Questions tagged [standard-error]

For basic questions in statistics involving the properties or use of standard error of the sample points present in a simple random sample.

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Standard deviation of values with uncertainty with respect to the expected measurement

I have some data measurements (satellite data from an object) with their uncertainty, so I have $x_i$ and $\sigma_i$. I want to measure the deviation of these measurements from the expected value $x_{...
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Instrument resolution or Standard Error of the mean

Say I tried to measure the length of an object with an instrument that has a resolution of of 0.1mm and got the following: 12.5,12.5,12.5,12.5,12.5,12.5,12.5,12.5, 12.5,12.5 (all in mm). The standard ...
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Help understanding the formula for relative error of a multivariable function

I am studying error theory. I don't understand from where does $\ln$ appear at the end Consequently, the marginal absolute error of the approximated value of the function $y^*$ is calculated by the ...
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Proving Central Limit Theorem

I need some help with proving the Central Limit Theorem. I understand that the distribution of the sample means should be approximately normal with a mean that is the same as the mean of the parent ...
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logit and probit models

Basic background Hi, I'm relatively new to statistics and mathematics stack exchange so please bear with me. I'm trying to learn about the probit and logit models where the observables $y$ can only ...
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95% CI of metric within Recurrent Neural Network

in one of my lectures, it's about predicting a time series with a recurrent neural network and computing some metric $X$ for each timesteps. On our slides, there are some fomular I don't understand. ...
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Solving the time required for two particles to move to a specified distance in two-dimensional space

Now there are two particles $j^{th}$ and $i^{th}$, Their coordinates are $\mathbf{r}_j (1.0, 0.0)$, $ \mathbf{r}_i (3.0, 1.0)$ respectively. Their speed $\mathbf{v}_j (-0.3, 0.0)$, $ \mathbf{v}_i (-0....
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Find the Mean Error of Irregularly Sampled Data [closed]

I am creating an algorithm that estimates the State-of-Charge (SoC) of a battery. The table below, compares my algorithm with the true SoC. Predicted SoC Real SoC Error 98.30% 98.19% -0.10% 96.43% ...
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Dealing with second derivatives in error calculation

I need to find the relative error in the error of $\log P$, i.e. $\frac{\Delta(\Delta \log P)}{(\Delta \log P)}$. I need to prove that this equals $2\frac{\Delta P}{P\log P}$. I have tried so many ...
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Uncertainty corresponding to bin population.

I have around 200 data points. I have separated these point into 7 bins. Some of these bins contain up to 50 points while some contain around 3-6 points. Some of these 200 points belong to a group C. ...
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Estimates of parameters of interest $θ_1$ & $θ_2$ ($\pm$ standard errors) were $25\pm10$ & $10\pm3$. Find estimate & Standard Error of $δ=θ_1/5−θ_2$

Problem: In two independent studies, the estimates of the parameters of interest $θ_1$ and $θ_2$ ($\pm$ their standard errors) were computed to be $25\pm 10$ and $10\pm 3$, respectively. If one is ...
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How to estimate the error of fitting in a simple least squares problem?

Suppose we have estimated the model parameters $m$ of the equation $y=G*m$ from data $y$ as $m=(G'*G)^{-1} * G' * y$. We have the measurement errors in $y$ from which we construct an error co-variance ...
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Determining the sample size to satisfy two tests

A survey of a university's students is to be carried out to estimate both the proportion, $P$, who own a bicycle and the average weekly spend on junk food, $\bar X$. It is desired to estimate $P$ with ...
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Standard error of slope when data is unknown

Let’s say I did a linear regression on a dataset with 10 observations, and I got the estimated slope as $b=0.5$ and residual variance as $\sigma^2=5.2$ and further, $$(A^TA)^{-1}=\begin{bmatrix} 2.54 &...
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MLE and standard error of $\lambda$ given $X \sim \exp(\lambda)$

Suppose $x_1 ... x_n$ are an iid sample from the exponential distribution with density: $$ p(x) = \lambda^{-1}e^{-\frac{x}{\lambda}}. $$ Derive the MLE for $\lambda$ and its standard error. My ...
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Incredibly low standard errors

