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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 ...
Tal Galili's user avatar
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173 votes
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207k views

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 ...
ako's user avatar
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116 votes
4 answers
121k views

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?
louis xie's user avatar
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100 votes
3 answers
50k views

Shape of confidence interval for predicted values in linear regression

I have noticed that the confidence interval for predicted values in a linear regression tends to be narrow around the mean of the predictor and fat around the minimum and maximum values of the ...
luciano's user avatar
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75 votes
4 answers
143k views

Standard error for the mean of a sample of binomial random variables

Suppose I'm running an experiment that can have 2 outcomes, and I'm assuming that the underlying "true" distribution of the 2 outcomes is a binomial distribution with parameters $n$ and $p$: ${\rm ...
Frank's user avatar
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70 votes
6 answers
19k views

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 ...
Rob Hyndman's user avatar
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53 votes
5 answers
306k views

What is residual standard error?

When running a multiple regression model in R, one of the outputs is a residual standard error of 0.0589 on 95,161 degrees of freedom. I know that the 95,161 degrees of freedom is given by the ...
ustroetz's user avatar
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46 votes
3 answers
76k views

Calculating confidence intervals for a logistic regression

I'm using a binomial logistic regression to identify if exposure to has_x or has_y impacts the likelihood that a user will click ...
celenius's user avatar
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44 votes
4 answers
78k views

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 ...
Richard Herron's user avatar
44 votes
2 answers
230k views

How to derive the standard error of linear regression coefficient

For this univariate linear regression model $$y_i = \beta_0 + \beta_1x_i+\epsilon_i$$ given data set $D=\{(x_1,y_1),...,(x_n,y_n)\}$, the coefficient estimates are $$\hat\beta_1=\frac{\sum_ix_iy_i-n\...
avocado's user avatar
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42 votes
1 answer
28k views

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 ...
Remi.b's user avatar
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42 votes
1 answer
9k views

Quantile regression: Which standard errors?

The summary.rq function from the quantreg vignette provides a multitude of choices for standard error estimates of quantile regression coefficients. What are the ...
Jase's user avatar
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38 votes
3 answers
107k views

How to interpret root mean squared error (RMSE) vs standard deviation?

Let's say I have a model that gives me projected values. I calculate RMSE of those values. And then the standard deviation of the actual values. Does it make any sense to compare those two values ...
jkim19's user avatar
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35 votes
4 answers
8k views

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 ...
Guillermo Perez's user avatar
35 votes
3 answers
27k views

Why is the formula for standard error the way it is?

So just "why" is $SE = \frac{s}{\sqrt n}$ ? How should one interpret/articulate the reason of having $\sqrt n$ in the denominator. Why do we divide sample mean by the square root of the sample size, ...
PhD's user avatar
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32 votes
4 answers
47k views

How to compute the standard errors of a logistic regression's coefficients

I am using Python's scikit-learn to train and test a logistic regression. scikit-learn returns the regression's coefficients of the independent variables, but it does not provide the coefficients' ...
Gyan Veda's user avatar
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30 votes
3 answers
33k views

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 "...
Dan Dunn's user avatar
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27 votes
1 answer
92k views

Converting standard error to standard deviation?

Is it sensible to convert standard error to standard deviation? And if so, is this formula appropriate? $$SE = \frac{SD}{\sqrt{N}}$$
Bern's user avatar
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26 votes
6 answers
71k views

Always Report Robust (White) Standard Errors?

It has been suggested by Angrist and Pischke that Robust (i.e. robust to heteroskedasticity or unequal variances) Standard Errors are reported as a matter of course rather than testing for it. Two ...
Graham Cookson's user avatar
26 votes
5 answers
147k views

What is the difference between "margin of error" and "standard error"?

Is "margin of error" the same as "standard error"? A (simple) example to illustrate the difference would be great!
Adhesh Josh's user avatar
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25 votes
3 answers
16k views

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 ...
James Davison's user avatar
25 votes
1 answer
13k views

How to use delta method for standard errors of marginal effects?

I am interested in better understanding the delta method for approximating the standard errors of the average marginal effects of a regression model that includes an interaction term. I've looked at ...
Thomas's user avatar
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24 votes
1 answer
75k views

Standard errors for multiple regression coefficients?

I realize that this is a very basic question, but I can't find an answer anywhere. I'm computing regression coefficients using either the normal equations or QR decomposition. How can I compute ...
Belmont's user avatar
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23 votes
3 answers
5k views

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 ...
luciano's user avatar
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22 votes
3 answers
41k views

Computing standard error in weighted mean estimation

Suppose that $w_1,w_2,\ldots,w_n$ and $x_1,x_2,...,x_n$ are each drawn i.i.d. from some distributions, with $w_i$ independent of $x_i$. The $w_i$ are strictly positive. You observe all the $w_i$, but ...
shabbychef's user avatar
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22 votes
7 answers
35k views

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 "...
Michael M's user avatar
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21 votes
6 answers
5k views

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 ...
Tor's user avatar
  • 467
21 votes
5 answers
10k views

How to display error bars for cross-over (paired) experiments

The following scenario has become the Most-FAQ in the trio of investigator (I), reviewer/editor (R, not related to CRAN) and me (M) as plot creator. We can assume that (R) is the typical medical big ...
Dieter Menne's user avatar
21 votes
3 answers
30k views

Derivation of the standard error for Pearson's correlation coefficient

I am wondering how to derive the formula for the standard error of Pearson's correlation coefficient which is given in Zar for example as $$ \newcommand{\cov}{{\rm Cov}} \newcommand{\var}{{\rm Var}} \...
R. Carlos's user avatar
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20 votes
1 answer
7k views

When an analytical Jacobian is available, is it better to approximate the Hessian by $J^TJ$, or by finite differences of the Jacobian?

