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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Calculating mean confidence intervals from a sample with low SEM

Given that: I. The distribution of means of large enough samples converge to a normal distribution (by CLT) II. The Standard Error of the Mean (SEM) of a sample approaches the Standard Deviation (SD) ...
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Different results when calculating confidence interval

I'm trying to replicate the results from a paper which states: "Estimated overall accuracy is 79.6% with a standard error of 5.1% which would yield a 95% confidence interval of 69.5% to 89.7%.&...
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Adjust results for a systematic error

My model identifies objects with a specific quality in a large population. I tested it on a sample of 500 and found that it fails to identify about 7% of the objects (false negatives) due to some ...
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Number of samples required to get mean of unknown function up to some standard error

So I have some code simulating the behavior of a complex system. The system works perfectly (with a "fidelity" of $f=1$) for some parameter $\beta=0$. For other values of $\beta$ the ...
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Three versions of the independent two sample t-test (and R)

This post concerns three versions of the independent two sample t-test: Student's t-test uses a pooled standard deviation in the denominator (all equations are shamelessly copied from Wikipedia - ...
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Can estimated values with wide confidence intervals be used calculate association or correlation coefficients?

I want to test for an association between socioeconomic deprivation and death rates. My data are raw death counts and deprivation ranks for a set of small geographic areas. Some areas have very low ...
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Computing standard errors when using stratified sampling

I am trying to understand the following formula for the standard error of the population mean as estimated through stratified sampling. On the CRAN site, the formula given is $$ S_{\bar{x}_{\textit{...
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Spatial Error Model vs Conley standard errors

What is the difference (pros and cons) of using an OLS with conley standard errors and a spatial error model? Is there a recommendation for when you should use one over the other? Thanks!
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Frisch-Waugh-Lovell Theorem: Different standard errors

The Frisch-Waugh-Lovell theorem states that the b1 vector (and e vector) in Y = X_1 * b_1 + X_2 * b_2 + e are equal to the b* vector (and e* vector) in M_2 * Y = M_2 * X_1 * b* + e*, with M_2 = I - ...
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Propagation of standard error of fit through to the average and standard deviation of replicates

I am using an equation to fit measured data. I have measured multiple replicates for each condition, each of which is then individually fitted to this equation. Once the data are fitted I obtain a ...
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Estimate standard error due to reduction in sampling rate for a time series data

I have a large set of time series data representing the progression of a variable during an industrial production process collecting at a certain frequency at regular intervals. The mean of each curve ...
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Why is standard error of the mean always calculated from the population variance?

The standard error of the mean is often calculated with the formula $\sqrt{\sigma^2 / n}$, which uses population variance (or an estimate of it). However, standard error of the mean is defined as the ...
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Does it make sense to calculate Relative Standard Error using population parameters?

Relative Standard Error (RSE) is one of the main measures to assess the quality of survey indicators. If only sample data are available, RSE can be computed using estimated mean $\bar{y}$ and ...
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Is the 'Std. Error' provided by lmer in lme4 actually Standard Deviation?

I have been working with lmer in lme4, and wanted to construct a density curve of the slopes produced by my model (rather than just confidence intervals). The model output of lmer produces a slope, ...
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Standard errors of Monte Carlo plus linear combination

I'm using Monte Carlo to estimate some quantity $V(x)$. To get an approximation of $V'(x)$ I would use the following $$ V'(x)\approx\frac{V(x+h)-V(x-h)}{2h} $$ so I can simply evaluate it with two ...
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Computing and simulating average marginal effect standard error using Delta Method with reproducible codes

I am trying to simulate calculating Average Marginal Effects on a basic linear regression with interaction on a binary variable and compare the empirical standard deviation I get from simulations and ...
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Standard Errors for Numerical Optimization using Chi-Square Objective Function

I am using a minimum chi-square estimator technique to estimate a set of parameters using some sample data (essentially, finding what set of model parameters minimize the difference between observed ...
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Bootstrap Standard Error vs Standard Error from sample

For doing inference of a population parameter from a sample, under which examples is better to calculate the standard error using bootstrap distribution of the mean than directly using the standard ...
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Calculation of the standard deviation of the power in dB

I wanted to find out the stability of my system so for that i calculated standard deviation of power samples data which is in dB but I am not sure whether i have used correct formula or not. As far as ...
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Error bars on error bars?

