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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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19 views

Can we use F-Test instead of pair t-test for the given question? [on hold]

Can we use F-test instead of pair t-test? And if not, then why?
2
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2answers
24 views

Getting variance of function of two uniform RVs [duplicate]

Have two independent RV's $X$ and $Y$ sampled uniformly from $[0,1]$ and $C = (X-Y)^2$. Want $V(C$). Rewrote as $V((X-Y)^2) = V(X^2) - 4V(X)V(Y) + V(Y^2)$ but that's too messy. Is it correct to write ...
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1answer
27 views

Explaining volatility with GARCH: one-step or two-step approach?

I am interested in seeing what could explain the volatility of certain financial series. I know that one can get estimates of conditional variance by running a GARCH model. My question is whether the ...
2
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1answer
20 views

Assessing normality assumption of effect sizes in meta-regression

I'm considering options for estimating tau-squared (the true between-study variance) in meta-regression, and I know method-of-moments (MM), unrestricted maximum likelihood (ML) and restricted maximum ...
2
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2answers
62 views

Finding OLS estimator for $\beta$ where $y_i=\beta+ 2 \beta x_i+\epsilon_i$

Consider the following model with the usual OLS assumptions: $\epsilon_i$ are uncorrelated random variables with mean zero and constant variance $\sigma^2$. $$y_i=\beta+ 2 \beta x_i+\epsilon_i$$ $(...
1
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0answers
15 views

Shouldn't we consider larger standard errors for effect measures or outcomes that are converted in meta-analysis?

There are methods to convert effect measures in meta-analysis (pdf). There are also methods to convert outcomes; at least, I am aware of the conversion described in Furukawa et al. (2005) from ...
0
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0answers
19 views

Deriving variance of the regression coefficient [duplicate]

I am after some help with this variance of regression coefficient derivation problem. Have already had a look at a similar question, posted a while ago but this one is slightly different. Am a novice ...
0
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0answers
7 views

Upper bound on single frequency error based on SSE of the full signal

I have an empirical signal: $y(t) = A_0 + \sum_{i=1}^{M}A_i \cos(\omega_i t + \phi_i) + \epsilon(t)$ The signal is tidal, and so dominated by a small number of frequencies and in particular there is ...
0
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1answer
32 views

Confusion about confidence interval

So far I understand, confidence interval (for mean) is defined by treating the sample mean as a proxy for population mean and then finding a interval where the true mean will be in certain percentage ...
0
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0answers
15 views

Variance of an ARMA process

I'm trying to obtain the variance function of an ARMA process and I'm in doubt if (any or all of) the following (due to the properties of a white noise process) is true: ${\operatorname{cov} \left( {{...
2
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0answers
41 views

Variance of 2 Protocols: Sampling Coloured Balls with Dots

Suppose, we have an urn where each ball has one of $M$ colours and some balls have a dot. We would like to estimate the proportion $p$ of balls that have a dot. We have two experimental protocols: We ...
0
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0answers
8 views

Measure variation in a time series

I have a series of values, they are a time series. I know what standard deviation is. I want to measure how much values in a series differ from one value to the next. ...
0
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0answers
14 views

R: detect outliers to find the 'real' weight

I have a question about labeling outliers in my data. My data is weights for several products. Of course, there is a 'true weight' of a product. I wish to find/approach that from my data (on average). ...
1
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1answer
34 views

Can someone explain variance and bias of data in natural language (not mathematically)

I read many tutorial but until now i don't understand what the variance and bias means. So can someone explain me what these words means clearly, not in mathematical language.
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0answers
27 views

Correlation coefficient $(Y=aX+b)$

Consider two random variables $X$ and $Y$. Assume now that $Y=aX+b$ where $a<0$ and $-\infty<b<\infty$. Determine the value of the correlation coefficient $\rho(X,Y)$. My attempt. $$\rho(X,...
0
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1answer
33 views

Odds ratio, Meta-analysis

I have the following for the data for the meta-analysis: OR , standard errors, logged OR , variance of logged OR I have generated a forest plots first using "OR" with "variance of logged OR" using ...
1
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0answers
22 views

What does it mean for a two dimensional feature vector to have unit variances?

