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 obtain significance tests (/standard errors) that are still valid after variable selection?

I want to do variable selection via information criteria like the AIC or BIC. However, I am struggling with how I can obtain valid standard errors after doing this such that I can properly interpret ...
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Is there ever a right time to not use Bessel's Correction? [duplicate]

I can not find a clear explanation for when NOT to use Bessel's correction and use N instead of N-1. As I understand it, Bessel's correction would apply to things such as clinical trials, sampling ...
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How to extract standard error from ARIMA output in R?

After I run the arima function in R, I get an output that gives me the coefficients and the standard errors of the coefficients. Pulling the coefficients is easy, ...
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How to find standard error or standard deviation of the percent difference between two prevalence values?

I am having trouble working out how to find the standard error or standard deviation for a column that contains the percentage points difference for two prevalence values. I have general practice ...
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Approximating the number of lines in an arbitrarily large file and calculating error/confidence?

First off, let me know if this is in the wrong stack exchange I wasn't sure where exactly to ask this. Okay so I came up with a scheme to figure out how to how many lines are in an arbitrarily large ...
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How do i predict with standard errors using betareg package in R?

I'm using 'betareg' package in R to perform beta regression. predict() function with se.fit=T is supposed to return standard errors along with the prediction but it doesn't. Is there any other way I ...
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Different Formulas for the Standard Error of Regression Coefficient

Premised that I am no expert in stats or algebra (but I am trying to learn), I have found these two different formulas for the standard error of the regression coefficient. \begin{align} \...
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Calculating the $\alpha$ probability confidence interval of the difference between the means of two data sets using the bootstrap method

Suppose I have a dataset $A$ of size $N_A = m$, and a dataset $B$ of size $N_B = n$. I would like to calculate the confidence interval which with probability $\alpha$ contains the true difference ...
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Standard deviation of sample proportions (standard error) in R

This resource states that the standard deviation of the sampling distribution (the standard error) is equal to: They provide an example where a population has p=0.6 and samples of n=25 are drawn from ...
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37 views

Error bars in a population and subtracting two populations with different error bars

Suppose I want to measure a physical quantity. Let's say that $N$ trials were performed each with individual outcome $x_i,\quad i\in (1,N)$. Then obviously the outcome of the experiment would be the ...
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597 views

Proof of the distribution of the residual standard error [duplicate]

In my notes from university I have written down that the residual standard error (from normal linear regression) has the following distribution $\frac{\hat{\sigma}^2}{\sigma^2}\sim \frac{\chi^{2}_{n-...
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Is the algorithm of calculating SEs of beta coefficients calculated by the nlme gls finally fixed?

I can read here: https://www4.stat.ncsu.edu/~davidian/st732/examples/dental_pa.R and here: https://math.unm.edu/~luyan/stat57918/week14.pdf that: WARNING: There is a MISTAKE in gls(), and it DOES ...
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120 views

Discrepancy between coefficient and mean difference in predicted values of logistic regression

I'm using a poisson-binominal logsitic regression model to analyze a list experiment (item count technique) where the outcome variable is a binary response of the respondent to a sensitive item (e.g., ...
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Standard error in estimated marginal means are all the same

I use the package emmeans to calculate estimated marginal means and I don't know why the standard errors are equal within the factors: ...
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1answer
167 views

quantitative relation between standard error of measurement and validity

Is there a function to estimate the gain in predictive validity with the decrease of the standard error of measurement? E.g. If the short version of a test has predictive validity of 0.35 and ...
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Interpreting standard errors of linear regression with logged dependent variable

I'm running a linear regression with a logged dependent variable. This is the only variable in the model that is logged. For interpretation, I've exponentiated the coefficients, subtracted one, and ...
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How is standard error of regression coefficient calculated (quadratic and logit)?

I was wondering what formula is used to calculate the standard error of quadratic and logit regression coefficients. I don't have much knowledge on statistics and I have had trouble finding sources ...
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1answer
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Can the Central Limit Theorem be used in this case? [closed]

A student investigating study habits asks a simple random sample of 16 students at her large high school how many minutes they spent on their Math homework the previous night. Suppose the actual ...
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why there different standard error form in Hypothesis testing

In Hypothesis testing,Comparison of a sample mean with an assigned population mean: $$Z=\frac{\overline x-\mu_0}{\frac{\sigma}{\sqrt n}}\text{ Or }Z=\frac{\overline x-\mu_0}{\frac{s}{\sqrt n}}$$ But ...
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Standard error higher than coefficient and SE of regression

I am having some problems with my regression where the SE is higher than the coefficient and sometimes even larger than the SE of regression. I am wondering what might be the underlying problem or is ...
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130 views

Formula to Calculate Confidence Interval of Marginal Means

What is the formula for the marginal means confidence interval in a regression analysis? Let us have the following regression $Y = b_0 + b_1X + b_2Z + b_3 XZ + b_4 Cov_1 + b_5 Cov_2$ If I get it ...
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How to calculate the standard error of a proportion estimate under misclassification?

