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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How to compare a Linear Regression’s Coefficients with the Coefficients for its Subgroups using Standard Error?

Assume a linear regression model has been made of an item’s overall utility value, and elements like durability and color availability have statistically significant coefficients in the overall value ...
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Error in linear regression as function of independent variable

I have some x and y data that are clearly correlated like this: So we can predict y if we know x. We can also calculate the mean error in our prediction by taking the root mean square of the ...
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How to report a +/- standard error for logarithmic data?

I have some data $y$ which varies logarithmically which I am fitting with MCMC methods. It makes more sense to do my analysis in the logarithmic space $z = \mathrm{log}(y)$. As I result, I end up with ...
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HAC variance to construct standard errors

I am facing some difficulties understanding this question. It hasn't been long since I started with econometrics, so I'm new to all of this. Suppose we have a function $$E[c_t|y_t,c_{t-1},y_{t-1},c_{t-...
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Why do two confidence intervals only overlap when their difference $(\theta_1 − \theta_2) \pm z(SE_1 + SE_2)$ includes 0?

I am able to check if the interval contains 0 which I can find out by just plugging numbers into the above formula but I am curious as to why this interval containing zero means that the two CI's of $\...
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Reference request: accounting for AIC stepwise model selection with bootstrapped standard errors

The use of the AIC for model selection via comparison over many models is well-known and rightly maligned. But I read an interesting passage from Hastie et. al.'s classic The Elements of Statistical ...
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Adding of two confidence intervals

Given two variables $\bar{A}$ with 95% confidence interval [$A_0$,$A_1$], and $\bar{X}$ with 95% confidence interval [$X_0$,$X_1$], how would one calculate the 95% confidence interval of a composite ...
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Similar estimate standard errors in GLMMs using a wide range of environmental variables [closed]

I have a data set on animal species diversity at 40 study sites from3 sub areas. The data comprise about 60 environmental variables. I am interested in the effect of each variable on the species ...
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Converting between confidence interval and standard error

In this link it says that we can convert a 95% confidence interval to the standard error by this calculation: $$SE = (upper limit – lower limit) / 3.92$$ For 90% confidence intervals divide by 3.29 ...
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The variance of variance-covariance matrix

Looking at answer on the standard error of the variances and this answer on the standard error of the covariances, and knowing that both are part of the variance-covariance matrix, $\Sigma$, I am ...
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Margin of Error in a NPS result with promoters only

This is a follow-up to the response provided by @whuber on the question How can I calculate margin of error in a NPS (Net Promoter Score) result? @whuber pointed out that there are more sophisticated ...
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Standard deviation of error (SDE) application

There are standard deviation, standard error (SE), standard error of mean (SEM), then there is standard deviation of error (SDE) intended as a measure of error variability used in device measurement ...
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How can sample SD be substituted for population SD in standard error of means formula?

Standard error of sampling distribution of means is generally defined as (population SD/sqrt(n)) where n=sample size. But where population parameters are not known I have seen sample SD being used in ...
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Does it make sense to use a population parameter like $\sigma$ (population standard deviation) in the formula for SE?

Correct me if I am wrong but in the formula for SE $\text{SE} = \sigma/\sqrt{n}$, the numerator refers to population parameter. But in practical life, we resort to sampling because we don't know much ...
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Simply correcting OLS standard error in time series context

In microeconometrics, it is sometimes advised to always use heteroscedasticity-robust standard error (instead of testing for heteroscedasticity and using generalized or weighted least squares or ...
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Converting standard error to sampling variance for meta-analysis

Is it possible to get sampling variance (vi) from a standard error for meta-analysis. Specifically, I am unable to obtain raw data from the computation of an SMD. However, the SMD and confidence ...
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Error in the fraction estimated from a finite sample?

This seems like a basic statistics question, but I (a non-statistician) have been unable to find a definitive answer in online searches, possibly because I'm not using the right search terms. Given a ...
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How to find se.fit in R by hand?

