The expected squared deviation of a random variable from its mean; or, the average squared deviation of data about their mean.

learn more… | top users | synonyms

0
votes
0answers
18 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
195 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
26 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
14 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.
2
votes
0answers
32 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
6 views

Problem with calculating the avarage power of a vector? [migrated]

I am calculating the average power of a vector. I would like to compare it the final expression with the simulation. However, they are not equal. Please help me to point out which steps are wrong. ...
0
votes
0answers
31 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
21 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
39 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
21 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
43 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
25 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
12 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 ...
1
vote
0answers
22 views

How to understand Demartines theorem [migrated]

Demartines theorem (page 3) explain why norm of a random vector increases with dimension, whereas its variance remains constant: Let $X \in \mathbb{R}^d$ be a random vector with i.i.d. components: ...
3
votes
1answer
41 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 ...
1
vote
0answers
26 views

Variance of sample mean in a binomial distribution

I'm trying to derive that the variance of phat = pq/n. I'm unfortunately not getting that. Please tell me where I'm going wrong... ...
2
votes
0answers
35 views

Where did the words bias and variance come from? [closed]

I understand that a bias model is more relaxed while a model with a lot of variance is more flexible. but, where did these terms come from, and, why 'bias' and why 'variance'?
0
votes
0answers
10 views

Scores derived from variance specific for a factor

I received a comment about my article from one of the reviewer but I do not understand what I should do. Here is a short explanation of the study: This study investigated the influence of lectures ...
1
vote
3answers
66 views

Correlation coefficient: If $\rho = 0$, then $r$ is normally distributed with mean 0. Why?

From this source, the estimation of the coefficient of correlation is $$r = \frac{\Sigma (X_i-E[X])(Y_i-E[Y])}{\sqrt { \Sigma (X_i-E[X])^2 \Sigma (Y_i - E[Y])^2}}$$ If the coefficient correlation is ...
1
vote
0answers
20 views

Standard Error of the Correlation Coefficient

As defined here, the estimation of the coefficient of correlation is $$r = \frac{\Sigma (X_i-E[X])(Y_i-E[Y])}{\sqrt { \Sigma (X_i-E[X])^2 \Sigma (Y_i - E[Y])^2}}$$ and the standard error of $r$ is ...
3
votes
1answer
41 views

Ratio of correlated sample variances (gamma distributed)

for $N$ samples of two correlated random variables $X \sim N\left(0,\sigma_X^2\right)$ and $Y \sim N\left(0, \sigma_Y^2\right)$ with correlation $\rho$, I am analyzing the ratio of the sample ...
0
votes
1answer
35 views

Cluster analysis on time series samples

In the follow-up to this Ways to understand 2-dimensional time-series data I'm working on 2D time series data where two attributes are depth and temperature. When I plotted depth-vs-temp curve and ...
3
votes
0answers
81 views

recommendations to analyze a survey of the entire sample frame with a 20% response rate

we surveyed all 10,000 professionals in a particular industry. The industry is highly-regulated, so we have contact information for everyone in our population of interest. We attempted to contact ...
1
vote
0answers
41 views

Does lots of bias==underfitting, while lots of variance==overfitting?

From what I understand, there is a relationship between bias and underfitting; as well as variance and overfitting. Is a 'biased model' another word for an 'underfitted model'? Likewise, is a ...
4
votes
0answers
74 views

Why does $r^2$ between two variables represent proportion of shared variance?

Firstly, I appreciate that discussions about $r^2$ generally provoke explanations about $R^2$ (i.e., the coefficient of determination in regression). The problem I'm seeking to answer is generalizing ...
1
vote
2answers
77 views

Ways to understand 2-dimensional time-series data

I'm working on 2D time series data where two attributes are depth and temperature. When I plotted depth-vs-temp curve and saw its variation over time, the fluctuation occurs at few places only. I'm ...
0
votes
0answers
29 views

Correction of variance structure in gls after selection of the fixed effects using R

I'm fitting a gls following these steps: I select the random effect holding the fixed part unchanged. I.e. I try different variance and correlation structures and random effect. Once I find my ...
2
votes
1answer
50 views

F test to test equality of variance

I have a single time series which will be divided on the date of the policy change before and after. I want to compare the variances between the two time sections and I am told to do an F test of ...
5
votes
0answers
73 views

If coefficient variance is incorrect (for a regression parameter), does that mean the model's log-likelihood is incorrect?

