

Derivation of Variance for formula of Cohen's d statistic

Cohen’s d is one of the most common ways we measure the size of an effecthttp://en.wikiversity.org/wiki/Cohen%27s_d. Cohen’s d simply a measures the distance ...
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46 views

Variance of slope

I have a bunch of data that I fit a linear regression to, and now I need to find the variance of my slope. Is there an analytical way to get this? If an example is necessary, consider this my data in ...
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50 views

Limiting variance of normal mean

In Casella's Statistical Inference,in Example 10.1.8 on page 470, it says that the limiting variance of normal mean $\bar X_n$, is $\lim_{n\to\infty}\sqrt n\text{Var}\bar X_n=\sigma^2$. However, since ...
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When the null model performs better than more complex models

Consider a matrix $X \in R^ {n \times m}$ representing $n$ samples and $m$ features. Also consider a matrix $y \in R^{n \times k}$ representing $n$ samples and $k$ target values. $y$ has continuous ...
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Time-partitions of sample size

I am struggling with explain something I read in a Whitepaper. The essence is as follows. Let's begin with a random variable $X$ defined as number of events in an hours. Further, we assume that $X ...