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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5
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2answers
90 views

Detecting whether website visits are automated

I am trying to detect automated visits to a website. A typical data set for an automated client is of the form: ...
0
votes
1answer
26 views

Random variable variance

I have the model $y_i=\beta_1+\beta_2 X_i+ u_i$ where $u_i\sim\text{iid } N(0,\sigma^2)$. I estimate $\beta_1$ and $\beta_2$ by drawing a straight line between the first $(x_1,y_1)$ and last dot ...
3
votes
1answer
50 views

Variance of random variable for normal distribution

How do I find the variance for $z_n=\prod_{i=1}^n(1-k_i e^{a_i x})$ where $x$ is the random variable with a normal distribution and is the same for all $i$ (which is a subscript for time dependency ...
1
vote
0answers
16 views

Calculate the variance explained in matrix Y by matrix X

I have two matrices corresponding to the same set of $n$ samples, with $j$ and $k$ variables, respectively ($j > 10000$, $k > 10000$). $X$ is an $n \times j$ matrix and $Y$ is an $n \times k$ ...
1
vote
0answers
11 views

Homogeneity of variance for time variable

I have four groups of plant treated with different temperatures and I conducted repeated measurement on their growth rate. I use ANOVA with Mixed Model to analyze the data by specifying both ...
2
votes
1answer
39 views

In OLS is it methodologically correct to use the variance of a variable as an explanatory variable?

Are some OLS assumptions not satisfied if I use the variance of a variable as a proxy of uncertainty in a regression? For instance, would it be methodologically correct if I use moving averages of ...
0
votes
0answers
16 views

Are time series variances additive? [closed]

If I have two variance measurements over two time series $X_1$ and $X_2$ over $t_1$ and $t_2$ respectively, and want to look at it as one variance, is the variance additive? If $S_1$ is variance for ...
1
vote
1answer
63 views

Proof of asymptotic variance

How do you prove that $X_n - E[X_n] = O_p(\sqrt{Var(X_n)})$ It's used in my textbook and I don't know where they get it from.
0
votes
0answers
22 views

P-value multiplied by 2 for two tail hypotheses F-test

There is a following answer to an exercise in a text book: The hypotheses are \begin{align*} H_0 &: Var_1 = Var_2\\ H_1 &: Var_1 \neq Var_2 \end{align*} Computation: $f = 78.800/913.333 = ...
2
votes
0answers
21 views

Is there a test for comparing principal components decompositions between samples?

Is there any test for comparing the directions, magnitudes, etc of PCA results for different samples? I'm leaving the nature of the test deliberately vague because I'd like to hear all the various ...
4
votes
0answers
30 views

Curve-fitting and variance-stabilizing transforms

I'm working with data corrupted by a mixed Poisson-Gaussian noise model (for example with images gathered in astronomy or electron microscopy), and have been using the generalized Anscombe ...
4
votes
3answers
51 views

Analytic or sample standard deviation with binomial data

I've been looking for recommendations on whether it's better to use the sample standard deviation (SD) for a binomial distribution or use the analytic SD (or variance). It's for experiments with ...
0
votes
0answers
17 views

Can you combined two sources with difference variance to reduce error? [duplicate]

I have two samples of data each estimates of a position x, y with Gaussian noise. One source has a larger variance than the other. Is this source in any way useful ...
0
votes
0answers
21 views

Comparing the distribution (or properties of distributions) of large datasets for practically significant differences

I have several populations with a large n (100,000 - 1M+ samples), which i wish to compare. I know that virtually any statistical test i apply will reject the null hypothesis due to the extreme power ...
5
votes
1answer
65 views

Why are Winsorized random variables independent?

While studying trimmed mean I understood that if I have some random variables $X_1, X_2, .., X_n$ by ordering them and trimming, the variables are no longer independent. However it is said that "by ...
0
votes
0answers
31 views

Finding the variance when you know the population mean

So my basic understanding is that I may end up in one of the following situations. I have a sample mean and therefore calculate a sample variance I have a population mean sand calculate a population ...
0
votes
0answers
27 views

model noise with Gaussian(0, Gamma)

Can anyone help me in understanding what kind of noise is it? Noise = Normal(0, v) v = GammaFromShapeAndRate(alpha, beta) I mean what is the advantage of making a normal noise with a Gamma ...
1
vote
1answer
18 views

Is there a value to show how fragmented is a group?