I am using logistic regression to estimate ~probability of a sample unit being used by an animal. Due to my sampling design it is unavoidable that there is overlap between 'used' sample units and ...
1
vote
1answer
37 views

Variance of sample correlation coefficient

On wiki page about Fisher transformation I read that variance of sample correlation coefficient becomes smaller as population correlation coefficient (in absolute value) gets closer to 1. Could ...
4
votes
1answer
28 views

Predicting variance of heteroscedastic data

I am trying to do a regression on heteroscedastic data where I'm trying to predict the error variances as well as the mean values in terms of a linear model. Something like this: $$\begin{align}\\ ...
1
vote
1answer
39 views

Variance of sample mean for dependent samples

Suppose I have two discrete independant random variables $X$ and $Y$, and that I'm interested in the expected value of the random variable $W$, where: $$ W= \text{sign}(X-Y). $$ So, W is 1 if ...
2
votes
0answers
30 views

Random vector times random matrix

$$ Y_i = \sum_j B_{ij} X_j$$ $$ covar(X_i, X_j) = V_X = \delta_{ij} var(X_i)^2 $$ $$ covar(B_{ij},B_{kl}) \neq 0 $$ $$ V_Y = ? $$ I know, that if $B$ was fixed, it is straight forward, but I would ...
4
votes
2answers
138 views

Why does PCA maximize variance of the projection?

Christopher Bishop writes in his book (Pattern Recognition and Machine Learning) a proof, that each consecutive principal component maximizes the variance of the projection to one dimension, after the ...
1
vote
1answer
41 views

Why is error variance important in CFA?

I am reading the book related to SEM (Byrne, 1998) and it is stated that regression of the observed variables on the factor, and the variances of both the errors of measurement and the factor, as well ...
13
votes
6answers
863 views

How to detect polarized user opinions (high and low star ratings)

If I have a star rating system where users can express their preference for a product or item, how can I detect statistically if the votes are highly "divided". Meaning, even if the average is 3 out ...
1
vote
0answers
28 views

Is the variance of the residuals of a linear regression useful for estimating experimental sample sizes?

I have a data set of $y$ values that is not particularly normally distributed. However, the $y$s do partially depend on several other parameters. A linear regression model $y=c+\mathbf{ \beta ...
0
votes
0answers
13 views

The estimation of variance in simulation

I am confused about the calculation of variance in a regression simulation. I can get the sample of the estimator from the simulation. So there are two ways to get the variance of this estimator: one ...
3
votes
0answers
41 views

Bias Variance tradeoff from a Bayesian perspective

I know the general question about bias variance has been asked before. I understand the frequentist approach and the concept of model selection and the impact of bias and variance on "accuracy" of a ...
0
votes
0answers
36 views

How to calculate the posterior distribution given Inverse Gamma conjugate prior?

I have a state-space model (actually belonging to a Kalman Filter) as in the given graphical model: This is a typical 1 dimensional Linear Dynamic System model. The variances $Q$ and $R$ have ...
2
votes
0answers
38 views

Variance of plugin estimator

This question related to my previous question. Let $$X_1,\dots,X_n$$ are i.i.d. with distribution function $F$ and $$Y_1,\dots,Y_n$$ are i.i.d. with distribution function $G$. Suppose that there ...
0
votes
0answers
18 views

calculate returns for volatile time series

Background: I want to compare two trading strategies in term of profitability. The red one is an active trading strategy, which involves many entry and exit to a specific market. The blue one is a ...
0
votes
0answers
21 views

Showing that the variance increases with the dimension of the random vector

This is actually related to a more complex question; but I want to re-ask it by trying to simplifying it as possible: 1- We have $n$ dimensional functions of the form $f_n:\mathbb{R}^{n} \mapsto ...
2
votes
1answer
43 views

How to present a one-way ANOVA when one of the group's variance is “unequal.”

I'm writing a research paper in entomology that compares 6 categorical variables (species) in terms of one dependent anatomic continuous variable. My samples look very normal by box-plots, etc. ...
0
votes
0answers
27 views

Evaluating differences between repeated measurements of one group to another

I'm having difficulties understanding what type of statistical testing I need for my questions. My measurements include the following: ...
0
votes
4answers
38 views

Did I pick the right t-test based on the results from the F-test?

I am presenting my thesis in two weeks and have some troubles with the statistical part, and I would be very grateful if someone could help me out since I dont really know what I am doing. I started ...
0
votes
0answers
31 views

a question on posterior distribution

Suppose that $E[T]=E[\gamma_i|X_1]+E[e_2|X_1]$ (1) where $\gamma_i$ and $e_2$ are distributed uniformly on the interval [0,1]. $X_1= \gamma_i + e_1$ So the background is that im trying to find ...