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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Error in the slope of a linear regression
I am trying to find the uncertainty/error in the slope of a linear regression of a data set where the data contain standard errors. However, searching for this online is very confusing as there are ...
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Estimating the contribution of each feature to regression model prediction variance
I have trained a multiregression model using non-linear SVM, and got quite good metrics, with no big differences between test (20% data) and train (80% data) metrics.
The following are the test/train ...
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Why doesn't the standard error depend on the number of samples taken?
I don't understand why the standard error of the mean does not depend on the number of samples of the mean that you take. To clarify, let's use a simplified version of the example in this answer. Two ...
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OLS model vs Mixed model in a between/within-effect model: mathematical notation for slopes and standard error
Given $N/2$ pairs of individuals clustered in $J=N/2$ groups, where $N$ is the total number of individuals, I consider:
An OLS model:
\begin{align}
y_{ij} = \beta_{W}(X_{ij}-X_{sj}) + \gamma X_{sj} + \...
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Why do tidycmprsk::crr() and survival::coxph() on survival::finegray() data give identical coefficients but different SEs, CIs and p-values?
I’m comparing the results of a Fine–Gray competing risks regression using tidycmprsk::crr() and a Cox model fitted to the Fine–Gray expanded data created with ...
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Bias in standard error of regression slope with not-independent data and effective sample size
Consider a sample of $N/2$ pairs of individuals. Each pair belongs to a group $j$.
For each individual $i$ from the $N$ sample, I measure two variables ($y_{i}$ and $x_{i}$) and the average per group $...
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Examining country-level effects based on individual-level data combined with country-level data
I am new to working with country-level effects in comparative OLS regression with individual-level data. Are there any good resources for this?
Suppose my dependent variable is social integration (an ...
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What are the limitations of AUC/ROC when used to evaluate effects over time (e.g., drug, electrophysiological signals) in inferential models?
I’ve been reading some papers in the neuroscience field, and I don’t quite understand the widespread use of AUC/ROC to test for group differences when analyzing neuronal firing over a range of seconds ...
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Standardization of regression coefficients and standard errors with different outcome variables
With reference to below links, I would like to confirm the following:
When the outcome variable is continuous, and is scaled (assume linear model),
When the outcome variable is binary (assume ...
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How accurate are the standard error formulas to find the standard deviation of the sampling distribution of a statistic?
1. Definitions
The standard error of a statistic is an estimate of the standard deviation of the sampling distribution of that statistic.
The sampling probability distribution of a statistic is the ...
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How can the standard error measure how accurately a sample represents the population, when we don’t have access to the population’s data?
If I got it correct, the standard error is a statistic that measures the variability of a sample’s data and how accurately a statistic represents the corresponding parameter.
Please suggest any ...
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Converting the standard errors from an IRF into a cumulative IRF
how can i sum up the standard errors of an IRF into a cumulative IRF please? Is there some analytic formula that I can apply? Below is the example from STATA, where example 1 shows the period-by-...
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Getting the confidence interval of the mean of values, each with its own SE
Assume I have several estimates each with its own SE. If I compute the mean of those estimates, how can I compute the final CI of the mean?
This is how I would do it if those values were random ...
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How to determine if 2 Pearson correlation coefficients are significantly different? (using Bonett's SE approximation)
I came across these solutions, but @Firebug's one doesn't seem to be using Bonett's approximation for the SE. Would it be possible to do something like this? Why is he converting r to z space, when we ...
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Standard errors when implementing the 'Poisson Trick' (estimating multinomial from two poisson regressions)
The 'Poisson Trick' allows us to estimate a multinomial logit model using multiple Poisson regressions (see section 6.2.5 in these notes by German Rodriguez https://grodri.github.io/glms/notes/c6.pdf)....
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Standard Error on the Circular Mean?
According to this article by Lee 2010 (paywalled) : https://wires.onlinelibrary.wiley.com/doi/abs/10.1002/wics.98
the standard error on the circular mean is given by :
Std Error on circ mean = $\delta/...
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Is the "Jackknife estimator of variance" the variance or the squared standard error?
