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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8 views

Minitab: Variance/standard deviation calculator problem [on hold]

I have a small problem with the calculator in Minitab. The question is shown in the picture, and the highlighted is the portion that I am having problems with. Now, this is how it looks when I ...
0
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0answers
8 views

Why does GEE produce the same parameter estimates as OLS?

The quasi-likelihood function optimized under GEE is: $S_k(\beta)=\sum_{i=1}^{K}\frac{\partial\mu_i}{\partial\beta_k}\nu_i^{-1}(y_i-\mu_i)=0,$ where $\mu_i=h(\textbf{x}_i,\beta)$ is the conditional ...
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0answers
32 views

4 cases of Maximum Likelihood Estimation of Gaussian distribution parameters

Let $x_1,x_2,...,x_n$ some normally distributed observations. So $\vec{x}=\begin{bmatrix}x_1 & x_2 & ... & x_n\end{bmatrix}^{T}$ In the context of my research I am trying to estimate ...
6
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4answers
585 views

Inverse function of variance

For a given constant number $r$ (e.g. 4), is it possible to find a probability distribution for $X$, so that we have $\mathrm{Var}(X)=r$?
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1answer
12 views

Cross-validating the tbats/bats function in forecast

Is there a way to cross validate the tbats/bats function in the forecast package in R? I have been trying to get CV weighted parameters which then I can pass to a function for revised estimates. ...
0
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0answers
5 views

Estimate variance of an arbitrary estimator using cross validation

Ron Kohavi's paper "A Study of Cross-Validation and Boostrap for Accuracy Estimation and Model Selection" explains very well how to compute the variance of the estimated accuracy when using CV (or ...
1
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0answers
14 views

Robust Estimators - Winsorized Variance degree of freedom (df)

this is my first question on this site. So, I'm currently working on my final year thesis, and it was on Robust statistics. In my work, I will use Trimmed Mean, Winsorized Mean and Winsorized ...
0
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0answers
7 views

How to estimate a chance of getting in the first positions, given previous tries?

I perform a series of experiments that return a number N that is between 1 and MAX. MAX varies between experiments. For example: ...
2
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0answers
26 views

Variance of compound distribution

The binomial distribution describes the probability of $k$ 'success' events given $N$ independent trials, each with a probability $p$ of being a success. The distribution is described by the formula ...
0
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0answers
12 views

Calculate the dispersion between of the sample variances and the population variance

Suppose that I have one population and 30 samples of these population. One variable of the population is the income. I would like to compare the variance of the income of the population with the ...
0
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0answers
11 views

Noninformative prior for variance, understanding and coding

I have three questions regarding the understanding behind and implementation of a noninformative prior for variance. I'm attempting to build a Metropolis sampler and I'm trying to sample from a ...
2
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1answer
34 views

Testing whether variance across 6 values is significantly above zero

We estimated a network via the Ising model procedure. The network contains 11 variables, and therefore 55 pairwise associations (these are called edges). We estimated this network in 6 different ...
5
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1answer
67 views

Are group effects in a mixed effects model assumed to have been picked from a normal distribution?

Say we're interested in how student exam grades are affected by the number of hours that those students study. We sample students from several different schools. We run the following mixed effects ...
0
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0answers
19 views

bias-variance tradeoff vs precision and recall

Can anyone explain the link between bias-variance tradeoff and precision-recall tradeoff. Are they effectively the same thing?
0
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0answers
8 views

How does the polr command in R handle partitioning variance?

I am using ordinal regression (MASS package, polr command) to analyze ranked coloration data (% piebaldism) of an iguana species based on sex, snout-vent length (SVL), and location. I'm concerned that ...
1
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2answers
21 views

Variance for Mixed Linear Model

In this mixed linear model(LMM) y is our response variable, XB is our fixed effects Matrix and Coefficient, Wu is our random effects matrix and coefficient and E is our error term with variance y for ...
1
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0answers
14 views

slope comparisons given by independant measurements

With the data used in a previous question matplot/ggplot2 ...
19
votes
2answers
783 views

Why does the variance of a sample change if the observations are duplicated?