What does it mean for a two dimensional feature vector to have unit variances? This is related to a Bayesian Discriminant Function problem. For example, the feature vector for one of the classes has ...
2
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1answer
54 views

Assumption of homoscedasticity/equal variance violated in a 2-way ANOVA

I'm analyzing results from an experiment where 56 samples were tested for a specific response to electrical stimulation. Electrical stimulation was done at 2 different stimulation frequencies, and at ...
3
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1answer
30 views

Interpretation of conditional variance of estimator of intercept in linear regression

$Y_i=a+bX_i+e_i$. $Y_i$ and $X_i$ are scalar r.v. We have, $$ V(\hat b|X)=\frac{\sigma^2}{n\left(\bar{X^2}-\left[\bar{X}\right]^2\right)} $$ and, $$ V(\hat a|X)=\frac{\sigma^2 \bar{X^2}}{n\left(\bar{X^...
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0answers
23 views

Unconditional Variance of X

The random variables X and Y are related as follows: $X$ conditional on $Y = y $ has a $N(2y, y^2)$ distribution. $Y$ has a $N(200, 100)$ distribution. Derive the unconditional variance of $X, V[X].$ ...
1
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1answer
81 views

Bayesian Statistics. Please help me to find an example where posterior variance is greater than prior variance

Suppose we observe y successes in n trials where the probability of success in each trial is θ. If we choose a Beta(1, 1) (Uniform) prior then the posterior variance will be smaller than the prior ...
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0answers
33 views

What problem or game are variance and standard deviation optimal solutions for?

For a given random variable (or a population, or a stochastic process), mathematical expectation is the answer to a question What point forecast minimizes the expected square loss?. Also, it is the ...
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0answers
21 views

Are the variance and the squared deviation similar?

I am confused about the difference between the variance and the Squared deviation. Are they similar? or what is the difference between them?
5
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1answer
363 views

Standardization of non-normal features

Suppose we have several features (e.g. $\geq20$) that do not follow a Gaussian distribution. Do we have to worry about the features not following a Gaussian distribution if we apply standardization on ...
0
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1answer
15 views

What are the differences of Standard Deviation, Variance, Co-variance, Coefficient of Variation when it comes to measures of dispersion or variation?

When we talk about measures of dispersion or variation(not sure if they are 2 different tools), then for what purpose we use what exactly? Where are we bound to use only Standard Deviation, not ...
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0answers
12 views

relationship between male gender and age variance

I would like to ask for help on the next question: In a logistic regression model, the male gender increased the risk of acut myocardial infarction at older age population, but in the young age ...
0
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1answer
27 views

Why is sample variance squared? (Basic Question) [duplicate]

I have two questions, each of which I think might be related to each other but I'm not sure. Both concern the definition of variance as: $var(x) = s_x^2 = \dfrac{1}{n-1} \sum_{i=1}^{n}(x_i - \bar{...
2
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0answers
51 views

Why does the variance of a Brownian motion increase linearly with time?

Brownian motion is said to follow a path where each value is normally distributed with mean $\mu t$ and variance $\sigma^2 t$. What is the basis for the relation that variance varies directly ...
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0answers
11 views

Equality of variances based on Rule of Thumb (for very small groups)

I have three groups with very small sample sizes (6 obs per each group). In order to use ANOVA I just want to make sure that the equality of variances in satisfies, As Levene'stest doesnot have very ...
0
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0answers
28 views

a simpler version of my original variance puzzle question

Hi: I think that I can simplify my original question a great deal so here's my attempt. Suppose I have a function $f(t) = t-10$. $t$ denotes time and starts at $t = 0$ and the units of time pass ...
0
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1answer
40 views

Distribution of the sample variance of values from a multivariate normal distribution

What is the sampling distribution of the variance of a collection of variables that follow a multivariate normal distribution? Specifically, assume that the $n-$dimensional vector $\boldsymbol{x} \sim ...
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0answers
30 views

Analysis ideas for difference in variances between 4 groups?

I have data for 100 different biomarkers. Each biomarker has data for 4 groups (A,B,C,D) with ~2000 observations in each group. I've read a lot about ANOVA but I'm not looking for a difference in ...
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1answer
40 views

The exponent delta of the variance recursion in a GARCH model

The function garchFit in R for GARCH modeling, among the various possibilities include a parameter "delta" described as the exponent of variance recursion. I've ...
1
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1answer
55 views

Is there any prediction model that takes into account the regression towards the mean?

