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

Analyzing time to event variable that has an upper limit cutoff

Setup: 4 different interventions, outcome metric: time for subject to respond. So lets say that for three of the groups of subjects they responded within 5 to 20 seconds. However, in one group, the ...
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11 views

Spurious regression /correlation

In a time series regression I am finding a certain predictor variable significant which should not be, according to the client. Could this be due to the higher variance that this predictor exhibits ...
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3answers
66 views

The role of variance in Central Limit Theorem

I've read somewhere that the reason we square the differences instead of taking absolute values when calculating variance is that variance defined in the usual way, with squares in the nominator, ...
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5 views

Objective evaluation of subjective data points and normalization

I want to write an access database that takes in inputs from instructors ranking a student on their performance in a handful of categories. (1 - below average, 2 - average, 3 - above average). They ...
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9 views

How to calculate the estimation error of portfolio variance using propagation results?

I am trying to find a conservative approximation for the propagated estimation error of a investment portfolio's variance (comprising two assets), given we know the estimation error for the variance ...
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1answer
28 views

Significance (p-value) in regression/size of parameter estimate

In a linear (OLS) regression, I find that the sizes of the coefficients vary a lot: one of them is about 0.0005 and another is ~150. The p-values are all under 0.1. Is this reliable result? These are ...
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1answer
13 views

Is SSB formula in ANOVA to find variance between groups valid for non-normal data?

I have two groups of non -normally distributed data (count data), and would like to find the variance between the groups. Am I able to use the SSB formula for this? The paper I have got the data from ...
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22 views

variance of the unbiased sample covariance matrix

Im interested of calculating the variance of the unbiased sample covariance matrix. The $x_1, ..., x_n$ are independent with $\bf{E[x_i]=\mu}$ and $\bf{V[x_i]=\Sigma}$. $\bf{S}$ ...
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1answer
19 views

Analytical expression for variance as a function of the mean value

I have a research problem that seems analogous to a 'draw balls from a bin' problem. Imagine an experiment where $N$ balls are drawn from an infinite bin containing '0' balls and '1' balls, where $N$ ...
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3answers
63 views

Variance of an average of random variables

This seems like it should be a pretty common problem. I have four estimates of fishing effort, each with its own variance. For subsequent calculations, I want the mean of the four estimates, and a ...
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0answers
22 views

Allocation of design points in an experiment

I would like some hints with the following problem. Thanks for any help in advance. An experimenter wants to design an experiment for estimating the rate of change in a dependent variable Y as an ...
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9 views

Sum of covariances equals variance of sum OR: how to estimate the relative importance of a time series for a sum of time series?

I have n time series x1, ..., xn and the sum of these time series xsum = x1 + ... + xn. I observed that the sum of all covariances between each time series and their sum equals the variance of that ...
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17 views

Testing wheither variance of 3 interaction terms differ from each, f test

I have performed a multiple regression with 3 independent variables (in-store factors) 1 moderator (involvement) and 1 dependent variable (store image). I made 3 interaction terms and tested the ...
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1answer
20 views

Comparing two samples, same mean but diferrent size and variance

I have two samples drawn from different distribution that I can assume the normality and the same mean for both, however, the variance and the size of samples are different. How can I compare the ...
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1answer
56 views

Percent of variation explained by individual covariates

I understand total variance and R squared in linear regression outputs, but I have difficulty to understand the percent of variation explained by each covariates in a multiple regression analysis. I ...
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2answers
57 views

How can I force my model to predict the samples that are close to zero?

I have a large amount of inventory data and I am trying to predict when the inventory gets low using one component of the change in inventory (yes I know this doesn't describe inventory very well by ...
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0answers
13 views

Bias Variance Trade Off Question [duplicate]

I am starting to get the hang of idea and I think I am close, but need one clarification. So suppose we are trying to create a model for a population. We attempt to create this model by taking ...
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1answer
26 views

Can I use PCA to study how variables affect each other?

