# 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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### Intuitive explanation for dividing by $n-1$ when calculating standard deviation?

I was asked today in class why you divide the sum of square error by $n-1$ instead of with $n$, when calculating the standard deviation. I said I am not going to answer it in class (since I didn't ...
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### How are the standard errors of coefficients calculated in a regression?

For my own understanding, I am interested in manually replicating the calculation of the standard errors of estimated coefficients as, for example, come with the output of the ...
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### Difference between standard error and standard deviation

I'm struggling to understand the difference between the standard error and the standard deviation. How are they different and why do you need to measure the standard error?
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### How can I calculate margin of error in a NPS (Net Promoter Score) result?

I'll let Wikipedia explain how NPS is calculated: The Net Promoter Score is obtained by asking customers a single question on a 0 to 10 rating scale, where 10 is "extremely likely" and 0 is "...
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### Shape of confidence interval for predicted values in linear regression

I have noticed that the confidence interval for predicted values in an linear regression tends to be narrow around the mean of the predictor and fat around the minimum and maximum values of the ...
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### How does the standard error work?

I have been looking into the inner-workings of the standard error recently, and I found myself unable to understand how it works. My understanding of the standard error is that it is the standard ...
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### Why is there a need for a 'sampling distribution' to find confidence intervals?

I understand the key principles behind confidence intervals, but there's something I want a bit of clarification on. Let's say I have a basket of apples that I picked at the orchard. The weight is ...
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### Standard errors for lasso prediction using R

I'm trying to use a LASSO model for prediction, and I need to estimate standard errors. Surely someone has already written a package to do this. But as far as I can see, none of the packages on CRAN ...
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### What is the standard error of the sample standard deviation?

I read from there that the standard error of the sample variance is $$SE_{s^2} = \sqrt{\frac{2 \sigma^4}{N-1}}$$ What is the standard error of the sample standard deviation? I'd be tempted to guess ...
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### Confidence intervals for median

I have a distribution of samples with a small number of values in each one (less than $10$). I have calculated the median for each sample, which I want to compare with a model and obtain the ...
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### Standard error of regression coefficient without raw data

After searching here: Perform simple regression without raw data I am still curious about this. Is it possible to derive the standard error of a regression coefficient from summary data alone? E....
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### Standard error clustering in R (either manually or in plm)

I am trying to understand standard error "clustering" and how to execute in R (it is trivial in Stata). In R I have been unsuccessful using either plm or writing my ...
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### Standard error of the median

Is the following formula right if I want to measure the standard error of the median in case of a small sample with non normal distribution (I'm using python)? ...
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### How can I estimate coefficient standard errors when using ridge regression?

I am using ridge regression on highly multicollinear data. Using OLS I get large standard errors on the coefficients due to the multicollinearity. I know ridge regression is a way to deal with this ...
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### General method for deriving the standard error

I can't seem to find a general method for deriving standard errors anywhere. I've looked on google, this website and even in text books but all I can find is the formula for standard errors for the ...
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### Converting standard error to standard deviation?

Is it sensible to convert standard error to standard deviation? And if so, is this formula appropriate? $$SE = \frac{SD}{\sqrt{N}}$$
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### Converting standardized betas back to original variables

I realise this is probably a very simple question but after searching I can't find the answer I am looking for. I have a problem where I need to standardize the variables run the (ridge regression) ...
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### Follow up: In a mixed within-between ANOVA plot estimated SEs or actual SEs?

I am currently finishing a paper and stumbled upon this question from yesterday which led me to pose the same question to myself. Is it better to provide my graph with the actual standard error from ...
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### How to deal with quasi-complete separation in a logistic GLMM?

Update: Since I now know that my problem is called quasi-complete separation I updated the question to reflect this (thanks to Aaron). I have a dataset from an experiment in which 29 human ...
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### Standard error of a ratio

I have a linear regression and two estimates, say A and B and their standard errors. I need to find the standard error of a ratio A/B [or A/(1-B)]. I guess the main problem is that I don't know the ...
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### Finding precision of Monte Carlo simulation estimate

Background I am designing a Monte Carlo simulation that combines the outputs of series of models, and I want to be sure that the simulation will allow me to make reasonable claims about the ...
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### Hausman test: the larger the sample the more significant the Hausman test statistic?

Hausman test statistic formula: $$H=(\beta_{f}-\beta_{r})' \left[\mathrm{Cov}(\beta_{f})-\mathrm{Cov}(\beta_{r})\right]^{-1}(\beta_{f}-\beta_{r} )$$ where $\beta_{f}$ is the beta of fixed effects ...
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### Standard deviation of a ratio (percentage change)

I have 2 data sets. The first data set, let's call it $X$ has an average value of ($\bar X$) and standard deviation of ($STD_X$), the second set of data also has the average value of ($\bar Y$) and ...
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### Why does standard error not involve population size?

$$SE = \frac{SD}{\sqrt{N}}$$ If N is the entire population, I would expect SE to be zero. If N is equal to population size - 1, I would expect SE to be lower than if N is a small fraction of the ...
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### Standard errors of a two stage least squares regression, Stata

I use Stata. I am trying to replicate the ivreg output of a regression performing manually the first stage, predicting the instrument after the first stage and running the second stage regression with ...
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### Not sure if standard error of p-values makes sense in Fisher Exact Test

I am working on implementing a Fisher Exact Test for some unemployment and wage data. The idea is to describe two populations (one receiving an assistance program (the "treatment") and one not ...
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### Is the residual, e, an estimator of the error, $\epsilon$?

This question has come up in another thread that I started so I thought I would get more people's opinions on it. My question is Is the residual, e, an estimator of the error, $\epsilon$? The reason ...
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### Robust standard errors in econometrics

I keep hearing my professor try to explain that we can use robust standard errors when we run a regression to confront the issue of heteroskedasticity. However I don't quite understand how telling ...
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### Why not report the mean of a bootstrap distribution?

When one bootstraps a parameter to get the standard error we get a distribution of the parameter. Why don't we use the mean of that distribution as a result or estimate for the parameter we are trying ...
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### How to calculate the standard error of the marginal effects in interactions (robust regression)?

what I am interested in learning is how to calculate the std error of the marginal effects of a X variable when it is part of an interaction, especially in robust regression. There are tipically two ...
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### Proof that regression residual error is an unbiased estimate of error variance

Consider the least squares problem $Y=X\beta +\epsilon$ while $\epsilon$ is zero mean Gaussian with $E(\epsilon) = 0$ and variance $\sigma^2$. I need to prove that $\frac{V(\hat{\beta})}{N-(n+m)}$ ...
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### Why do we say “Residual standard error”?

A standard error is the estimated standard deviation $\hat \sigma(\hat\theta)$ of an estimator $\hat\theta$ for a parameter $\theta$. Why is the estimated standard deviation of the residuals called "...
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### Standard error of the sampling distribution of the mean

I found an equation that says the standard error of the sampling distribution of the mean is: $$\sigma_{\bar{X}} = \sigma \cdot \sqrt{\frac{1}{n}-\frac{1}{N}}$$ And when the population size is very ...
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### Standard error from OR and HR

I'm planning to combine several observational studies, some of which have produced odds ratios and some hazard ratios. How do I get the standard error from the odds ratio $1.57$ ($95\%$ CI: $1.08-2.27$...
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### Understanding standard errors in logistic regression

I am having trouble understanding the meaning of the standard errors in my thesis analysis and whether they indicate that my data (and the estimates) are not good enough. I am performing an analysis ...