The Jackknife estimate for the variance is
$$\text{var}_\text{jack}(\theta) = \frac{n-1}{n}\sum(S_{(i)} - S_{(\cdot)})^2$$
well known, e.g. from Efron & Stein, "The Jackknife estimate of ...
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Error propagation when taking the mean of uncertain variables
I have a set of N observations X and their corresponding standard deviations S. I calculate the mean of these observations, but I need the associated error as well. My current approach, which I'm ...
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Why is the residual standard error a measure of the standard deviation of $\epsilon$? [duplicate]
I have been working through the book "Introduction to Statistical Learning". Here is how I have come to understand a regression problem is set up:
We choose to do a simple linear regression....
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Standard error of the root mean squared predition error (RMSE) and its use in simulation studies of prediction models
In the context of statistical prediction models, one is often interested in the predictive accuracy of the model. A common model choice is the root mean squared error (RMSE), which is also also called ...
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Converting poll results to odds of specific outcomes?
Given a poll result for a yes/no vote, how do you determine the odds yes will receive less-than X% of the vote?
For example, given the following:
sample size n
95% confidence margin of error ...
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How to estimate the variance of a vector that is a mixture of known and modeled values?
Problem
Imagine we have $X^k_i$, where $i = 1, 2, 3, ..., N$ and $k \in \{train, test, modeled\}$. Each $x^{train}_i$ was used to train a model from covariates to predict $x_i$, and each $X^{test}_i$ ...
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How to get standard error for Pearson r from confidence intervals? [duplicate]
I use this formula to obtain the confidence intervals:
...
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What is SD, SE, and Coverage Probability in research report?
When I read paper, in the simulation study, I often see they report the table similar as follows
I think
the estimate is the average over 2000 simulation runs
the sd is the standard deviation of the ...
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Standard error of $x_1+x_2 + \cdots + x_n$
I'm trying to find the confidence interval of $x_1+x_2 + \cdots + x_n$, which means I am supposed to find its standard error.
I guess that if the standard errors of $\sigma_i$, and they are ...
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Nested linear model comparison and regression parameter testing in LOOCV setting?
How do I obtain a reasonable parameter estimate (regression beta) for the single predictor of interest in a multiple regression model and appropriate standard errors for this estimate using holdout ...
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Using sample estimates of parameters and their standard errors without knowing their dependence from each other
In scientific papers of my field, the results of regression analysis are often reported in such way: if function $f$ of independent variable $X$ (or multiple variables) and parameters $β_j$ is fitted ...
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Comparing two odds ratios without the original data
My question is the same as this, but I do not have access to the original data. I have two estimates of a particular odds ratio $\mathrm{OR} = \exp(\beta_i)$ with confidence intervals from logistic ...
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Which one is the right SE and why?
I was not sure if it was more of a stackoverflow question, but I think here might be better, as I am trying to understand how to identify the right answer.
I created a small reproducible example:
<...
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Why is standard error always zero
Hypothetically, I want to determine if a coin will be heads every time I flip it. So I design an experiment with $N=5$. So I toss it 5 times and I get 5 heads.
I want to measure my confidence ...
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Why does duplicating a dataset reduce the variance of parameter by 1/2 in OLS? [duplicate]
Say I'm running OLS on a dataset $D$ and a linear regression model $y = \beta_0 + \beta_1x + \epsilon$. If I now duplicate my dataset to obtain $D'$ and run OLS again I get $y = \beta_0' + \beta_1'x + ...
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Propagate degrees of freedom from lmer model
I am not sure what are the correct degrees of freedom to use. I am interested in calculating whether the ratio of two slopes is significantly different than '3'.
I ran a linear mixed effect model such ...
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Should I scale point size (area) proportion to 1/standard error or 1/SE^2?
I have a bunch of estimates that I want to plot on the y-axis vs. something else on x-axis. I want to convey a sense of uncertainty in each point (the x-axis value is known, the y-axis value is ...
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Correcting factor for error estimation with weighted logistic regression on duplicated data
Suppose a dataset is duplicated but the 1st copy is assigned one set of probability weights $w_1$ (not tied to sampling) and the 2nd copy has another set of weights $w_2$ where the weights are derived ...