I am currently estimating the parameters of an interest rate model by means of a maximum likelihood estimation in combination with the iterated extended Kalman filter, and I obtain incredibly low ...
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How to calculate the standard error of sum of probability estimators

I have a sample of size $n$ from a wider population of size $N$ and two binary variables, $X$, which takes values $A$ or $B$, and $Y$, which takes values $1$ or $0$. $X$ is known across the wider ...
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Standard normal distrubtion, standard error

According to data obtained by a management consulting firm, the mean working hours per week for accountants in a country is 48 hours, with a standard deviation of 7 hours. Let X be the number of the ...
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estimated standard error for mean of Bernoulli random variables

I know that if $X_1,...X_n$ are Bernoulli(p) then to calculate the estimated standard error is $$\hat \sigma_{\bar X_n}= \sqrt{\frac{\frac{1}{n-1} \sum_i (\bar X_n - X_i)^2} {n}}$$ however, often, I ...
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What does the bracket way of showing error means?

The value of avagadro number is given in my book as 6.02217(4). Does this mean 6.022174 or 6.02214? Even some numbers have (12) like two digit numbers. Also what is this notation called? Why is it ...
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How to find the approximate error in Stirlings Formula

If we have the stirlings formula: $$N!=\sqrt{2\pi N}(\frac {N}{e})^N$$ And I am asked to find how big the N must be so our error is less then 1 %. Because the error is in percentage, I am considering ...
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How can I derive OLS predicted error term $\hat{e}_i$ as a function of $e_i$?

First of all, I'd like to say that any kind of help would be really helpful, whether it's a hint or a good grad/undergrad book. Right now I'm working with Econometric Analysis of Cross Section and ...
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measures of uncertainty for summary statistics in circular data

I have a set of $N$ samples $\{x_{i}\},\,{i=1,\cdots,N}$ sampled from a circular random variable $X$ (wrap around at $\pm\pi$) that is NOT von-Mises distributed but is unimodal. I can calculate ...
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How to compute confidence intervals and standard error for nonlinear regression with three parameters?

I have been working on a personal project trying to emulate the nonlinear regression functionality of Mathematica for three free parameters. I am able to accurately fit functions, yet I am unsure how ...
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Bayes theorem with errors

I have a situation in which I want to calculate, for a given $y$ (which I measure experimentally), the probability distribution of $x$ i.e. $p(x|y)$ (actually what I need is the value of x for which ...
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STD of response change of linear regression

Let's suppose I have a single predictor linear dependence: $y = kx+b + \epsilon$. A linear regression was performed on the available data and we have the estimates of $\epsilon$, $k$ and $\sigma_k$. ...
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No. of significant figures in absolute value w.r.t true value and relative percentage error

To find the no. of a significant figure in absolute value $= 0.05411$ with respect to true value $= 0.05418$ and the relative percentage error. Here's my solution: But I ain't sure whether it's ...
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Statistics - What is the random error of a measurement with one reading?

To calculate the random error in a set of measurements this is what I would do. Get the standard deviation of the measurements: $$ \sigma=\sqrt{\frac{1}{N-1}\Sigma_{i=1}^N(x_i-\bar{x})^2} $$ Where $...
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Standard deviation formula for coefficients in multiple regression analysis

I am trying to understand how to calculate the individual deviation in this regression analysis table. $(HH Size)_{se} =$ $stderr \over \sqrt{S_{xx}} $ $=$ $ {0.444400903 \over \sqrt{10}} = 0.14053$ ...
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How to derive $SE(\hat{\beta_0}+\hat{\beta_1}x_0)=\hat{\sigma}\bigg[\frac{1}{n}+\frac{(x_0-\bar{x})^2}{(n-1)s^2_x}\bigg]^\frac{1}{2}$

I am trying to derive the following formula given by the lecture notes $$SE(\hat{\beta_0}+\hat{\beta_1}x_0)=\hat{\sigma}\bigg[\frac{1}{n}+\frac{(x_0-\bar{x})^2}{(n-1)s^2_x}\bigg]^\frac{1}{2}$$ My ...
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Distribution of relative error.

Suppose I have a random variable $X$ with unknown mean $\mu$ and I can draw $n$ random samples (possibly from a Monte Carlo method, but I believe that's beside the point) from its distribution. I wish ...
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How do I calculate this sampling error?

