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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Computing sample size for a sample to estimate binomial distribution when point estimate of proportion is 0

For example, I have a estimate of p = 0 (95% CI: 0, 0.01), and I want to know the sample size for this sample. For $p\not =0$, I can compute the s.e. by $\sqrt(p(1-p)/n)$ to get the $n$, but not sure ...
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Estimation of standard error in observables generated from time series data

Imagine that I have time series data which are time-correlated, non-scalar, and of unknown, but identical distribution From this time series I have a function that takes an subset of X as input to ...
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Can a transformed variable's SE be meaningfully interpreted?

Suppose, for simplicity, I have a simple linear regression model, and I have transformed the response variable by taking the square root. The pre-transformed standard error is equal to 17, and the ...
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Why is Listwise Deletion Standard Error Too Small?

I am going over Stef Van Burren's "Flexible Imputation of Missing Data" and don't understand why Table 1.1 from section 1.3 below gives the standard error for listwise deletion as too large. ...
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What is the error of the mean of data that have uncertainty values attached to them?

Given a set of $n$ values, the error associated with their average will be $$\text{standard deviation}/\sqrt{n}.$$ But if the values themselves have an uncertainty attached to them, such as $100\pm 1,$...
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Correcting repeated measures data to display error bars that show within-subjects differences

I have some data containing within-subjects observations for two factors: y as a function of timepoint (300 'levels') and ...
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How to describe the method to compute standard errors of a difference?

I wonder how to name or describe some methods of computing the standard error $se$ or confidence interval $ci$ of a difference (or sum or whatever). For example, if the bootstrap method is used I ...
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Question about confidence interval and standard errors on graphs

So I made a graph in R, it’s a linear regression of the same sample at different concentrations. It has a confidence interval built into it of 95%. Then I had to determine the concentration of an ...
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Standard error of product of coefficients

Suppose that I have a regression model: $$ y=\beta+\beta_{1}T+\beta_{2}M+\epsilon $$ and $$ M=\alpha+\alpha_{1}T+v $$ In this model, $y$ is the outcome variable, $T$ is treatment, and $M$ is the ...
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For all datasets with a binary outcome, will linear regression always yield betas with a smaller standard error compared to logistic regression?

Any cases where the betas' standard errors from logistic regression will be smaller than linear regression, after converting from log odds space to probability space?
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Compute the standard error of the difference of two coefficients from two different regressions

I am estimating two different regression discontinuity models on the same data but using two different cross-sections. I need to subtract one RD estimates from the other in order to obtain a ...
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Generalized linear mixed effects models - Poisson family with log link

When fitting a GLMM with family=poisson(link="log") in lme4, I understand that the coefficients for the estimates of ...
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How to obtain the standard errors in Mean Group (Pesaran, 1995) estimator for panel data?

My question is very specific. I want to know how to obtain the standard errors of the Mean Group coefficients obtained by the Mean Group estimator developed in "Estimating long-run relationships ...
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Converting difference in means with standard error of difference to percentage difference with standard error of difference

I have two means with standard errors associated. I am able to calculate difference between the means and standard error of the difference. I can calculate percentage difference. I am not sure how ...
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Why such a big difference in t values calculated using 2 different formulae?

I'm new here, please bare with me. Now I was calculating the t-value to get the probability and check the significance of the slope of a regression equation. I don't have a stat calculator (I can't ...
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Arguments for Percentile Interval over standard error

Suppose I am trying to estimate the mean of a population through a sample average and I would like to get a sense for how many participants I will need in the sample to attain an acceptable average. I ...
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Robust standard errors for poisson/negbin panel data estimators

I am trying to calculate robust and clustered standard errors for Poisson and Negative Binomial panel data estimators. I am using 'pglm' package. Ideally, I would be able to use the ...
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Z-Score and Bootstrap Distribution

Suppose one wants to know whether the mean income of workers in country A is 20,000 per month. Suppose from collected sample, one gets 21,000 as the mean income in one's sample. I remember in stats ...
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Finite population correction factor for A/B testing

Generally when reading about statistics in A/B testing, most hypothesis tests are done assuming that the distribution of the sample mean follows a normal distribution where the standard deviation is ...
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What is the difference between Standard error and Relative std. error?

I have a report with both Standard error and Relative std. error for a same metric for two years. What is the difference between Standard error and Relative std. error in this example? How should I ...
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Making difference-in-differences(DiD) table like Card&Kruger(1994)

My team is using difference-in-differences(DiD) method for our empirical project. Before we show the regression DiD results, we wish to present 3X3 table - like in Card&Krueger(1994) - which shows ...
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Standard error of slope when data is unknown [duplicate]

Let’s say I did a linear regression on a dataset with 10 observations, and I got the estimated slope as $b=0.5$ and residual variance as $\sigma^2=5.2$ and further, $$(A^TA)^{-1}=\begin{bmatrix} 2.54 &...
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How to assess the "reliability" of standard errors?

I am studying linear regression and in particular, I am trying to solve an exercise from my book. The model I am focusing on is about wages and education and the text gives me the output of the ...
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Convert T-values from Poisson regression to Standard Errors

I am trying to summarize results from an article for a review (available for free here, I am looking at table 3), and thus want to find Standard Errors (SE) to compute confidence intervals. The ...
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Inference on ratio of coefficients

Question: How to construct standard errors and test statistics for a ratio of regression coefficients? Background: I am running the same regression on two related outcomes $$ Y_1 = \alpha_1 + \...
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How to incorporate standard error into non-linear model?

