Questions tagged [standard-error]

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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Delta Method Average Marginal Effects Multinomial Logit

Following the incredible demonstration in Statalist by Jeff Pitblado on how to calculate - using the Delta Method - the Standard Errors for Average Marginal Effects of a Logit Model. Q: What would ...
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The Standard Error in R language lm (linear regression) is Standard Deviation or Standard Error of the Mean?

When we are estimating the coefficient in R, "Std Err" will be produced by "lm". Is it Std or SEM? How is it calculated? Run lm function with any R data set will give an example.
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154 views

Standard error of median small sample

I tried to find this question but what I've found provides answers for normal distributions and large sample sizes. I'm analyzing some data from an experiment with different groups. Each group has ...
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81 views

How to calculate standard error of the difference between two random variables which are dependent?

I know that standard error between two independent variable can be calculated as below. SE(1,2) = SQR(SE1^2 + SE2^2) where SE1 is standard error for variable 1, SE2 is standard error for variable 2. ...
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The link between error bars representing the standard error of the mean and statistical significance

I have read the following on many websites: What can you conclude when standard error bars do not overlap? When standard error (SE) bars do not overlap, you cannot be sure that the ...
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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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70 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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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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304 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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48 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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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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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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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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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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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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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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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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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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132 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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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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539 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
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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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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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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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49 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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34 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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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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39 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
79 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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369 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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110 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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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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145 views

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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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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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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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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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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145 views

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 ...
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SLR: why residual 'standard error' actually refers to RSS/(n-2) and not standard error?

From what I've learnt, standard error is a concept related to sampling distribution. So why is the term 'residual standard error' used to refer to $\sqrt{\frac{RSS}{n-2}}$ and not $\sqrt{E(r_i - E(r_i)...
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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 ...
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Averaging of two or more standard erros

I have calculated two standard errors for two fishers z correlations from the same study , both measuring the same variable. Is it acceptable for me to average the two standard errors into one? If so ,...
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Sample sizes without significance levels

I would like to know about a strategy for estimating sample sizes when you're not concerned with statistical significance hypothesis testing (e.g. along the lines in Abandon statistical signficance - ...
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How to estimate the standard error of the leave-one-out cross-validation estimate of the prediction error?

How does one estimate the standard error of the leave-one-out cross-validation estimate of the prediction error? For each fold (leave out the $i^{th}$ observation), the LOOCV estimate of the ...
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Why does higher variance of independent variables decrease standard errors of the estimator?

Some time ago, reading Advanced Data Analysis from an Elementary Point of View by Cosma Rohilla Shalizi, I found this statement in a section about significant coefficients: Moreover, at a fixed ...
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Obtaining standard errors from forecast object in R [closed]

I am using an ARIMA model to forecast a few periods ahead of my data in R. To do this I begin by estimating the ARIMA model using the ...