I would like to know if there is a way to calculate a number that can show how fragmented is a group? It should be something like "variance of categorical data"? For example I want to see how ...
3
votes
1answer
78 views

Should you report variance of asymmetrical data, such as ratios?

I have measured the time taken to solve a problem by algorithm $X$ and by algorithm $Y$. It takes a quite long time, so I have only 10 data for each algorithm: $$ X : ( x_1, x_2, \dots , x_{10}) \\ Y ...
0
votes
0answers
20 views

Answering Research Questions with Multi-level Structural Equation Modeling (ML-SEM)

This time, I have a more theoretical than computational predicament. I have a path model that I am interested in testing on a data set with two groups. It is a very simple two predictor model outlined ...
0
votes
2answers
29 views

Model regression of means different size and variance

I want to explain the relation between getting a reply and posting in a e-commerce. I want to know how much a reply increases postings. I know I could do a regression of postings=f(replies) but the ...
1
vote
1answer
25 views

Variance of a variable constructed from parameter estimates and predicted values of a linear regression

My data set is an annual panel data set on individual income, the year of unemployment and a number of demographic variables. I run an OLS regression of the form $y_{it} = \sum _{j=1} ^n D_{j,it} ...
0
votes
0answers
27 views

Mean and variance of a general multivariate skew normal distribution

I have a problem about a general multivariate skew normal distribution. There is a $p\times 1$ vector, $\mathbf{y}=(\mathbf{y}_1',\mathbf{y}_2',\ldots,\mathbf{y}_n')',p>n$, which has the density as ...
3
votes
4answers
41 views

Conditional variance - $Var(X + U | X) = Var(U)$?

I am wondering if the following equality holds - $Var(X + U | X) = Var(U)$? where $X$ and $U$ are two independent random variables? It seems can we say $Var(X + U | X) = Var(X|X) + Var(U|X) = ...
2
votes
2answers
27 views

Multiple comparisons with t-test: one group with different variance

If I have 3 groups that I want to compare with a t-test (correcting for multiple comparisons afterwards) but one of the groups has different variance than the other two, should I use a Welch ...
1
vote
0answers
23 views

Mean accuracy for sum of squares/variance

Formality says that when computing the sample variance or sum of squares one computes a sample mean with the sample data given. If for some reason I had access to a better estimate of the mean (from ...
0
votes
0answers
28 views

Web Videos that can provide me with a better understanding of statistical concepts

I have an exam coming up and I would like to know are there youtube videos/playlist or any videos online that can explain the following concepts below in a simple manner. The concepts are: ...
0
votes
0answers
21 views

Beta-t-EGARCH model, what is the unconditional variance

I am trying to implement Beta-t-EGARCH model in R, however, I fail to understand what is the unconditional variance of this model. I know for simple GARCH model, unconditional variance is ...
3
votes
3answers
66 views

What do I need in order to draw conclusions from this data?

I have three techniques, called A, B and C. Each can be used independently when trying to perform four related tasks (Tasks 1, 2, 3 and 4). I have run lots of tests, trying all combinations of each ...
0
votes
0answers
75 views

Calculating average variance extracted (AVE) in AMOS discriminant validity

I was asked to calculate average variance extracted (AVE) to establish discriminant validity; I've ran CFA but ask how to calculate AVE following Fornell & Larcker’s (1981) test when having two ...
1
vote
1answer
60 views

How to calculate the variance for mean of means?

I have been reading up on how to calculate variance for different situations and the following has me confused….. If I take a number of samples (e.g. choose 5 kids in a class and ask them how many ...
0
votes
0answers
36 views

How to convert daily variances to a monthly volatility and then annualize it?