Suppose you have some function $f(x)$ which represents the mean value of an experiment related to $x$. Then $\epsilon = \sigma(x)/\sqrt{n}$ is the error associated with each point $x$. Assuming that ...
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How to compute standard error if I only have mean percentage and interquartile range and sample size?

If I only have the sample size, average percentage and interquartile range, how could I compute the standard error? I can make an example about the percentage. It is like testing each of the kids in ...
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How to find 95% CI of CI of Mean?

We know that the 95% confidence interval around the population mean is calculated as x̄ ± 1.96* σ/√n, where x̄ is the sample mean, σ is the sample standard deviation and n is the sample size. On the ...
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How does one calculate the significance of the coefficients of a linear regression? [duplicate]

When I run a linear regression in the form of $y$ = $\hat{β}_0$ + $\hat{β}_1x$, I not only can calculate the values and SE of $\hat{β}_0$ and $\hat{β}_1$, but also their z-scores. Now what I don't ...
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Evaluating randomized algorithms on randomized problem instances

Suppose we want to compare the performances of two algorithms — call them A and B — on a problem X. In particular, suppose that we want to evaluate the algorithms on random instances of X drawn from ...
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When do control variables increase precision?

Suppose we're interested in the effect $\beta$ of a treatment $D$. To increase the precision of our estimate (ie., reduce the variance of $\hat{\beta}$), we can include a control variable $X$ that ...
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I cannot understand the formula for between-imputation variance in multiple imputation

Multiple Imputation (MI) for estimating desired a desired statistic but with missing data Following ^Shafer (page 4), and ^Austin et al. (section "Analyses in the M imputed data sets"), ...
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Standard Error on the Mean for Asymmetric Distributions

Gaussian - symmetric case: consider a statistically independent sample of N observations from a normal distribution.The mean (loc) of the population is the results on which you would like to make a ...
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How does one compute standard errors for coefficients in multinomial logistic regression?

I am currently engaged in a project to try and compute standard errors for coefficients for multinomial logistic regression. I saw answers with code in this post here How to compute the standard ...
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How do I reconcile all these different formulas for the standard error of the difference between means?

I'm trying to make sense of the different formulas I see for the standard error of the difference between two (sample) means. I'm struggling to reconcile the different formulas. All formulas below use ...
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Checking whether improvement is significant

I am looking to compare if there is a significant improvement between two test trials. As a background: some time ago as a practise I created a simple app aimed at improving pressure force accuracy. ...
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Residual standard error for multiple imputed regression

How to calculate the standard deviation of the residuals for a pooled regression? (The idea, formula and/or R code are all welcomed) As far as I understand it is the standard deviation of the ...
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Logistic Regression Manual Calculation of se.fit of predicted values?

Very similar to this; How are the standard errors computed for the fitted values from a logistic regression? Although after manual calculation of se.fit with glm ...
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How to prove equality of standard errors for two-sample t-test and linear regression?

Using classical linear model assumptions, we know that $$\frac{\hat \beta_j - \beta_j}{se(\hat \beta_j)} \sim t_{n-k-1}$$ meaning that the ratio of regression coefficients to their standard error ...
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Comparing margins of error of confidence intervals before and after new data is collected

Consider the following question: I have calculated: margin of error for the first 50 jumps is 0.127, margin of error for the last 10 jumps is 0.248, margin of error for all 60 jumps is 0.156. The ...
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How to determine power using standard error and effect size?

I was reading this article published from airbnb around gaurdrail metrics. In it, they discuss this power guardrail they derived but it's very unclear how they went about it. How are they determining ...
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What is the relationship between confidence intervals that are build with bootstrapping vs t-distributions?

I've seen a few resources online that construct confidence intervals (CI) in different ways. One is through bootstrapping which essentially samples with replacement from a group of measurements and ...
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Getting the confidence interval or some sort of range for predictions from optimizations

I am trying to calculate range for my model predictions after performing optimization and getting values of the optimized parameters. I am aware that we can get a standard error of the optimized ...
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How to estimate standard errors and R2 from variance-covarariance matrix? [duplicate]

This is what says "the following table shows the variances and convariances of the logarithms of the importations, PIB and IPC in USA between 1975 and 2005. Here is the table with variances/...
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Standard error vs. Standard Deviation

In the linear regression model: $Y = X\beta + e$ When we estimate $\hat{\sigma^2}$ = $\frac{\hat{e}'\hat{e}}{(n-p)}$ Is $\hat{\sigma}$ standard error or standard deviation? My thinking is that $\sigma$...
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Standard error for the median value of estimated means

I apologize in advance if this is a very basic question, but I can't find a straight answer so far. I have a country level dataset that contains the means and standard errors of a health indicator ...
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Different standard errors in Stata and R for instrumental variables (ivreg)

Working with instrumental variables (IV), I noticed differences between reported standard errors in Stata (e.g., using ivreg2) and R (e.g., using AER:ivreg2). In R I found ways to replicate Stata's ...
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Question On T-Statistic in Regression Example

I am reading through The Effect: An Introduction to Research Design and Causality and in chapter 13 on regression, there is a code example of calculating regression that I am not fully grasping. It is ...
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How does the standard deviation of the errors change when the scale of x changes in a SLR model?

How does the standard deviation of errors change when the scale of x changes by a multiplier of 3 in a simple linear regression model?
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I was studying about probable error and I couldn't understand the reason behind using 0.6745 of standard error. Could someone please explain it?

P.E=0.6745(S.E) Probable Error = 0.6745 × 1−r2/√N
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