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Refers to the standard deviation of the sampling distribution of a statistic calculated from a sample. Standard errors are often required when forming confidence intervals or testing hypotheses about the population from which the statistic was sampled.

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General formula for standard error of the regression coefficients

Can this formula be used for calculating standard error of the regression coefficients? $$ SE(\hat{\beta}_{j})^{2} = (1 / (1 - R_{j}^{2})) * (\sigma^{2} / \sum_{i=1}^{n}(x_{ij} - \overline{x_{j}})^{2}...
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Meta-analysis in metafor package with within-subjects standard error?

I am conducting a meta-analysis with metafor in R. For the majority of articles, I managed to extract means and standard deviations, which I need for the escalc function to calculate an effect size. ...
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26 views

What is the standard error of the difference in means scaled as percent difference?

Biologists frequently report the effect B-A as a percent difference (or relative effect), for example "Y was 25% bigger in treatment B than treatment A", where 25% = 100*(B-A)/A and A and B are the ...
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Defining a range from mean value using nominal error estimate (normal distribution)

I have to run an uncertainty analysis for a project in my university, but I have no statistics background. The thing is: I have a mean value of 88 for a normal distribution and I need to obtain a ...
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Calculating Standard Error of Tau - Meta Analysis

I am conducting a meta analysis using the metafor package in R and am trying to calculate the Standard Error (if possible) of the Tau statistic. The S.E of the tau-...
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15 views

Standard Errors for estimates obtained from custom objective function

I want to find standard errors of estimates obtained by optimizing a custom objective function, which I will explain further below: The objective function is: $L(a,b|y,X_1) - \lambda \times RSS(f(y),...
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23 views

Finding standard errors of maximum likelihood estimates

Suppose we use Maximum Likelihood estimation to estimate certain parameters in a model. Furthermore, suppose that the log likelihood function can not be solved analytically and thus must be optimised ...
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28 views

Sample size and standard errors in OLS estimation

The standard errors of the estimated parameters from OLS estimation strongly depend on the sample size (n). Indeed, the standard errors tend to decrease when the sample size gets larger (ceteris ...
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48 views

My Tobit model gives all infinite standard deviations

I am trying to do a Tobit estimation (in R) because my dependent variable ranges from 0-100 with many values at a 100. ...
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41 views

Why doesn't clustering bias the standard errors in this very simple simulation?

I simulate a very simple model with one regressor and a random intercept: $y_{ij} = \beta_0 + \beta_1x_{1,ij} + u_j + \epsilon_{ij}$ I run model <- lm(y ~ x1) ...
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24 views

Are standard errors for different statistics comparable?

Can you please help me to understand whether a SE, for example, being 0.7 for Hedge's g (effect size statistic) is comparable with a SE being 0.7 as well for let's say odds ratio (being used as an ...
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How can regression parameter SEs decrease when predictors are removed from the model?

What are some reasons that regression parameter $SE$s can decrease when predictors are removed from the model? Generally, adding predictors reduces the model's variance (MSE) which should shrink the $...
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14 views

standard deviation (percent) of the regression error

What would be the formula for standard deviation (percent) of the regression error? I currently compute it as the standard error of the regression divided by the mean of dependent variable.
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31 views

If $|r| < 1$, how extreme is $y$ for a change in $x$?

This is regarding one of problem sets in Udacity Intro to Statistics course. Problem: X and Y are given variables, and the correlation coefficient $|r| < 1$, the question is how extreme our ...
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1answer
42 views

my error bars cross zero, is this ok?

I have plotted the total consumption (g) of a solution by my experimental organisms. However, when I plotted the error bars (s.e.m) a few crossed zero (see image). (1) is this correct/plausible? (2)...
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How can I assess the position of a novel point in among other points

I have data about the nutrient ratio an animal wants to consume and the available nutrient ratio of grasses in it's environment. The data looks like this: The black dots represent plant nutrient ...
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16 views

Where does the standard error come from in Lasso?

