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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Aggregating forecasts and their standard errors over time periods

Good day all, I have an ARIMA model which gives me a weekly forecast and standard error for each period. If I were to aggregate the forecasts into monthly time-windows (for simplicity sake, let's ...
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Standard error for Rate differences

I have a database structured like this: ...
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Why are the standard errors of these two outputs so different? [duplicate]

Context of the question: Two professors want to look at the effect of students’ high school math marks on their marks in their first calculus course. All marks are between 0 and 100. Using data from ...
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Standard Error of Coefficient of regression [duplicate]

In the Introduction to Statistical Learning book it is mentioned that SE(B1) is smaller when the xi are more spread out; I cant understand why data spread out will resulting in smaller SE and ...
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Intro to Statistical Learning - Solutions for 2.1

I am reading An Introduction to Statistical Learning with Applications in R (ISLR) and I wonder what would be the answer for exercise 2.1 part (d). The question is, If the variance of the error terms $...
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Calculating the variance of a function which depends on the standard deviation and mean of a random variable

I am a bit new to statistics and had some conceptual questions regarding the calculation of variance. I want to calculate the variance of a function $y=\frac{\sigma_{X}}{g(\overline{X})}$. As seen in ...
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How do I test for significant differences given only means and standard error?

I'm in a situation where I have two (equally long) lists of means, with sample sizes and stderr for each mean. The variance for these means are all variable and different, and so are the sample sizes. ...
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Which standard errors do I use for the Fama-French three-factor model?

I am doing a linear regression with the Fama-French three-factor model with data from the stock market I built a portfolio out of. (I also use Betting Against Beta, Short Term, Long Term and Momentum ...
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Estimation of standard error of the median from median and confidence intervals for meta-analysis?

I have a dataset of median survival time and their confidence intervals. One way of pooling these medians using meta-analysis requires an estimate of the standard error of the median / variance of the ...
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How to adjust the standard error for a standardized beta after squaring the beta

I have a standardized beta from a regression, which is equivalent to a correlation. I also have it's standard error (SE). I want to plot the R2 (explained variance) with an error bar, and to get the ...
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Can bootstrapping be used to find the standard error of variance?

I am a bit new to the field and had a question regarding bootstrapping. As bootstrapping gives an idea of the standard deviation of the sampling distribution of the mean, does it also give an idea of ...
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How to include standard deviations in diversity calculations?

I have community abundance data where each species has a mean and a standard deviation (determined by replicate samples). I am comparing the diversity of two communities. The various diversity metrics ...
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Mean Accuracy and Standard Error of the Accuracy for KNN Classification algorithm

The given below code snippet is from the assignment of online course IBM ML with Python. Here's the assignment. The used variable names :mean_acc and ...
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Calculating a variance term for AUC using data points extracted from a figure

I am currently performing a meta-analysis where I am pooling area under the curve values. For some papers I only have access to the figure. For example: Using WebPlotDigitizer I can extract the mean ...
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Bias of standard errors as estimates

I'm reading on the standard errors used in various hypothesis tests. For example, in tests of one population proportion, we use $\sqrt{p(1-p)/n}$. For comparison of two population proportions, we use $...
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Confusion (possibly due to terminology)

Disclaimer.. This is a post regarding help with homework but I have done some work. I am stuck between C and D since they both seem right. First of all, I think since the variance explained by the ...
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Why can we mix standard errors with raw covariances when calculating standard error of sum of regression coefficients?

Let's have a look at this post: Standard error for the sum of regression coefficients when the covariance is negative We have: $SE_{b_{2+3}} = \sqrt{SE_2^2 + SE_3^2+2Cov(\beta_2,\beta_3)}$ But why do ...
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Bootstrapping Standard Error vs Standard deviation

I am studying for an exam and would really appreciate some guidance as I am new to stats. I am and having difficulty understanding the difference between the: standard error of a bootstrap ...
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Underestimation of standard error

The formula to calculate standard error (aka standard deviation of the sample mean) is $\sigma_{\bar{x}} = \frac{ \sigma} {\sqrt{n}}$. But we generally don't know the population standard deviation $\...
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t-test vs linear regression: how are standard errors calculated?

Consider Stata's auto dataset. I am interested in finding the difference in the mean weight of foreign and domestic cars. To do this, I can do a two-sided unpaired ...
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Why is the standard error in a diff-in-diff with 4 datapoints 'not well defined'?

I was looking at this online book https://matheusfacure.github.io/python-causality-handbook/15-Synthetic-Control.html in order to learn about synthetic control. The author gets two cities in a panel ...
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Why the standard errors of logistic regression are of that form?

In Elements of Statistical Learning, page 125 it is written that the coefficients of a logistic regression converges to $\mathcal{N}(\beta, (X^T W X)^{-1})$ with: $X$ the $N \times (p+1)$ matrix of ...
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95% Confidence interval for extrapolated value from linear regression?

I'm writing a program to estimate the lower limit of detection for a nucleic acid assay. A typical analysis will have 5 concentrations with 10 independent replicates each, the dependent variable being ...
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Robust standard errors (White) under homoscedasticity

Robust standard errors (White standard errors) are given by: $$\hat{V}(b)=(\sum_{i=1}^N x_ix_i')^{-1}(\sum_{i=1}^N e_i^2x_ix_i')(\sum_{i=1}^N x_ix_i')^{-1}$$ This helps us to estimate a asymptotic ...
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Hetereskedasticity - how to find standard error of the response?

