The expected squared deviation of a random variable from its mean; or, the average squared deviation of data about their mean.
-2
votes
0answers
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
votes
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 ...
1
vote
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
votes
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
votes
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
vote
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
vote
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.
0
votes
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.
$$\rho(X,...
0
votes
1answer
33 views
Odds ratio, Meta-analysis
I have the following for the data for the meta-analysis:
OR , standard errors, logged OR , variance of logged OR
I have generated a forest plots first using "OR" with "variance of logged OR" using ...
1
vote
0answers
22 views
What does it mean for a two dimensional feature vector to have unit variances?
What does it mean for a two dimensional feature vector to have unit variances?
This is related to a Bayesian Discriminant Function problem.
For example, the feature vector for one of the classes has ...
2
votes
1answer
54 views
Assumption of homoscedasticity/equal variance violated in a 2-way ANOVA
I'm analyzing results from an experiment where 56 samples were tested for a specific response to electrical stimulation. Electrical stimulation was done at 2 different stimulation frequencies, and at ...
3
votes
1answer
30 views
Interpretation of conditional variance of estimator of intercept in linear regression
$Y_i=a+bX_i+e_i$. $Y_i$ and $X_i$ are scalar r.v. We have,
$$
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^...
0
votes
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
vote
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 ...
4
votes
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 ...
1
vote
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
votes
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
votes
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 ...
1
vote
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
votes
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
votes
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 ...
0
votes
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
votes
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
votes
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 ...
1
vote
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 ...
1
vote
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
vote
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
vote
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
votes
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
votes
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
votes
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 ...
1
vote
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
votes
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
votes
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
vote
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
votes
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
votes
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
votes
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
votes
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
vote
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
votes
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
vote
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
votes
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 ...