Inspired by my recent attendance at an environmental toxicology conference, I have the following question about error bars: Let's say that I'm drawing samples from some unknown distribution, with ...
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Why Does Standard Error for Individual Predictors Not Increase in Multilevel Modeling?

I have been trying to teach myself multilevel modeling through R and I am relying on the W. Holmes Finch book. According to them, and any resources in general, not doing multilevel modeling causes an ...
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Should we always minimize squared deviations if we want to find the dependency of mean on features?

It is known that for any distribution a minimization of squared deviations from a value $c$ gives mean of the distribution. In other words, if we generate many values $y_i$ using our distribution, and ...
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Standard error between experiments

I need to open a new question regarding the already largely discussed "standard error". I have performed twice the same experiment on the same area. Each experiment includes the measurements ...
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Interpreting standard error for dummy variables in linear regression models

Is there any way to interpret the standard error of dummy variables created to represent a categorical variable in a linear regresion model? I saw a great mathematical explanation here, but I am still ...
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Is it safe to say that this set of data is constant with x because of their standard deviation?

Is it safe to say that Y does not change with X because if you take the mean of Y and calculate the standard deviation all of the values fall with 1 standard deviation ?
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Standard error for a difference-in-difference estimate

I am trying to calculate a difference-in-difference estimate. I have a binary outcome variable, and have estimated risk differences for my intervention and control groups. If we take an example where: ...
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How to calculate the Fisher Information Matrix in GARCH?

How to calculate the Fisher Information Matrix in GARCH? I want to know how to calculate the standard errors in them and without the empirical fisher information, empirical likelihood, I have no idea ...
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How to deal with redundant data within a sample when calculating the standard error?

In my research, I analyse pixel data from a 2D microscope image. Each pixel represents a unique spatial position. In my image, each pixel $i$ has a corresponding brightness value $x_i$. I assume the ...
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For bivariate linear model, if the residuals ARE normal, but the data is NOT normal, can I make inferences about the slope coefficient? [duplicate]

For convenience and context, I'm looking at the formula for standard error of the slope coefficient from here: https://www.statology.org/standard-error-of-regression-slope/ If X is not normally ...
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Standard error of sampling distribution mean vs standard deviation of the sampling distribution?

In this resource, towards the bottom, the authors write: The next step is to estimate the standard error of the mean. If we knew the population variance, we could use the following formula, $sigma_M = ...
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Does the standard error of fixed coefficients take into account sampling error of random effects?

Not sure if I have phrased the title of my question properly but I will attempt to explain- I understand where the standard error of the my regression coefficients come from in regular linear ...
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Does the "type" of standard error affect the relationship between the standard errors of standardized vs. unstandardized estimates?

While previous answers explain how to convert between standardized and unstandardized coefficients and their standard errors, it is not clear if this formula applies across different types of standard ...
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Error bars or standard deviation around means from zero-inflated heterogenous data?

I've constructed a plot of mean values per group (year) solely for the purpose of examining my data and have been told to always include either standard error (S.E.) or confidence intervals (C.I.'s). ...
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Is there a standard error of the mean for when population size is known?

Background Let us suppose that we are sampling from a finite population which is itself drawn from a univariate normal distribution. This accomplishes (1) having an underlying probability model and (2)...
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SE Interpretation

Can you help me to interpret the following standard deviation? It is a linear regression problem, I need to predict Rent which depends on the size of an Apartment. Rent=23.411+13.806. The question is ...
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Why is the value of SE for the transformed regression model higher than the initial model with autocorrelation?

Is it right that with positive autocorrelation in the errors, the model underestimates the SE? Hence, using generalized differencing (such as Cochrane-Orcutt), the transformed model has a higher value ...
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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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