Let's take a sample of size n from an infinite population. The population comes in three kinds ('red', 'black' and 'blue') and we want to know the proportions of each kind. For 'red' we would have $p =...
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1answer
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Determining standard deviations and standard errors for non-Gaussian distributions

I have several questions about constructing error bars and using them as weights in the context of fitting, or indeed any kind of weighted statistic -- especially with regards to error and noise ...
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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, $\...
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Calculating parameter's SE of poisson regression by hand in R

I'd like to know how to calculate by hand parameter's Standard Error of poisson regression in R(0.4749, 0.1593). I could get the values by the following program, but I'd like to know the more detail ...
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Comparison of parameters across multiple panel data regressions

I am estimating a set of ten different regression using two different samples. The first sample includes all observations in the panel while the second panel is restricted since observations prior to ...
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Calculating standard error of coefficients in segmented regression

Consider the following equation resulted from segmented regression: $$\hat y_i = \begin{cases} \hat\beta_1 x_i + (\hat\beta_0 - \hat\beta_1 \cdot c) &\text{if } x_i \le c \\ \hat\beta_2x_i + (\hat\...
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Cross validation from Jacobian matrix of likelihood for glm(poisson, identity)

The difference of Standard Error between glm(y~x, family=poisson(link=identity)) and optim() in R Following the above question... And actually, I have an another question now. I could cross ...
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Are there special techniques to combine estimates and standard errors from a complex discrete-event simulation?

My discrete-event simulation works as follows: A sample is drawn from a simulated population The simulation is run a few times for that sample Each run produces k estimates and their corresponding ...
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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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On the Mathematical Interpretation of Standard Error

:) My colleagues are using Standard Error in a way that I do not find intuitive. Here is the situation we are dealing with: We take the average for the last 12 months worth of sales data. We take ...
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Should I use Student's t-distribution to evaluate my measurement's confidence interval?

I'm an experimental physicist who mainly needs statistics for the calculation of uncertainties/confidence intervals. Since my results are usually normally distributed, I simply take $N$ measurements ...
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The difference of Standard Error between glm(y~x, family=poisson(link=identity)) and optim() in R

I'm executing the following program glm(y~x, family=poisson(link=identity)). I can't understand the difference of SE from glm(y~x, family=poisson(link=identity)) and optim(). Please give me some ...
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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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1answer
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How can the clustered robust standard errors be smaller than the model based ones?

I ran a GEE model and I used it to check the difference between the empirical standard errors and the model-based one. For almost the variables, the empirical standard error was greater than the OLS ...
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1answer
199 views

Standard error of components of coefficient estimate in linear regression

As I understand it, $\text{standard error} = \frac{\text{standard deviation}}{\sqrt{n}}$, where $n$ is the number of observations. I also know that $cov(\hat{\beta}) = \sigma^{2}(X^{T}X)^{-1}$; this ...
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1answer
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Overview Standard Error Correction in Time Series / Panel Literature

In microeconometrics, the time component is usually short (meaning that $T$ is fixed in $t=1,\ldots,T$). Serial correlation is here usually just seen as a negligible issue affecting the standard ...
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What is the estimate of $\mathrm{Var}\left(\frac{nM}{X}\right)$ where $X$ is hypergeometric?

Consider the classical capture-recapture method, where we are to estimate the number of deer (say) in a sanctuary. So a certain number of deer is captured, tagged and released. Then a random sample 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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How to interpret the results of this conditional model?

I have a conditional model such as: y= b0 + b1*a + b2*previous1 Previous1 contains all the measurements of ...
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1answer
45 views

multiple regression coefficients - Standard error of intercept

I am implementing an R-type summary() function in python with the restriction to exclude use of scientific libraries. (assignment) I found this https://www.nd.edu/~rwilliam/stats1/x91.pdf material ...
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HAC Confidence Interval in Interrupted Time Series

I have a dataset about quarterly deaths over the last 18 years (Q1 2000-Q4 2018). In Q3 2004 there was a policy change which might had lead to an increase in the number of deaths. I fitted an ...
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Why is the denominator of z-score for linear regression coefficients called standard error?

In machine learning and linear regression applications, the z-value is given by the following formula: $$z_j = \frac{\beta_j}{\hat{\sigma}\sqrt{v_j}}$$ where $$\hat{\sigma}^2 = \frac{1}{N-p-1}\sum_{...
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Why do t-test use standard error and not standard deviation?

Maybe the solution is obvious, but I don't fully understand why. Is it related with the fact that the SE takes into account the sample size?
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1answer
45 views

Standard error in multiple regression

I want to calculate standard error of y-intercept or constant term in the multiple regression equation $Y = b_0 + b_1X_1 + b_2X_2$ I found the formula for standard error estimation of co-efficient $...
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Does a lower standard error of coefficient in linear regression means a better sampling method and a reliable coefficient?

Considering the following senario: We want to user linear regression to find the relationship between two variables x and y. Since we can't access the population, we need to use some sampling method ...
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How to correct standard errors for heterogeneity and intra-group correlation?

I got my article manuscript back from review and one notion from a reviewer was that in my analyses "[s]tandard errors are not corrected for heterogeneity or intra-group correlation", s/he apparently ...
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How to build standard error and confidence intervals from Buckland variance estimator after variable selection

In this paper https://www.sciencedirect.com/science/article/pii/S0167947307003957 it is shown how to build an estimator of the variance of estimates computed after variable selection. It evaluates ...
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3k views

Overlapping standard errors and statistical significance

I have a paired data set which I have placed into $x$ and $y$ columns where $x$ are the control values and $y$ are the values following drug treatment. $N=10$ for both $x$ and $y$ columns as they are ...
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Standard error of the $n^n$ bootstrap means

I need to show that the standard error of the $n^n$ bootstrap means is $SE^*(\bar{Y^*}) = \frac{S\sqrt{n-1}}{n}$, where $\bar{Y^*}$ is the sample mean of a randomly drawn bootstrap sample, and $S^2 = \...