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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Formula for variance of an individual regressor in multiple regression context with non-spherical disturbances

if I run the regression: $Y_i= \sum_{j=0}^{k} \beta_j x_{i,j} + \epsilon_i$, where $x_{i,0}$ = 1, i.e. the intercept term. My understanding, is from the Frisch-Waugh-Lovell theorem, the formula for $\...
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Confidence interval of the sum or product of multiple sample means

Given two sample means ($\bar x_1, \bar x_2$) and population standard deviations ($\sigma_1, \sigma_2$) of two independent variables ($x_1, x_2$), the standard deviation ($\sigma_3$) of the sum or ...
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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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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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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 ...
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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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Can we calculate the standard error of prediction just based on simple linear regression output?

The standard error of prediction in simple linear regression is $\hat\sigma\sqrt{1/n+(x_j-\bar{x})^2/\Sigma{(x_i-\bar{x})^2}}$. My question is to calculate the standard error of prediction for $pop=...
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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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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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How to calculate the standard error of the mean for circular data?

I followed the suggestions here to calculate the SD from circular data in the R circular package: How to calculate standard deviation of circular data However, I need the SE of the mean for a number ...
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Does estimated standard error of the mean says something about the population mean?

The "normal" standard error of the mean (SEM) is the population standard deviation divided by the square root of the sample size. Wikipedia states that the SEM is an estimate of how far the sample ...
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Why are the upper bounds of my poisson gam so high?

Question I am wondering why, when I run a gam() with family = poisson in R. I get really ...
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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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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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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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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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Help with Difference in Difference Variance Estimator (SEO Experimentation)

I found the following article https://medium.com/airbnb-engineering/experimentation-measurement-for-search-engine-optimization-b64136629760 regarding search engine optimization (SEO) frameworks. It ...
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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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Calculating the Standard Error and Confidence Interval for Cohen's Quadratic Kappa

I need to evaluate the performance of a machine learning application. One of the evaluation metrics chosen is Cohen's Quadratic Kappa. I found this Python tutorial on how to calculate Cohen's ...
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How can I compute the standard error of the Wald estimator?

According to Cameron and Trivedi Microeconometrics 2006, page 98-99, the Wald estimator can be written : $$ \widehat{\beta}_{Wald} = \frac{(\bar{y_1} - \bar{y_0})}{(\bar{x_1} - \bar{x_0})} $$ with :...
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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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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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Can I add a random effect accounting for huge differences within one factor?

The Experiment and Data The experiment I am working on has the following design: A B C D E F B A D E F C A B E F C D B A F C D E Each Letter represents a different level of ...
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Log odds Standard Error?

I am reading a paper on how the authors calculate the variance/standard deviation of what appears to be log(odds). The paper is a medical paper (Discontinuation of Oral Antivirals in Chronic Hepatitis ...
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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 of the estimate in phylogenetic generalized least squares regression

I have a dataset of log-transformed data (length and body weights) that I am trying to create a regression equation for in the hope of predicting new data. The residuals of my dataset have a high ...
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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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Explaining the change of the standard errors in the regression model

Use the odor dataset with odor as the response and "temp" as a predictor. Consider all possible models that also include all, some, or none of the other two predictors. Report the ...
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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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Standard errors with overlapping observations

Consider two samples $x$ and $y$ both with $N$ observations. I build overlapping observations $x^*$ and $y^*$, such as: for $h>1$, and for any $i=1,...,N-h+1$: $x^*_i = f(x_i,x_{i+1},...,x_{i+h-1})$...
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Explanation for regression coefficient $\beta= 0$ and standard error $\sigma(\beta) = 0$

one of the coefficients in an OLS regression turned out zero and its Standard error is zero as well. Would you be suspicious of this result? Is there any possible explanation for this?
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How to characterize variance with large datasets

I have a large dataset (> 100,000 rows) of ecological data. In some of my first attempts to visualize the data, I used bar plots with calculated means and error bars (see below plots). My go-to for ...
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160 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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Non-independence of trial likelihoods in a staircase procedure?

In psychometrics, we often want to know, for instance, a given participants' perceptual threshold: the intensity of a stimulus that they can detect 50% of the time. It's common to use staircase ...
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Question about standard errors of regressions/means

I just had a question about standard errors of sampling statistics/estimators. Is for example, the standard error of a regression coefficient, a true population value, that is estimated? Should I ...
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How do I calculate a margin of error when there is no standard deviation to calculate?

I have a graph that I was asked to add error bars to, but I'm not exactly sure how to calculate them. The data consists of measurements from two different groups, and the graph is a line graph where ...
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Confidence interval for the difference of two fitted values from a linear regression model

Assume that we have a linear regression model of the form $y=\beta_0 + f_1(x_1) + f_2(x_2) + \ldots + f_n(x_n) + \epsilon$. I have written $f(x)$ to indicate that we could model the relationship ...
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OLS regression problem in R, where intercept is function of the other parameters [duplicate]

I'm having problems doing OLS in R using the lm() function on the following linear model: $Y_t = \bar{Y} \cdot (1-a-b-c) + a \cdot X_{1t} + b \cdot X_{2t} + c \cdot ...
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CLT - Adding small samples to one big sample

According to CLT, the SE is the SD of the distribution of several samples means. This SE depends on each sample mean, the SD of each sample and N (the size of each sample which I test). Since there ...
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Zero-inflated negative binomial model standard error too high?

I've been trying to analyze count data for ant foragers visiting on extrafloral nectaries with R. My data is both overdispersed and zero-inflated, so I used a zero-inflated negative binomial model to ...
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Where do the values for t tables come from? [duplicate]

For a given normal distribution, figuring out what percentage of scores fall between two bounds is straight forward. Calculate the z score and look it up on a z table. Or one can also evaluate the ...
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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 differentiate constructing confidence intervals?

I am a bit confused when looking at the confidence interval formula for one of my class and I am looking to see if anyone can clarify it. When constructing, let's say, a 95% confidence interval of a ...
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Multiple regression with dummy variables: identical VIF, Tolerance and Standard Error

Im fairly new to stats and regression but trying to learn and I've come across something that doesn't seem right to me. I have used dummy variables to run a multiple regression model to predict the ...
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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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How do I obtain the standard errors for Ornstein Uhlenbeck parameter estimates?

I have used least squares estimation to obtain estimates for parameters to be used in Ornstein Uhlenbeck process. Now, I would like to compute the standard errors of estimates. $𝑑𝑆𝑑=πœ†(πœ‡βˆ’π‘†π‘‘)𝑑𝑑+...
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Trying to calculate error for equation with dependent variables

I have the following equation for which I am trying to calculate the error in: $$v=b+c/t$$ $t$ is error-less but $b$ and $c$ depend on each other and therefore I cannot use the standard addition in ...
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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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