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Why do we define the standard error to ignore bias (unlike MSE which includes bias)?
Why is standard error of an estimator $\hat \theta$ defined as $$se = \sqrt{Var(\hat \theta)}$$ and not $$se = \sqrt {MSE(\hat \theta)} = \sqrt{Bias^2(\hat \theta) + Var(\hat \theta)}.$$
That is, ...
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What is the significance of this equation for safely estimating a lower-bound value?
I have encountered a formula for safely estimating a lower-bound value of some property from a number of test results. In our field, we often have less than 10 test results (which isn't even enough to ...
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What is the relationship between OR, se, and CI
Apologies if this is a duplicate question, but I have been unable to find a clear answer.
What is the relationship between Odds Ratio, standard error, and confidence intervals?
I try to do a meta-...
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Wald test with permutation standard error?
Many statistical tests are based on a Wald-like z-statistic: $z = \frac{\hat{\theta} - \theta_0}{\text{SE}(\hat{\theta})}$ where $\theta$ is the parameter of interest, $\theta_0$ is the value under ...
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SE of a product
How can I compute the standard error from this formula below if each variable $X_i$ is the correlation coefficient of samples with a different sample size.
$$\begin{align}
\operatorname{var}(X_1\cdots ...
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Unreliability attenuation correction affects Cohen's d and its standard error. How do I use uncertainty propagation to estimate the correct SE?
Assume I am using Cohen's d to quantify some kind of effect. Since Cohen's d is defined (simplified) as $$d = \frac{MD}{\sigma_x}$$ $MD$ reflects a differences in means, which is standardized by the ...
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Confidence interval - CLT, beginner level
I'm taking an online course about statistics and more precisely about the confidence interval.
Below is an exercise in which they are trying to estimate the number of shoes that can be sold for each ...
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Standard error is too small on "perfect" data
While studying linear regression, I encountered this weird situation.
I am fitting a data to a linear model $\beta_0 + \beta_1 x$, and running a Wald test to check if $H_0: \beta_0 = 0$. Here is a ...
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Figure that shows both mean, standard deviation, and standard error?
I’m novice working with a set of behavior data (e.g. duration) that’s non-normal due to A LOT of variability. The data also has a lot of zeroes, which is why I plan to present it using means as ...
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How to compute a pooled standard error [duplicate]
I am comparing $m$ methods across $d$ datasets. Through my experiments I have obtained the mean, the standard deviation, and the standard error for all methods and all datasets, hence I have the means
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Repeated measurements on the right hand side of the regression equation
Suppose I observe an outcome $Y$ (e.g., survival binary) and I have variables $X_1, X_2, \dots, X_m$ that all refer to the same entity (e.g., health condition assessed by rater $1, 2, \dots, m$). So ...
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Clarifying the default "standard error" for error bars in Microsoft Excel/Powerpoint plots (calculated without N or SD) [closed]
I have noticed that Excel allows you to toggle "error bars" for any given plot and one of the options is to have the error bars denote standard errors. This is peculiar since if you do a ...
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Error propagation in variance calculation
Let's assume that I have $n$ measurements $\mathbf{x} = (x_1, ..., x_n)$ of a given quantity $X$, e.g. regression coefficients. Each $x_i$ has a corresponding standard error $SE_i$. I'd like to ...
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How do I compute the Standard Error for summed percentages?
I feel profoundly stupid for having to ask this question--it feels like the answer should be obvious, or at the very least that it should be easy to find on the internet, but so far I have been unable ...
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Simulate difference-in-difference process with correlated errors
I am trying to create a dgp for difference-in-difference estimation that requires clustering of standard errors in the estimation step for correct inference. I envision a process with two groups and ...
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Literature reference for variance of the variance of the binomial proportion
If K is the number of successes after $n$ Bernoulli trials with success probability $p$, it follows the binomial distribution: K $\sim$ Bin(n, p). The estimated proportion $\hat{p}= \frac{K}{n}$ is ...
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