The variance is said to be a measure of spread. So, I had thought that the variance of 3,5 is equal to the variance of 3,3,5,5 ...
0
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1answer
22 views

Correct notation for unbiased estimate of population variance

I've seen the notation $s^2$, ${s}_{n}^2$, and ${s}_{n-1}^2$ used to represent the unbiased estimate of population variance. Is there a standard notation?
4
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3answers
100 views

How to calculate the p.value of an odds ratio in R?

I have following table of values: 25 75 38 162 The odds ratio is 0.7037 and log(OR) is -0.3514. For a contingency table with values a, b, c, and d, the ...
2
votes
1answer
53 views

Method of meta-analysis of studies to determine mean blood level

Generally meta-analysis is done to determine the efficacy of some treatment as compared to controls. Is it possible to do a meta-analysis of different studies for mean blood level of a chemical, its ...
1
vote
1answer
35 views

Proof for the sampling variance of the Neyman Estimator

I'm going through Imbens and Rubin's new book and I just for the life of me can't figure out 1 minor detail in their proof for the sampling variance of the Neyman estimator $\bar{Y}^{obs}_{t} - ...
1
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2answers
58 views

What is the problem of singular (non-invertible) covariance-variance matrix?

What exactly is the problem of having non-invertible covariance matrix? Why is getting the inverse of this matrix so important? This problem is often encountered when doing regressiong works on ...
3
votes
1answer
71 views

Variance of the future value of a cash flow

I want to compute the variance of $FV =A\sum_{k=1}^n(1+r)^k=:g(r)$, assuming interest rate $r\sim\mathrm{N}(\mu,\sigma^2)$ and constant equal payments $A$. As discussed in the comments, the Delta ...
4
votes
1answer
38 views

Is precision-based (i.e. inverse-variance) weighting integral to meta-analysis?

Is precision-based weighting central to meta-analysis? Borenstein et al. (2009) write that for meta-analysis to be possible all that is necessary is that: Studies report a point estimate which can ...
1
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1answer
27 views

Bayesian model selection, functional form of variance

I'm working on a linear regression model of the form, $$y = X\beta + \epsilon(X) $$ where each $$\epsilon_i \sim N(0, \sigma^2_i)$$ My variance term is depends on a subset of the regressors $X$. ...
-1
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1answer
39 views

which statistical t-test to use when having data from different demographies?

I would like to know whether Blood Pressure is significant in contributing to a diseaseHypo. I have data from three different ...
0
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0answers
13 views

How to assess accuracy of phone GPS in measuring distance run on a 400m track, at a given speed?

Just read How to assess accuracy of phone GPS in measuring distances? and I was wondering in anyone fancies taking it a bit further and propose a solution for estimating the intervals / error expected ...
0
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0answers
12 views

Estimate variance from multiple distribution

Suppose I have $N$ feature vector and for each feature I have calculated the mean and variance. Now suppose I concatenate all the feature vector (appending one behind the other) and now if I want to ...
5
votes
1answer
71 views

Does binomial distribution have the smallest possible variance among all “reasonable” distributions that can model binary elections?

