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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Calculating mean confidence intervals from a sample with low SEM

Given that: I. The distribution of means of large enough samples converge to a normal distribution (by CLT) II. The Standard Error of the Mean (SEM) of a sample approaches the Standard Deviation (SD) ...
8 votes
2 answers
697 views

Does the Central Limit Theorem hold if you replace the true variance with the sample variance?

I'm currently doing a self-study of Wasserman's All of Statistics. Theorem 5.10 states that for $X_1, ..., X_n$ IID with mean $\mu$ and variance $\sigma^2$, we have $\frac{\sqrt{n}(\bar{X}_n - \mu)}{...
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Three versions of the independent two sample t-test (and R)

This post concerns three versions of the independent two sample t-test: Student's t-test uses a pooled standard deviation in the denominator (all equations are shamelessly copied from Wikipedia - ...
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1 answer
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What if sample size is larger than population size?

I read something about standard error, which tells that sample mean is not accurate estimation because we do not sample full population of size N. But, what if sample size n = N or exceeds N, i.e. n > ...
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Different results when calculating confidence interval

I'm trying to replicate the results from a paper which states: "Estimated overall accuracy is 79.6% with a standard error of 5.1% which would yield a 95% confidence interval of 69.5% to 89.7%.&...
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1 answer
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what is the difference between Standard error of the means vs Sampling error?

I am confused after learning about the different terms. I understood Standard error of the means to be the Standard Deviation of the sample means, whilst Sampling error is the Standard Deviation ...
1 vote
1 answer
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Adjust results for a systematic error

My model identifies objects with a specific quality in a large population. I tested it on a sample of 500 and found that it fails to identify about 7% of the objects (false negatives) due to some ...
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1 answer
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Convert T-values from Poisson regression to Standard Errors

I am trying to summarize results from an article for a review (available for free here, I am looking at table 3), and thus want to find Standard Errors (SE) to compute confidence intervals. The ...
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1 answer
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What is the connection between SEM and confidence interval

I have a results of sessions where for each $i\in\mathbb N$ the $i$'s session contains $n_i$ Bernoulli trials. I want to analyze the narrowness of my sample distribution. From online reading I see ...
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Number of samples required to get mean of unknown function up to some standard error

So I have some code simulating the behavior of a complex system. The system works perfectly (with a "fidelity" of $f=1$) for some parameter $\beta=0$. For other values of $\beta$ the ...
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Can estimated values with wide confidence intervals be used calculate association or correlation coefficients?

I want to test for an association between socioeconomic deprivation and death rates. My data are raw death counts and deprivation ranks for a set of small geographic areas. Some areas have very low ...
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1 answer
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Computing standard errors when using stratified sampling

I am trying to understand the following formula for the standard error of the population mean as estimated through stratified sampling. On the CRAN site, the formula given is $$ S_{\bar{x}_{\textit{...
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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 \mathrm{Cov}_1 + b_5 \mathrm{Cov}_2$...
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Spatial Error Model vs Conley standard errors

What is the difference (pros and cons) of using an OLS with conley standard errors and a spatial error model? Is there a recommendation for when you should use one over the other? Thanks!
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Frisch-Waugh-Lovell Theorem: Different standard errors

The Frisch-Waugh-Lovell theorem states that the b1 vector (and e vector) in Y = X_1 * b_1 + X_2 * b_2 + e are equal to the b* vector (and e* vector) in M_2 * Y = M_2 * X_1 * b* + e*, with M_2 = I - ...
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Propagation of standard error of fit through to the average and standard deviation of replicates

I am using an equation to fit measured data. I have measured multiple replicates for each condition, each of which is then individually fitted to this equation. Once the data are fitted I obtain a ...
7 votes
2 answers
937 views

Standard Error of the cumulative value for time series

I have two time series, as in the picture below. The data was gathered experimentally. A practical example could be a measured mass flow rate, where I measure the mass flow rate over a certain time ...
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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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Estimate standard error due to reduction in sampling rate for a time series data

I have a large set of time series data representing the progression of a variable during an industrial production process collecting at a certain frequency at regular intervals. The mean of each curve ...
6 votes
1 answer
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Standard errors in linear mixed models

I'm trying to understand how standard errors for the parameter estimates are calculated in linear mixed models, and why I don't get the same output with different methods. I've made the following ...
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1 answer
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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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2 answers
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Why is standard error of the mean always calculated from the population variance?

The standard error of the mean is often calculated with the formula $\sqrt{\sigma^2 / n}$, which uses population variance (or an estimate of it). However, standard error of the mean is defined as the ...
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Does it make sense to calculate Relative Standard Error using population parameters?

Relative Standard Error (RSE) is one of the main measures to assess the quality of survey indicators. If only sample data are available, RSE can be computed using estimated mean $\bar{y}$ and ...
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1 answer
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Is the 'Std. Error' provided by lmer in lme4 actually Standard Deviation?