I have data that looks like a classic image below. How do I find the standard error in the predicted response y, where y is from a linear fit? Edit: Standard error perhaps is not the right term. I ...
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Bootstrap Standard Errors: should I divide the sampling standard deviation by $\sqrt{n}$?

Suppose I am bootstrapping an OLS regression and want the standard error of the coefficient $\beta_1$. I estimate the following regression on 1000 resamples of the data (where $B$ indexes the ...
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Manually calculate the standard error for instrumental variable in R

I am working on a project that need to use instrumental variable. I use the ivreg package and train on the CigarettesSW dataset from the AER package. I follow the training from this site : https://www....
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Unbiased estimate of standard error of sample by bootstrapping

I'm trying to compute the standard error for a statistic on a small sample. Currently, what I'm doing is bootstrapping using the following pseudocode: ...
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Trouble identifying what data analysis to use

I am currently undergoing a soil research project in which 3 soil samples was taken from 3 different depths each (30cm, 60cm, 90cm) therefore totalling 9 samples overall. With these samples, I am ...
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Differing standard errors with jackknife dataset - R compared with Stata

I am working with a stratified international assessment (14 countries from IEA's ICCS 2016 assessment) and am trying to understand why R's survey package and Stata's survey module differ slightly in ...
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Is there a relationship between the standard error of a fixed effect and the standard deviation of a random effect?

library(lme4) data("sleepstudy") head(sleepstudy) m1 <- lmer(Reaction ~ 1 + (1|Subject), data=sleepstudy) summary(m1) In the above example we get a ...
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Standard error in a group of samples

I just want to check my understanding around a standard error in a group of samples. Let's imagine I am measuring the water use a household at a certain hour of the day. Some data: The population is ...
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Two Proportions Z-Test Accounting for Sample Standard Error

I have been using this equation for the two proportions z-test. However, what if each population sample from which proportions were derived has a different or considerable degree of sample standard ...
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How to derive NW standard errors for impulse responses from lpirfs package in R or calculate them?

In my thesis, I have to derive impulse responses with IV using 2sls. I use the package in R "lpirfs" and specifically the lp_lin_iv function. My results have F stat and P-value. But I want ...
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Plug-in estimator $1/\lambda$ and standard error

Let $X_1, \dots, X_n ∼ \mathsf{Pois}(λ).$ Find the plug-in estimator $\hat \tau$ for $\tau = 1/λ$ and calculate the standard error. I thought: $\hat\lambda =\bar X $ (sample mean) so $\hat\tau = 1/\...
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Cluster-robust standard errors after vglm

I have estimated an ordered logistic regression with the vglm function of the VGAM package in R. Here is a minimalistic example of what I did: ...
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How to best represent uncertainty in a time series forecast model?

Now that I know why it is important to represent the uncertainty of a model, I would like to know how to best represent uncertainty in a time series forecasting model. My previous question introduced ...
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Standard error with maximum likelihood estimation

ASTM E2238 describes the prediction of the largest inclusion in a polished steel surface of 150,000 mm² based on a Gumbel distribution of the largest inclusions measured in each of 24 polished ...
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How do we calculate Standard Errors for effect-coded variables?

I'm a beginner following this UCLA tutorial to figure out how to interpret coefficients for effect-coded categorical predictors and have a couple of questions regarding their regression table below, ...
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What is empirical standard error and how to calculate it from lm in R?

I read from some articles saying that "empirical standard error is the standard deviation of the point estimates. For a general linear model, the point estimates are the model coefficients, such ...
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How do I propagate the error in the elements of a set through to the mean of the elements?

I need to understand how to propagate the errors in the elements of a set through to the mean of the set and correctly determine the estimate for the error value of the mean. I am designing an ...
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Calculating the standard error for the ratio of 2 random variables?

I have 2 40x10 matrices, $X$ and $Y$. Each row represents a sample, and each column represents a different trial. Its OK to assume that $X$ and $Y$ are random normal variables if that's relevant. I ...
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Standard Error of Estimate

In a simple regression analysis based on the least squares regression equation, I got the predicted value of 7.15 for the predictor value of 11. The sample size is 35. I computed the Standard Error of ...
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Confidence interval for combined populations

I'd like to compare two approaches for calculating the confidence interval ($CI$) when estimating the mean for a sample of weighted values: The first approach is based upon the standard error of the ...
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How to compute standard errors of an estimator with antithetic variates?

I'm pricing American options using Longstaff and Schwartz Least square method. When using the following Python code, I obtain nearly the same prices and standard errors as in the Valuing American ...
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Log and exponential uncertainty propogation

I am processing data on a radioactive decay experiment, and need to find the errors on some quantities that I can get from some fit parameters. I would like to obtain: $\sigma A$ from $A = e^{a}$, ...
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standar error of non-linear regression

I'm trying to compute the standar error of a non-linear regression fit, I find the answer in this post Non-linear regression confidence interval But i did't find that formula in any other place,and I ...
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Question about confidence intervals and prediction intervals

Considering following linear multiple regression model: \begin{equation} y=X\beta + e, \end{equation} where observations $y\in\Re^n$, coefficents $\beta\in\Re^p$ and $e\sim N(0,\sigma I)$ is a white ...
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Clustering standard errors at individual and/or organisation level with fixed effects

So, I have a relatively large panel dataset (26,000 observations) with data on speech by individuals belonging to political parties. The data is grouped by individual-week (i.e. an observation for ...
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Any index/parameter to evaluate std error and std deviation?

I saw there are tons of good questions on standard error y deviation. I read many of them and I think I got the point. However I am still not sure that showing one over the other is correct. Unless ...
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