Let's say I'm computing some model parameters my minimizing the sum squared residuals, and I'm assuming my errors are Gaussian. My model produces analytical derivatives, so the optimizer does not need ...
Colin K's user avatar
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19 votes
5 answers
35k views

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)? ...
mary's user avatar
  • 211
19 votes
2 answers
22k views

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) ...
Baz's user avatar
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18 votes
2 answers
24k views

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 ...
Py-ser's user avatar
  • 451
18 votes
2 answers
40k views

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 ...
Daniel Gardiner's user avatar
17 votes
2 answers
26k views

Standard error of a count

I have a dataset of incident cases by season of a rare disease. For example, say there were 180 cases in the spring, 90 in the summer, 45 in the fall, and 210 in the winter. I'm struggling with ...
half-pass's user avatar
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16 votes
3 answers
2k views

Why do we need Bootstrapping?

I'm currently reading Larry Wasserman's "All of Statistics" and puzzled by something he wrote in the chapter about estimating statistical functions of nonparametric models. He wrote "Sometimes we ...
matanc1's user avatar
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16 votes
3 answers
2k views

Why does this excerpt say that unbiased estimation of standard deviation usually isn't relevant?

I was reading on the computation of the unbiased estimation of standard deviation and the source I read stated (...) except in some important situations, the task has little relevance to ...
BYS2's user avatar
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16 votes
2 answers
6k views

If "Standard error" and "Confidence intervals" measure precision of measurement, then what are the measurements of accuracy?

In book "Biostatistics for dummies" in page 40 I read: The standard error (abbreviated SE) is one way to indicate how precise your estimate or measurement of something is. and Confidence ...
vasili111's user avatar
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16 votes
1 answer
16k views

Why does the standard error of the intercept increase the further $\bar x$ is from 0?

The standard error of the intercept term ($\hat{\beta}_0$) in $y=\beta_1x+\beta_0+\varepsilon$ is given by $$SE(\hat{\beta}_0)^2 = \sigma^2\left[\frac{1}{n}+\frac{\bar{x}^2}{\sum_{i=1}^n(x_i-\bar{x})^...
elexhobby's user avatar
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15 votes
3 answers
24k views

Proof for the standard error of parameters in linear regression

In the book Introduction to Statistical Learning, the authors describe the relation between predictor $X$ and response $Y$, by linear regression as: $$ Y = \beta_{0} + \beta_{1}X+\epsilon$$ Here, $\...
Mooncrater's user avatar
15 votes
3 answers
10k views

Adding coefficients to obtain interaction effects - what to do with SEs?

I have a multivariate regression, which includes interactions. For example, to get the estimate of the treatment effect for the poorest quintile I need to add the coefficients from the treatment ...
Sarah  's user avatar
  • 481
14 votes
2 answers
122k views

Extract standard errors of coefficient linear regression R [duplicate]

Possible Duplicate: How do I reference a regression model's coefficient's standard errors? If I have a dataset: ...
Michael's user avatar
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14 votes
4 answers
6k views

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 ...
Henrik's user avatar
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14 votes
1 answer
10k views

Calculate Newey-West standard errors without an lm object in R

I asked this question yesterday on StackOverflow, and got an answer, but we agreed that it seems a bit hackish and there may be a better way to look at it. The question: I would like calculate the ...
Richard Herron's user avatar
13 votes
2 answers
31k views

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 ...
Charlie's user avatar
  • 491
13 votes
3 answers
5k views

Why is the standard error of a proportion, for a given $n$, largest for $p=0.5$?

The standard error of a proportion will be the largest it can be for a given $N$ when the proportion in question is $p=0.5$, and gets smaller the further the proportion is from $0.5$. I can see why ...
edstatsuser's user avatar
13 votes
2 answers
7k views

How do you calculate the standard error of $R^2$

I would like to confirm something. I know that $R^2$ (in a linear regression) can be found by taking the square of Pearson's $r$. The standard error of Pearson's $r$ is calculated using the ...
Andy's user avatar
  • 287
13 votes
1 answer
61k views

Is it correct to use plus or minus symbol before standard deviation?

I have represented standard deviation as "±SD" before in publications. But I like to have opinions on this. Is it appropriate to use the notation '±' with SD ? Or is it only for Standard error ?
Veera's user avatar
  • 549
12 votes
2 answers
12k views

How to calculate the standard error of a proportion using weighted data?

I know the "textbook" estimate of the standard error of a proportion is $SE=\sqrt{\frac{p(1-p)}{n}}$, but does this hold up when the data are weighted?
simudice's user avatar
  • 145
12 votes
2 answers
4k views

Meaning of 2.04 standard errors? Significantly different means when confidence intervals widely overlap?

The image below is from this article in Psychological Science. A colleague pointed out two unusual things about it: According to the caption, the error bars show "±2.04 standard errors, the 95% ...
octern's user avatar
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