I'm using Lasso to get the best variables to predict an outcome. I understand that this graph gives me λmin and λ1se However, I don't understand how to get that standard error theoretically. Where ...
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20 views

Variance of the average of two (or more) Net Promoter Scores?

As per Wikipedia, "The Net Promoter Score is obtained by asking customers a single question on a 0 to 10 rating scale, where 10 is "extremely likely" and 0 is "not at all likely": "How likely is it ...
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How to determine the standard error of the prediction from an MLR?

I have a multiple linear regression model that I have built in SAS that's fairly simple: it predicts someone's blood pressure based on four variables: age, race, gender, and level of depression. ...
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26 views

Why is $\sigma^2 = Var(\epsilon)$ when computing the standard error of a simple linear regression slope parameter

Assume the true underlying linear approximation of a set of data is equal to $Y=2+3X +\epsilon$ where $\epsilon$ represents the irreducible error that is inherent in a linear approximation. I then ...
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23 views

Cohen's d and Sten scores

Can someone explain why Cohen's d of sten score is 2 times of Cohen's d of SD? Thanks. The question is based on the paragraph below: *When looking at differences it is useful to remind ourselves of ...
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21 views

How to calculate residual standard error for a regression model with log link in R

I want to compare residual standard error across a series of different model specifications as one way of assessing model fit. I assumed that calling sigma on a ...
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1answer
81 views

Interpreting the standard error from emmeans - R

I am using the emmeans package to run post-hoc analysis on linear mixed models. The results provide what I would expect except for the standard error. I run the ...
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82 views

Standard error for the sample distribution of a random binomial variable

This is a followup question to Standard error for the mean of a sample of binomial random variables The previous answer mentions that the standard error of the sampling distribution is sqrt(kpq/n), ...
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Estimated Standard Error of a Method of Moment Estimator, Poisson Example

For X randomly sampled from a Poisson(lambda) population, the method of moment estimate of lambda is the sample mean: lambda_hat = X_bar Now, say we are interested in the variance of lambda_hat (...
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10 views

What determines whether relative or absolute Gaussian noise should be added to data?

Suppose I have some data vector, $\mathbf{d}$ with length $N$. I want to add "Gaussian noise" to the data. My understanding is that there are two ways to do this. 1) Relative noise percentage $$\...
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34 views

Standard error of a sample

I want to calculate a standard error of a sample. I have a distribution of the IQ of the general population with a mean of 100 and a standard deviation of 19. Now I take a random sample of 30 students ...
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1answer
15 views

Network meta analysis without standard deviations

I am trying to compute Cohen's in some studies that I gathered in a Systematic Literature Review. Unfortunately, almost none of them report the standard deviation (nor df/t, or something for back-...
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1answer
30 views

variance of P(null hypothesis is true)

If I can calculate the probability of null hypothesis $H_0$ being true, based on posterior observations x, that is, if I can estimate $P(H_0 | x)$, is there a way to calculate standard error(se) or ...
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40 views

Bayesian inference on Beta distribution and its standard error

Assuming random variable p and Y, $p\sim Beta(\alpha, \beta)$, $Y|p\sim Binomial(n,p)$ When Y=y is observed, it is known that $p|Y=y \sim Beta(\alpha+y, \beta+n-y)$ (1) What would be the estimate ...
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42 views

Statistical significance of percentage difference for a poll question with multiple options?