I work out the conditional variance using a GARCH model based on daily returns as follows: ...
2
votes
0answers
22 views

Correlation fitted-residuals in mixed models

IN OLS linear models, fitted (predicted) and residuals scores are uncorrelated. I was under the impression that the same held true in mixed models. However, I have here an example model where fitted ...
0
votes
0answers
9 views

Adding the variances of spatially correlated data

I have a geographical grid, for every cell in that grid I know that the variable I am looking at is normally distributed and I have its mean and variance. Now, imagine I am looking at an individual ...
0
votes
0answers
21 views

Variance of parameters

I have three estimated parameters, $\hat{\beta_0}$,$\hat{\beta_1}$ and $\hat{\beta_2}$, these follow the ordering $\hat{\beta_1}\leq\hat{\beta_0}\leq\hat{\beta_1}$, where these parameters are ...
7
votes
5answers
218 views

If two time series $X$ and $Z$ follow $0 \leq Z \leq X$, can we say that $\text{var}(Z) \leq \text{var}(X)$?

Now I see it can't hold. Thank you for the counter examples... You guys rule! Thank you very much for your comments! I added, however, some observations that were missing. Most importantly is the ...
3
votes
1answer
48 views

Confidence interval for the standard deviation on a bimodal distribution

I have a bimodal distribution, and I wish to estimate the mean and standard deviation of the population (well, these could be 2 sub-populations according to the shape). With the mean I have no ...
0
votes
0answers
16 views

How do I account for within-subject variance to produce the standard error of the mean for different between-subject groups?

I have a mixed design with 25 subjects each with 4 repeated measurements in each of three different between subject treatment groups (total n=75). I want to produce the standard error of the mean for ...
2
votes
1answer
14 views

f test of equality of variance on error variances

Is it all right to do an F test of equality of variances on error variances (RSS divided by degrees of freedom)? Thanks a lot.
3
votes
1answer
53 views

Are significance tests only about sampling error or other forms of variation also?

When we study differences between a treatment and control group in an experimental setting, we want to test whether those differences are big enough that we can conclude they are not simply due to ...
0
votes
0answers
43 views

Help in fitting multilevel model using the MCMCglmm library in R

I am trying to fit a multivariate model using the R library MCMglmm. The data I have are testscores from c.a. 4736 students from different schools. For each student, also the socio-economic status ...
0
votes
0answers
30 views

Calculating Hedge's g and its variance from t-statistic

I believe there is a way to calculate Hedge's g and its variance from a t-statistic. I have found the formulas to calculate Hedge's g from one-sample t, and from independent groups t. one sample: ...
2
votes
1answer
44 views

Variance Covariance for logit with elastic net

How do you calculate an estimate for the variance covariance matrix of a logistic regression with elastic net regularization? Starting from the variance-covariance matrix of a plain vanilla logistic ...
0
votes
1answer
42 views

Variable bounds from infinity to negative infinity - Change Limits

I have a variable whose values vary between $-\infty$ and $\infty$. I'd like to change its limits from $0$ to $1$. I want to give extremely low values when the values are less than $-1$ or greater ...
1
vote
0answers
27 views

glm or glmm model with unequal variance

I am applying a GLM model with binomial family: glm(response ~ Treatment, family = binomial, data=dat) The only explaratory variable treatment is a categorical ...
0
votes
0answers
15 views

A method to find the inconsistency or variation in the data

I am running an experiment (it's an image processing experiment) in which I have a set of paper samples, and each sample has a set of lines. For each line in the paper sample, its strength is ...
2
votes
1answer
44 views

Finding the uncertainty in a Binomial probability estimate

In order to make some predictions for my work I have modeled a process using a binomial distribution, but in my case every single experiment must be a success and I am just changing the probability ...
0
votes
0answers
26 views

Estimation of Noise Level in the High-Throughput Cancer Data

Assume that I have made a coverage log ratios signal by dividing the coverage data coming from a tumour sample over the reference sample and then taking the log2 of this division. My question is: ...
0
votes
0answers
16 views

Time interval histogram (tih), Fano factor, coefficient of variance

I'm given this: A pacemaker neuron fires 10 spikes/s in a fairly regular manner, with interspike intervals (ISIs) that are distributed according to $\mathcal N(100, 5)$. I'm asked to draw the time ...
6
votes
1answer
71 views

Asymptotic distribution of sample variance of non-normal sample

This is a more general treatment of the issue posed by this question. After deriving the asymptotic distribution of the sample variance, we can apply the Delta method to arrive at the corresponding ...