I'm trying to find by hand the se.fit. Focusing on the first observation (weight=$1.9$), when we write the following code: ...
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How to estimate the standard error of a particular effect size when authors reported exactly as zero?

Currently, I'm working on a meta-analysis that is basically based on data obtained from individual-studies. However, there are some cases where the authors report effect size value with exactly zero ...
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Confidence intervals with sums of transformed regression coefficients?

I have an index that is formulated as follows, for party $j$, group $s$, where $w$ indicates weight of party or group as share of population : $$ \lambda =\sqrt{\sum^J\sum^S w_j w_s(\alpha_j+\beta_{js}...
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Nonparametric estimation of standard error on large samples

The bootstrap seems to be the gold standard for attaching a standard error to a point estimate on a sample. However, if the sample size is very large, it can be prohibitively expensive to repeat the ...
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How to derive the kth coefficient standard error?

Given a multiple regression with the usual assumptions satisfied, with $X \in R^{n \times p}$ $$ y = X \beta + e $$ I know that the estimated variance is given by $\sigma^2 (X^TX)^{-1}$. But what I ...
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The Standard Error of Mean (SEM) and Non-normal sampling distributions

I know that as the sample size increases, the sampling distribution of the mean will become normally distributed, even if the population data are skewed (non-normal). So we can safely assume that the ...
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means and errors for election polls

I'm trying to assess how to compute the errors associated with a numbers of likely voter polls of the Warnock Georgia Senate race. I have estimates of the margin of victory from 9 surveys of varying ...
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Correcting for robust/clustered standard errors within the lm function or replacing the results

Cross posted on Stackoverflow with a bounty of 200. EDIT: I think I have to clarify this question a little bit more. So what I am looking for, is a function in which I can provide both the vcov matrix ...
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Manual calculation - instrumental variable with a tobit distribution in the 2nd stage, different results with robust errors

Cross Posted at Stack Exchange. I am trying to correct my standard errors, when using an ols distribution in the first stage and using a tobit distribution in the second. For some reason, I am getting ...
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Ways to shrink standard errors in models for discrete dependent variables

Consider a simple Probit model $$ Y_i=1\{X_i\beta+\epsilon_i\geq 0\} $$ where $\epsilon_i$ is standard normal independent of $X_i$. (1) Cardinality of the support of $X_i$ Is it true that (and, if yes,...
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What's the difference between regressing $y$ on $x_1$ and $x_2$ rather than on their sum $z = x_1 + x_2$ or their difference $d = x_1 - x_2$?

I remember reading about this somewhere, but I cannot find the source anymore and I'm not sure what the benefit of doing it would be. Do the results of the regressions have anything in common (e.g. ...
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How to calculate the MSE for altered data

I am working on a simulation study on income. To make things simpler and since I will not do any further analysis with low & high incomes, I set all citizens with annual income less than $\$10,000$...
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Standard error for panel data models and heteroscedastic robust SE

There is something I do not understand on a deeper level on standard errors for panel data models. I know the reason for not using usual heteroscedastic-robust standard-errors is because of auto ...
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How to correctly transform estimated marginal means and SEs from binomial (logit) model?

Let's say I have this simple GLMM model in R: model = glmer(correct ~ treatment + (1|id), data = DATA, family = binomial(link=logit)), where correct is my dependent ...
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Standard errors propensity score matching

I am currently working on a causal inference project via several panel regression specifications, and one of the methods I'm using to obtain more robust results is propensity score matching (PSM). For ...
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Standard Error and Coefficient Calculation

I'm trying to calculate the missing coefficient and standard error from the question posted below. The question does not provide any information beyond the excel output of a 3 variable regression on ...
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Confidence interval for Standardized Mortality Ratio

So in a number of places, for example here, I've seen stated without explanation that the standard error of the SMR (at 95% confidence threshold) is simply $$ SE_{SMR} = 1.96 * \frac{\sqrt O}{E} $$ ...
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Standard error of estimated sum or product mean

Updated question: Given two sample means ($\bar X, \bar Y$) and sample standard deviations ($S_X, S_Y$) with different sample sizes ($n_X, n_Y$), I want to calculate the standard errors ($SE_\theta, ...
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Why is the standard deviation of the average of averages smaller than the standard deviation of the total?