I have been working with lmer in lme4, and wanted to construct a density curve of the slopes produced by my model (rather than just confidence intervals). The model output of lmer produces a slope, ...
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1 answer
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Clustering Standard Errors for Panel Data with multiple groupings

I have a Group-Firm-Year panel data set (i.e., multiple firms make up a group). Suppose I have exogenous variation at the group level over time. In a panel regression with firm and time fixed effects ...
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1 answer
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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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Computing and simulating average marginal effect standard error using Delta Method with reproducible codes

I am trying to simulate calculating Average Marginal Effects on a basic linear regression with interaction on a binary variable and compare the empirical standard deviation I get from simulations and ...
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Standard errors of Monte Carlo plus linear combination

I'm using Monte Carlo to estimate some quantity $V(x)$. To get an approximation of $V'(x)$ I would use the following $$ V'(x)\approx\frac{V(x+h)-V(x-h)}{2h} $$ so I can simply evaluate it with two ...
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1 answer
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Why Does Standard Error for Individual Predictors Not Increase in Multilevel Modeling?

I have been trying to teach myself multilevel modeling through R and I am relying on the W. Holmes Finch book. According to them, and any resources in general, not doing multilevel modeling causes an ...
2 votes
1 answer
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Standard Errors for Numerical Optimization using Chi-Square Objective Function

I am using a minimum chi-square estimator technique to estimate a set of parameters using some sample data (essentially, finding what set of model parameters minimize the difference between observed ...
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1 answer
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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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Should we always minimize squared deviations if we want to find the dependency of mean on features?

It is known that for any distribution a minimization of squared deviations from a value $c$ gives mean of the distribution. In other words, if we generate many values $y_i$ using our distribution, and ...
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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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1 answer
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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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Bootstrap Standard Error vs Standard Error from sample

For doing inference of a population parameter from a sample, under which examples is better to calculate the standard error using bootstrap distribution of the mean than directly using the standard ...
5 votes
2 answers
3k views

Appropriate error bars for repeated-measurements designs

I conducted a t-test / ANOVA (both repeated measurements) and I want to represent the difference in the mean via a bar graph. There are several different views about the appropriate error bars for ...
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Calculation of the standard deviation of the power in dB

I wanted to find out the stability of my system so for that i calculated standard deviation of power samples data which is in dB but I am not sure whether i have used correct formula or not. As far as ...
20 votes
6 answers
4k 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 ...
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1 answer
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Is it logical to report standard deviation of the coefficient of Regression model?

I had determined the coefficient for the variables using Multinomial Logit model. The software reported coefficient, t-value and standard error for the variable. One of my senior want to include ...
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Standard error between experiments

I need to open a new question regarding the already largely discussed "standard error". I have performed twice the same experiment on the same area. Each experiment includes the measurements ...
5 votes
1 answer
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Interpreting standard error for dummy variables in linear regression models

Is there any way to interpret the standard error of dummy variables created to represent a categorical variable in a linear regresion model? I saw a great mathematical explanation here, but I am still ...
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Is it safe to say that this set of data is constant with x because of their standard deviation?

Is it safe to say that Y does not change with X because if you take the mean of Y and calculate the standard deviation all of the values fall with 1 standard deviation ?
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Standard error of estimated sum or product mean

Updated question: Given two sample means ($\bar X, \bar Y$) and sample standard deviations ($S_X, S_Y$) with different sample sizes ($n_X, n_Y$), I want to calculate the standard errors ($SE_\theta, ...
1 vote
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Standard error for a difference-in-difference estimate

I am trying to calculate a difference-in-difference estimate. I have a binary outcome variable, and have estimated risk differences for my intervention and control groups. If we take an example where: ...
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How to calculate the Fisher Information Matrix in GARCH?

How to calculate the Fisher Information Matrix in GARCH? I want to know how to calculate the standard errors in them and without the empirical fisher information, empirical likelihood, I have no idea ...
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How to deal with redundant data within a sample when calculating the standard error?

In my research, I analyse pixel data from a 2D microscope image. Each pixel represents a unique spatial position. In my image, each pixel $i$ has a corresponding brightness value $x_i$. I assume the ...
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2 answers
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Bootstrap Standard Errors: should I divide the sampling standard deviation by $\sqrt{n}$?

Suppose I am bootstrapping an OLS regression and want the standard error of the coefficient $\beta_1$. I estimate the following regression on 1000 resamples of the data (where $B$ indexes the ...
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For bivariate linear model, if the residuals ARE normal, but the data is NOT normal, can I make inferences about the slope coefficient? [duplicate]

For convenience and context, I'm looking at the formula for standard error of the slope coefficient from here: https://www.statology.org/standard-error-of-regression-slope/ If X is not normally ...
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Standard error of sampling distribution mean vs standard deviation of the sampling distribution?

In this resource, towards the bottom, the authors write: The next step is to estimate the standard error of the mean. If we knew the population variance, we could use the following formula, $sigma_M = ...
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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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