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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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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109 votes
4 answers
114k 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?
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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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22 votes
3 answers
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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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17 votes
2 answers
18k 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 ...
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5 votes
2 answers
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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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67 votes
6 answers
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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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32 votes
1 answer
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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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34 votes
2 answers
176k 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\...
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15 votes
3 answers
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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 ...
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24 votes
1 answer
66k 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 ...
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9 votes
2 answers
6k views

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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9 votes
2 answers
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Why autocorrelation affects OLS coefficient standard errors?

It seems that OLS residuals autocorrelation is not always an issue, depending on the problem at hand. But why residuals autocorrelation would affect the coefficient standard errors? From the Wikipedia ...
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15 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})^...
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2 answers
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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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12 votes
2 answers
3k 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% ...
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42 votes
4 answers
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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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38 votes
2 answers
54k 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 ...
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19 votes
2 answers
33k 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 ...
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25 votes
6 answers
64k 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 ...
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16 votes
3 answers
1k 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 ...
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15 votes
4 answers
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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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24 votes
3 answers
14k 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 ...
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18 votes
2 answers
17k 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) ...
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13 votes
2 answers
26k 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 ...
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9 votes
2 answers
25k 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}} \...
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25 votes
3 answers
38k 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' ...
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27 votes
1 answer
86k views

Converting standard error to standard deviation?

Is it sensible to convert standard error to standard deviation? And if so, is this formula appropriate? $$SE = \frac{SD}{\sqrt{N}}$$
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14 votes
4 answers
5k 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 ...
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9 votes
2 answers
5k views

Confidence interval for the median

I have a set of values ${x_i}, i=1, \dots ,N$ of which I calculate the median M. I was wondering how I could calculate the error on this estimation. On the net I found that it can be calculated as $1....
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12 votes
2 answers
4k views

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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9 votes
3 answers
18k views

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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6 votes
3 answers
1k views

How to get the standard error of linear regression parameters?

I am reading through the textbook An introduction to Statistical learning with Applications in R, and got stuck: When doing linear regression, we can write the relation as: $$Y = \beta_0 + \beta_1X + \...
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9 votes
2 answers
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How do regression results change after standardization, as a general rule?

Based on the simulation below, it appears that standardizing all variables in a data set affects OLS results in the following ways: Coefficient estimates change Standard errors change P-values ...
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6 votes
1 answer
4k views

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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64 votes
4 answers
122k 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 ...
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36 votes
3 answers
88k 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 ...
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41 votes
1 answer
7k 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 ...
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20 votes
5 answers
9k 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 ...
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9 votes
2 answers
9k views

How do you calculate standard errors for a transformation of the MLE?

I need to make inference about a positive parameter $p$. To acomodate the positiveness I reparametrized $p=\exp(q)$. Using MLE routine I computed point estimate and s.e for $q$. The invariance ...
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4 votes
1 answer
10k views

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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11 votes
2 answers
10k 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?
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6 votes
2 answers
46k views

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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3 votes
1 answer
7k views

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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8 votes
1 answer
2k views

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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7 votes
4 answers
8k views

Standard errors for covariance estimate in R

This is a very simple question: how does one get the standard error for the covariance estimate in R? I estimate the covariance using the cov function but there ...
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5 votes
3 answers
26k views

How to calculate SE of an odds ratio

If one is calculating odds ratio with a,b,c and d counts, I believe variance of log(OR) is given by var_log_OR = (1/a + 1/b + 1/c + 1/d) Hence one can calculate ...
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  • 9,183
5 votes
2 answers
1k views

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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