The question is: how to calculate the statistical significance of difference between percentages in the case described below? Suppose we have a poll question with $n$ answer options $A_1, …, A_n$, ...
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1answer
35 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 ...
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1answer
23 views

Monte Carlo Metropolis: Standard Error and Acceptance

In a time series data generated by Monte Carlo Metropolis algorithm, when is the standard error (correlation between two data points is assumed to be negligible) is higher - when the change in the ...
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17 views

Monthly and Annual Standard Errors

Suppose the annual return is estimated as $\hat{r} = (1 + \hat{\mu})^{12} - 1$ where $\hat{\mu}$ is the expected monthly return. How do you find the standard error of $\hat{r}$ if $SE(\hat{\mu})$ is ...
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Calculating the Standard Error of A Weighted Average From ACS Data

I am aggregating some lower level ACS data through a weighted average, taking the estimated median rent from census tracts up to a neighborhood level. Each record has an estimate and a margin of error ...
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44 views

Interpretation of Tensor product splines with multiple terms and their standard errors?

I am trying to understand the tensor product splines such as ...
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21 views

Logistic Regression: Using weights?

I am running a logistic regression model with the following data and variables: Independent variables (characteristics of a person coded as dummy) Test score (continuous variable between 0 and 1) ...
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Standard error and scaling

I have calculated the equity Beta (Share beta) for a company which resulted in a Beta of $B_e$, a standard error of $SE_e$ and a confidence interval $B_e (+/-)SE_e$. Q) Given that the asset Beta is $...
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Two point estimates fall into same confidence interval

Say I have two populations, and I am computing a sample mean and a corresponding (1-$\alpha)100 \%$ confidence interval for each. Now, I understand that if the confidence intervals are disjoint, then ...
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Murphy-Topel standard errors correction for GMM?

I employ a two-stage estimation routine: In the first stage, a large vector $\hat \theta_1$ (around 2000 elements) is estimated with maximum likelihood. In the second stage, I estimate $\hat \theta_2 (...
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Standard error of circular standard deviation

How to calculate the standard error of circular standard deviation estimated with equation $s = (2(1 − R))^{-\frac{1}{2}}$ or $s_{0} = (−2 \ln{R})^{-\frac{1}{2}}$ where R is the length of the mean ...
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Why do we plot the standard error of the mean as both positive and negative?

When we plot the mean of a variable on a scatter plot or a bar plot, why do we plot the standard error of the mean in both directions: positive and negative?
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50 views

Expressions for standard error

Most of the statistics textbooks claim that point estimator $\hat\theta_n(\mathbf{X})$ is asymptotically normal if $$\sqrt{n}(\hat\theta_n - \theta) \, \overset{d}{\longrightarrow} \, \mathcal{N}(0, \...
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39 views

Sample size for a research paper (for Mean+SD type of data)

In my research paper I proposed a software and have experiment it on 72 users. But the reviewer has objected on the sample size and asked to justify it or increase it. below is the results of our ...
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1answer
52 views

Multivariate statistics sampling and standard error problem

I have a group of workers listening to audio from many various audio files and typing it out. I want to compare the average transcription accuracy of these old workers with 2 new workers. I have a ...
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12 views

Standard error of coefficient in moving average model

I'm working with an asymmetric moving average model and I want to interpret the standard error of the coefficients in a similar model: I'm confused about what the standard error of a coefficient ...
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27 views

Autocorrelation, Autocovariance and Large lag Standard Error

I have time series generated data from Monte Carl-Metropolis Simulation. I have estimated correlation coefficients using: $r_k = \frac{c_k}{c_0}$ where $c_0$ is the varaiance and $c_k = \frac{1}{N}\...
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Is it statistically valid to compare error measures for different sized samples?

I have forecasts for different sized samples using a variety of methods like DES (Double Exponential Smoothing), SES, MA and WA (Weighted Average) to test the strength of the forecasting models. The ...
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Why don't we use the n-1 correction for standard error of sample proportion?

From my understanding, when we construct a confidence interval for a sample mean with a sample size of n, we try to estimate the standard deviation of the sampling distribution $$σ_{\overline{x}} = \...
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Standard Error in Auto correlated Data

I have time-series data generated via Metropolis algorithm - Monte Carlo simulations. Since these data must have some correlation between them, the formula of the standard error for IIDs variable must ...