I'd like to know what PCA tells me about how the variables affect each other. For example, let's say I've three variables Cholesterol, Exercise, Calorie Intake and Sleep. I want to know how Exercise, ...
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1answer
21 views

Unequal sample sizes in t test with homogeneity of variance

I have looked at the other similar questions on here, but I can't seem to understand whether power is still an issue for unequal sample sizes with the homogeneity of variance being met. Yuen (1974) ...
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1answer
46 views

How do you calculate the standard deviation and error for a difference between two different means?

I have 40 people that I measure at baseline, getting their mean level of X at time zero. I also calculate the standard deviation and standard error of the mean of X. Then after 100 days I measure ...
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2answers
46 views

Difference between MSE and variance

In statistics, sometimes we use mean sum of error, and sometimes variance. I just want to know what is the difference between mean sum of error and variance?
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0answers
21 views

Variance as a function of the mean. Why does this affect linear regression? [duplicate]

I'm currently studying university level statistics and I'm struggling to wrap my head around the concept of variance as a function of the mean. How does this affect linear regression and why does it ...
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0answers
26 views

Alternative to ANOVA (beginner)

I have run 15 experiments to compare the effect of different hormone combinations on the maturation on Xenopus oocytes (immature eggs). I am hoping to find the best performing variable. I have 4 ...
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16 views

Taking longer sample should not reduce the variance of the mean

I have not realized completely why n times longer samples should give you n times shorter variance. However, I measure performance of my programs and there are some fluctuation due to PC state ...
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10 views

Calculate the aggregated standard deviation of several samples

I have the following survey-based data, where the first row is the aggregate of the other rows (Emp1-Emp5). ...
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35 views

95% confidence interval for an estimate average

I have a single dataset - from that dataset I have used four methods ($i=1, 2, 3, 4$) to estimate a parameter ($u_i$) and to generate a 95% confidence interval. In other words, I know $V[u_i]$ but not ...
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26 views

Given the mean and standard deviation of a change, when can we expect to reach a threshold?

Suppose I am playing a game in which I start with 1000 points and my point total changes every turn. I lose when I reach 0 points. I know that after every turn I can expect that my point total will ...
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1answer
31 views

Modify standard deviation with fixed mean

I have a set of pipes that are supposed to receive balanced load from a source. For instance, with 100 of inputs if I have 5 pipes each is supposed to handle 20. But that's not the case in reality and ...
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17 views

Variance of model-averaged predictions?

I have several prediction surfaces (and the associated uncertainty surfaces), which are defined over the same spatial extent with the same resolution. I want to take a weighted average over all the ...
3
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1answer
94 views

What's the maximum expectation of a conditional variance, $E[Var(X+Z_1 \mid X+Z_2)]$?

Let $X,Z_1,Z_2$ be 3 mutually independent RV's, with $Z_1, Z_2$ assuming $N(0,1)$ distribution. $X$ is constrained to have unit 2nd moment, i.e. $E[X^2] =1$, but may take arbitrary distribution. The ...
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1answer
42 views

Which one is the correct formula of confidence interval of variance?

I got the following formula of confidence interval of variance in this site $$\frac{(n-1)s^2}{\chi^2_{1-(\alpha/2),n-1}}<\sigma^2<\frac{(n-1)s^2}{\chi^2_{(\alpha/2),n-1}}$$ And this following ...
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1answer
39 views

bias-variance decomposition and independence of $X$ and $\epsilon$

I took a look at a couple of derivations of this decomposition and I think they all require that $E[\epsilon \hat{f}] = 0$. The most transparent one I found was from Wikipedia here. I reproduce the ...
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18 views

Permanent and temporary shock income, variance decomposition

I have a balanced panel data (N= 190, T=5) on income and personal characteristics of the householder. I would like to estimate the coefficients and variances of a temporary and of a permanent income ...
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17 views

Two-way ANOVA - discrepancy between main result and model parameters

I am running a two-way ANOVA examining the influence of both school and gender on Likert scale answers. The Type III SS results show school significant (p=0,001), but gender or gender*school not ...
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30 views

Calculate Var(X/Y) for dependent variables?