If I sample individual integer values $0$ to $100$ from a distribution $100000$ times and record the counts for all integer values between $0$ and $100$, how do I calculate the $95$% error bars for ...
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Z Test and Standard Error

Before televised debates, a poll of 800 registered voters showed 560 in favor of a particular candidate; after the debates a poll of 600 voters showed 450 in favor of the candidate. A political ...
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standard error formula for Bernoulli distribution

I am confused about the formula here about standard error. I know that standard error of the sample average Y_bar should be an estimator of the standard deviation of the sampling distribution $\bar Y$....
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Standard error question. Why can't this be equal to 1?

So I've been working on this question related to standard error and I managed to show that it can't be less than $1$. But how do you show that this has to be greater than $1$ (as in cannot equal $1$)? ...
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Order of Convergence when working with errors

I am looking at the numerical solutions of a problem when using the boundary element method, the exact solution is 0.25 I have 3 errors corresponding to using 20,40 and 80 boundary elements. I have ...
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How to calculate the error due to expected value?

I am currently trying to work out the probability of winning a game. This is proportional to another value however the I dont have the true value of this other quantity. Instead it is the sum of ...
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Approximate standard error of the maximum likelihood estimate

Question: Suppose that $X$ is a discrete random variable with : \begin{array}{|r|r|r|r|} \hline X & 0 & 1 & 2 & 3\\ \hline \mathbb P(X=x) &\frac{2}{3}\...
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How to derive the kth coefficient standard error?

Given a multiple regression with the usual assumptions satisfied, with $X \in R^{n \times p}$ $$ y = X \beta + e $$ I know that the estimated variance is given by $\sigma^2 (X^TX)^{-1}$. But what I ...
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Standardized residuals

I am having a hard time understanding the concept of standardizing residuals and how the variance of a residual is decomposed. In a linear model, we defined residuals as: $e = y - \hat{y} = (I-H)y$ ...
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Estimated standard error of the mean (easy points for the answer)

Trying to wrap my mind around the intuition of the standard error of the mean is the mission. I was trying to make a really basic example with simple number to give myself more a sense of what is ...
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Explanation on the different forms of proportion standard error and population variance of proportion (Stats)

Let $\sigma^2$ be the population variance, $p$ be the population proportion, and $\hat{p}$ be the sample proportion. My understanding is that $\sigma^2_p = p(1-p)$ (bernoulli trial) and the standard ...
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How is type 1 error related to precision?

I was going through the Wikipedia of Precision and Recall and it was written that "Type II errors can be said to be the complement of Recall but Precision and Type I errors are related in a more ...
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Is there a such thing as "standard error of random variable?"

I am wondering if there is a such thing as "Standard Error" of a random variable? If so, is it simply just the standard deviation of the random variable?
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Statistics 101: T test vs Z test. Sample proportion vs Sample mean

Sorry, I'm just on Khan academy and can't seem to grasp the essence of statistics. Hope to find some help out here. Both are samples, but why when looking for confidence interval of a: sample ...
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Calculating a confidence interval

In a random sample of $n=400$ people, 136 said they liked the product. Construct a $95\%$ confidence interval for the population proportion who might like the product. The sample proportion $\hat p$ ...
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What's the difference between 'standard error' and 'estimated standard error'?

100 people are given a standard antibiotic to treat an infection and another 100 are given a new antibiotic. In the first group, 90 people recover; in the second group, 80 people recover. Let $p_1$ be ...
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Estimation of the standard deviation for Power Law distribution

I've understood everything in the picture (source) below except for this equality: $$\hat{\sigma} = \frac{\hat{\alpha} - 1}{\sqrt n}$$ Can someone please explain where does it come from?
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AP STATISTICS 2008 EXAM Question on standard error of estimated proportion

This question is taken from the 2008 AP Statistics free-response question 4) An experiment was conducted to study the effect of temperature on the reliability of an electronic device used in an ...
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Uncertainty in Grabbing Colored Coins

Suppose I have a source of red and blue coins that have a red composition of absolute percentage $a_r$ with uncertainty $\sigma_r$, and similar measures for blue. If I take $N$ coins randomly from the ...