Say I want to estimate the test error. I can either get $N$ batch $B_i$ then take the average of their average error (so the R.V. is the mean): $$ \frac{1}{N} \sum^N_{n=1} \mu(B)$$ or I can take ...
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Why errorbars shouldn't be SEM*√2 long by default?

There is no standard recommendation for length of errorbars to be used while showing spread of data or means in graphics. Standard deviation (SD), standard error of mean (SEM) and 95% confidence ...
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Does Null Hypothesis affect Standard Error?

Here under $H_0:P_1=P_2$ the standard error gets some common $P$ value which is computed from a pooled estimate. Why is the $\sigma$ value not calculated in a similar way in the next one? There under ...
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How to calculate standard error of prediction [duplicate]

Is it possible to approximate the standard error of the prediction based on the standard errors of intercept and coefficients?
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How to obtain standard error of parameters in maximum likelihood when reparametrized/transformed?

Sometimes parameters in the maximum likelihood estimation process are reparametrized for numerical convenience. As an example if I'm fitting maximum likelihood estimation (MLE) to a data that is ...
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Hodrick Standard Errors in R? [closed]

Does anyone know how to implement Hodrick Standard errors in R? I could not find any package for it in R. Is anyone aware of the same or any open source code that implements it? I want to use Hodrick ...
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3 votes
3 answers
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Standard error of estimated covariance

Let $X_1,...,X_n$ and $Y_1,...,Y_n$ be two independent random samples from $\mathcal{N}(\mu, \sigma^2)$ where both $\mu$ and $\sigma$ are unknown parameters. I estimate their covariance using: $$\hat{\...
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1 vote
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Should se.fit = TRUE in predict.merMod() be used, now that it is functional again?

I know the functionality of se.fit was removed from the predict() function in lme4 for mixed effects models a long time ago (due to not properly accounting for variations due to the random effects and ...
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Intuition Standard Error of the Mean

Trying to understand the intuition behind the standard error of the mean. Starting from this formula: $Var(\bar{X}) = Var(\frac{\bar{X}_1+\bar{X}_2+...+\bar{X}_n}{n})$ The formula talks about a ...
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Can a confidence interval have boundaries that are different in size in relation to the mean?

I saw a poll for local elections where 9.3% of the respondents said that they would vote for John Doe. The poll put the lower bound at 8.3% and the upper bound at 11.3%. From, what I have learned from ...
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calculate Standard Error of mean of (means over distinct distributions)?

As a motivating example, I want to pick the best racecar. The best racecar is the one that has the highest mean speed across 3 different racetracks (each racetrack is weighted equally). If I take ...
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Standard Error, Standard Deviation and Variance confusion

I am quite confused in these terminologies (especially but not limited to regression) I do understand what Variance and Standard Deviation means, they measure the dispersion / variability of the data....
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What is the formula for the standard error of Cohen's d

I found different answers to the question how to calculate the standard error (SE) of Cohen's d. First formula is (see here, here or here): $$ SE_d = \sqrt{\frac{n_1 + n_2}{n_1 n_2} + \frac{d^2}{2(n_1+...
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How to calculate SE for interaction in GLM

I am struggling mightily trying to figure out how to calculate the SE related to an odds ratio for a linear combination of two factors in a logistic regression model with an interaction term included. ...
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How to interpret the standard error for a factor regression?

I would like to know how to interpret the coefficient standard errors of a factor regression when using the display function in R. I have a data set which has three variables: winner of 2016 elections,...
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