Imagine an election where $n$ people make a binary choice: they vote for A or against it. The outcome is that $m$ people vote for A, and so A's result is $p=m/n$. If I want to model these elections, ...
4
votes
1answer
21 views

Determine RMSE for tracing an object on a touchscreen

I have a study in which participants have to trace two computer generated objects (a circle and a square) shown on a touchscreen. I need to calculate how accurately they are able to trace these ...
0
votes
1answer
37 views

Variance of a Sum

I've got the following random variable for which I must find the expected value and variance: $X_h =\sum_{i=1}^{15} X_i$ Where $X_i$ is a random variable of the set $s = \{0, 1, 3\}$, corresponding to ...
1
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0answers
19 views

Bias and variance of amplitude estimator [closed]

I'd like to estimate the amplitude $a[n]$ of the following measured signal, $$ s[n] = a[n] \sin(\omega_0 T n + \phi ) + w[n] $$ where $w[n]$ is assumed to be unbiased Gaussian white noise with ...
0
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0answers
18 views

Homoscedasticity - constant second moment or constant variance

I found the following different definitions of homoscedasticity and I'm wondering which is the correct one. The second moment is constant, i.e. E(X²)=s² (see e.g. p.11 ...
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0answers
4 views

statistical analysis of intervention bases research

I'm doing a study and asking the research question, does teacher immediacy behaviours improve cognitive learning in ESL students? I am training teachers in immediacy behaviours, then seeing if this ...
1
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1answer
76 views

Confusing variance question

$E(x) = 4$ and $V(x) = 6$ What is the variance of $y=5x+2$? $E(5x+2) = 5\times 4+2 = 22$ I don't get how the answer is 150 I thought it was $(x-\bar{x})^2$ $(4-22)^2 =324$ very ...
2
votes
3answers
49 views

Comparing four classifiers

I have trained and tested four different classifiers, and I would now like to compare them. The classifiers have accuracies 95, 90, 81, 75. I know that there is no unbiased estimator of the variance ...
3
votes
1answer
25 views

The valid variance components to include in a generalizability theory model (anova) involving nesting? Are these correct interactions?

My question is about generalizability theory. A study by Bergeron, Floyd, McCormack, and Farmer (2008) is only adding to this confusion. Basically, in G-theory you want the first model you run to ...
0
votes
0answers
14 views

How do I analyze the effect of a tool on multiple subjects, when the tests also vary?

I have a set of programs, and a number of tools that can cause small faults in the programs (faulty versions of the program are called variants henceforth). Each program comes with a set of tests that ...
1
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2answers
41 views

averaging after n trials of monte carlo simulation or not? which is better statistically?

related to my job I want to code a realistic monte carlo simulation for availability, reliability and related sensitivity analysis. Scenario will be complex and there will be many parameters. What I ...
2
votes
1answer
83 views

Monthly realized variance, different number of observations per month

The monthly realized variance is usually computed as: $\sum_{i=1}^n (r_i-\bar{r})^2$, where $\bar{r}$ denotes the average return of the month, or as $\sum_{i=1}^n r_i^2$ (I am not sure which ...
3
votes
1answer
80 views

How to detect noisy datasets (bias and variance trade-off)

Studying the bias-variance trade-off: expected loss = bias + variance + noise I understand that we minimize this quantity by finding the "best" balance between ...
-1
votes
1answer
47 views

What is Bootstrapping in statistics? How can I use it to determine error in the mean, variance, kurtosis and skewness of a data set?

From what I understood from searching randomly is that it has something to do with resampling. What does this resampling mean? Is it selecting random data from a distribution or is it getting data ...
1
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0answers
25 views

How do you test if there is a statistically significant change in variance using dependent variarables?

Given a group of subjects and a value measured across a baseline period and a measure period, how do I test if the spread of the data is statistically significantly different?
1
vote
1answer
29 views

How to compare different variances of the same population? [closed]

Lets say I have a set of numbers distributed as {5, 5, 5, 5} which has a mean value 5 and variance of 0. Now I can redistribute the data in different ways like for instance {4, 3, 5, 8}; mean = 5, ...
2
votes
0answers
37 views

Help explain the “redundancy” of canonical correlation

I am reading a material about canonical correlation and it introduces a concept named "redundancy". I have been puzzled for one day but still could not get a understanding. The following is a screen ...
4
votes
3answers
118 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 ...
3
votes
1answer
70 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
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0answers
22 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
35 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?) ...