I am studying performance of football and basketball teams. The regression towards the mean is quite common in sports. One really great performance is usually followed by a less perfect one. So are ...
1
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1answer
28 views

Test whether the variance in one group is higher than In another

I have 63 groups of microbes that elicit a specific reaction of the immune system (cell frequency). In each group, there are 3-10 replicates and I want to check in which groups the variance is ...
0
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1answer
23 views

checking the equality of variances when we have very small data sets

I have two groups with very small sample sizes. Each group has around 6 observations. I was wondering which test I can use in order to check the quality of variances? Is there any cutoff value in ...
0
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1answer
18 views

How to compute the proportion of variance explained by a variable while accounting for covariance?

I am trying to do a manual calculation of the proportion of variance explained by one variable, relative to the total explained variance. However, this variable is correlated with another variable ...
0
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0answers
28 views

covariance matrix in OLS for dummies

I know that formal definitions of the variance covariance matrix has been given elsewhere. However I am not a mathematician and it was very difficult for me to follow them. Thus, I'll make a few short ...
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0answers
10 views

How can I show that the cross product in the partitioned sum of squares is zero for a two-variable experiment?

Background For the model $$ y_{ti} = \beta_i + \tau_j + \epsilon_{ij} + \mu, $$ where $\beta_i$ is the $i^{th}$ block effect, $\tau_j$ is the $j^{th}$ treatment effect, $\epsilon_{ij}$ is the $(ij)^{...
0
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0answers
20 views

Variance vs Sample Variance [duplicate]

I am not sure if I formulated the question correctly as similar questions (Standard Deviation and Variance in Sample and Population Formulas for all?) and (Population Variance and Sample Variance) are ...
0
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1answer
20 views

Calculating a mixed model using pdIdent var-cov matrix

I have a question in mixed models. I'm quite new at this field and I'm trying to calculate a model in which "y" is predicted according to multiple covariates (Age,gender,BMI) and the random variable "...
1
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1answer
22 views

Potential bias of effect sizes due to ceiling (or floor) effects when weighting effect sizes by their variance for meta-analysis

Regarding meta-analysis, I am wondering whether there is a potential bias due to the ceiling effects (or floor effects) when weighting effect sizes by their sampling error variances. In case of ...
2
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1answer
32 views

How to check if a process has constant variance?

I am using KPSS test to verify if my process has constant variance around the mean, but I am not sure if this is the correct test for my case. In KPSS the null hypothesis is that the process is ...
0
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1answer
23 views

Computing Var of mean of a sample from a normal distribution

I need to calculate $\text{VAR}[\bar X]$ where $X_i$ are random sample of size $n$ from a normal distribution with mean $\theta$ and variance $\sigma^2$. So I do $\text{VAR}[\bar X] = E[\bar X^2] -(...
5
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1answer
74 views

Effect of adding and removing data on variance

Consider a set of distinct numbers. After removing both the max and the min from the set and adding the median to the set, the set of numbers obviously becomes less dispersed and the variance should ...
0
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0answers
14 views

Deriving the Ridge approximation for the lasso variance

I am trying to derive the ridge approximation formula for the lasso variance, but I am stucking at one point. As statet in the originial paper of tibshirani the penalty term can be transformed to $\...
1
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0answers
33 views

Variance of the product of correlated normal variables

Suppose that $X$ and $Y$ are scalar random variables that are jointly normally distributed: $$ \begin{pmatrix} X \\ Y \end{pmatrix} \sim N \left( \begin{pmatrix} \mu_x \\ \mu_y \end{pmatrix}, \begin{...
0
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0answers
28 views

how to train model with features have low variance in train set

Assume that I trained a nonlinear model , one feature of the training data has very low variance, because of this, the same feature of the test could be quite different, at least in scale, from the ...
1
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1answer
37 views

What is the maximum entropy distribution given the median (instead of the mean)?

Given that the median seems to be a more robust statistic than the mean/average, I was wondering if there is a solution of the maximum entropy distribution given the median (or the median and some ...
0
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1answer
21 views

Average sample size of two fishers z correlations

I am conducting a meta analysis of Pearson's r correlations. As there are two correlations , sometimes three , for the same study and dependent variable I have averaged the correlations via fishers z ...