# 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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### 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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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, $$(A^TA)^{-1}=\begin{bmatrix} 2.54 &... 0 votes 1 answer 50 views ### MLE and standard error of \lambda given X \sim \exp(\lambda) Suppose x_1 ... x_n are an iid sample from the exponential distribution with density:$$ p(x) = \lambda^{-1}e^{-\frac{x}{\lambda}}. $$Derive the MLE for \lambda and its standard error. My ... 1 vote 0 answers 27 views ### Incredibly low standard errors I am currently estimating the parameters of an interest rate model by means of a maximum likelihood estimation in combination with the iterated extended Kalman filter, and I obtain incredibly low ... • 11 0 votes 0 answers 20 views ### How to calculate the standard error of sum of probability estimators I have a sample of size n from a wider population of size N and two binary variables, X, which takes values A or B, and Y, which takes values 1 or 0. X is known across the wider ... 0 votes 0 answers 17 views ### Standard normal distrubtion, standard error According to data obtained by a management consulting firm, the mean working hours per week for accountants in a country is 48 hours, with a standard deviation of 7 hours. Let X be the number of the ... • 117 0 votes 1 answer 67 views ### estimated standard error for mean of Bernoulli random variables I know that if X_1,...X_n are Bernoulli(p) then to calculate the estimated standard error is$$\hat \sigma_{\bar X_n}= \sqrt{\frac{\frac{1}{n-1} \sum_i (\bar X_n - X_i)^2} {n}}$$however, often, I ... • 125 0 votes 0 answers 18 views ### What does the bracket way of showing error means? The value of avagadro number is given in my book as 6.02217(4). Does this mean 6.022174 or 6.02214? Even some numbers have (12) like two digit numbers. Also what is this notation called? Why is it ... 0 votes 1 answer 101 views ### How to find the approximate error in Stirlings Formula If we have the stirlings formula:$$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 ... • 251 0 votes 0 answers 24 views ### 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 ... • 21 1 vote 0 answers 19 views ### 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 ... • 641 0 votes 1 answer 38 views ### 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 ... 0 votes 0 answers 40 views ### 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 ... 0 votes 0 answers 15 views ### 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. ... 0 votes 0 answers 35 views ### 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 ... 3 votes 1 answer 164 views ### 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} $$Where ... • 33 0 votes 0 answers 26 views ### Standard deviation formula for coefficients in multiple regression analysis I am trying to understand how to calculate the individual deviation in this regression analysis table. (HH Size)_{se} = stderr \over \sqrt{S_{xx}}  =  {0.444400903 \over \sqrt{10}} = 0.14053 ... • 195 2 votes 0 answers 69 views ### How to derive SE(\hat{\beta_0}+\hat{\beta_1}x_0)=\hat{\sigma}\bigg[\frac{1}{n}+\frac{(x_0-\bar{x})^2}{(n-1)s^2_x}\bigg]^\frac{1}{2} I am trying to derive the following formula given by the lecture notes$$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 ... • 1,031 0 votes 1 answer 46 views ### 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 ... 0 votes 1 answer 67 views ### 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 ... • 11 0 votes 1 answer 57 views ### 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 ... 0 votes 1 answer 511 views ### 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.... 0 votes 1 answer 35 views ### 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)? ... • 91 0 votes 0 answers 100 views ### 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 ... 0 votes 0 answers 45 views ### 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 ... • 11 2 votes 1 answer 397 views ### 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}\... • 537 2 votes 1 answer 56 views ### 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 ... • 205 1 vote 1 answer 109 views ### 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 ... 0 votes 0 answers 20 views ### 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 ... 0 votes 1 answer 26 views ### 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 ... 1 vote 0 answers 105 views ### 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 ... -2 votes 1 answer 76 views ### 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? • 615 2 votes 0 answers 108 views ### 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 ... • 645 1 vote 1 answer 106 views ### 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 ... • 2,627 1 vote 1 answer 93 views ### 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 ... 0 votes 2 answers 508 views ### 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?
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 ...