I understand that you can calculate Var(X*Y) through Bienayme, whether variables are dependent or not. I am wondering if there is a similar way of calculating Var(X/Y) when variables are dependent? ...
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11 views

What is the best way to analyse data comparing one by one and stipulate the accuracy?

Follow the example: The first line is the data I got. The second line is the target data. | 154.0 | 784.4 | 854.1 | 789.3 | | 153.5 | 789.7 | 892.3 | 903.2 | I ...
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0answers
10 views

Statistically verifying distribution of users within an A/B Test

Hoping you can help me determine the best way to statistically verify that an A/B test was set up in an unbiased way. The A/B test was set up to split users on my website 50/50 into a test/control ...
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40 views

How to analyze survey data, interval or ordinal, and how to account for nonresponse bias?

I have a question regarding a survey. I gave a test to people and they were asked to rate the tester on a scale of 1 to 5, 5 being they liked it and gave it the highest rating, with 1 being the ...
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1answer
38 views

RBF transformation on a Normally Distributed Random Variable

I have a random vector $\mathbf{X} \sim \mathcal{N}(\mathbf{m,\Sigma})$ which is transformed by a Gaussian Radial Basis Function into the random variable $\mathbf{Y} = K(\mathbf X) = \exp(-\lambda ...
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14 views

Variance of sum of datasets with different sampling intervals

I have two randomly distributed datasets which are to be added together element-wise, and I am looking to calculate the uncertainty of the mean of the result. One dataset had a sampling rate of 1 ...
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14 views

conditional/unconditional expectation and variance for an AR(1) process

We have an AR(1) process, $X_t=\alpha X_{t-1}+\varepsilon_t$ with $\varepsilon\sim(0,\sigma^2)$, $X_0=0$ and $|\phi|<1$. We have the conditional expected a value with respect to $X_{t-1}$: ...
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0answers
10 views

Variance of the logarithm of a binomial distributed random variable

What is the variance of $\log(1+X)$, where $X \sim Bin(n,p)$. I am looking for an approximate solutions depending on n and p. I have tried Taylor expanding the logarithm, but it didn't lead to a ...
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1answer
41 views

Estimating population variance through simulation in R

I want to estimate the variance of the exponential distribution with a rate of $\lambda=0.2$. I'm drawing a sample of 5 exponentials 1000 times, and know that the theoretical variance of my ...
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1answer
36 views

What is the origin of squaring centred data as way to model variances instead of means?

I recently came across this Answer by @mpiktas wherein he suggested a transformation of $y_i \rightarrow y_i^{\prime}$ $$y_i^{\prime} = (y_i - \overline{y})^2$$ followed by fitting a model for ...
4
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1answer
143 views

Estimate variance of a population if population mean is known

I know that we use $\frac1{n-1}\sum\limits_i(x_i - \bar{x})^2$ to estimate the variance of a population. I remember a video from Khan Academy where the intuition given was that our estimated mean is ...
2
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0answers
30 views

Estimating the prediction variance in kernel ridge regression

I'm trying to estimate the variance of predictions for a kernel ridge regression model. The model is simply kernel ridge regression: $$\hat{y} = K(K+\lambda I)^{-1}y = A y$$ $K$ is the $n \times n$ ...
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1answer
95 views

Find standard deviation of arbitrary game with multiple payouts

This earlier question asked how to get a 5.76 standard deviation for a single number bet on Roulette. The answer gave the formula, but unfortunately, the formula doesn't easily generalize to more than ...
2
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1answer
50 views

Kriging with individual errors

When evaluating a Kriging prediction, it is possible to include a hyperparameter $\lambda$ to account for noise in the data. $\lambda$ can be estimated as a parameter in a maximum likelihood ...
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6 views

Is there a quantifiable way to find the optimize the minimization of variance in our sample without increasing our bias too much?

Due to the bias-variance trade off, whats the best way to test to see whether decreasing your variance has increased our bias too much? Or is there a way? Since we cannot quantify the bias of the ...
4
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1answer
42 views

Partition data into two sets such that the difference of their variance is minimal

Suppose there are $n$ data values $x_1<x_2<\ldots<x_{n-1}<x_n$,and I've found a partition number $k$, such that $$ ...