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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21 views

Confidence Interval of linear regression model - Standard Deviation vs Standard Error

For a (large) experimental dataset I am assuming a quadratic model and perform a regression analysis. Then I'd like to have some information about the accuracy of my model parameters, so I'm ...
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16 views

Standard error in Data for regression

I am working on my thesis and there I need to approximate a function in the sense of sum of the square differences, i.e. $$ \min \sum_{i=1}^{n} (y_i-\eta_i)^2$$ for the function $y$ and Data $\eta$....
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22 views

Standard Error propagation for correlated variables

The following is a toy problem to illustrate my question. Let $[A_{1}, ... ,A_{n}]$ be a series of $n$ random variables. Each variable has $m$ observation under two experimental conditions resulting ...
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34 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 ...
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12 views

What is suitable error measurement to find time error that cause from different values of parameter?

This is the figure I obtained from Maple software. Now I need to find time error from this figure. The exact solution is in blue line and the other line are approximated solutions. Can someone suggest ...
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34 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 $\hat p$ ...
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1answer
36 views

How to calculate the threshold value to change the Welch's T-Test? [closed]

Given I have two samples where for each sample I know: Number of Values: $n_1, n_2$. The means: $m_1, m_2$. Standard Deviation: $s_1, s_2$. Also each sample share a min and max value that it can ...
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27 views

How to incrementally update a Welch's $t$-Test?

Say I have two sample distributions where for each distribution I know: Number of Values: $n_1, n_2$. The means: $m_1, m_2$. Standard Deviation: $s_1, s_2$. With this information I am able to ...
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27 views

Variance of Sum to Sum of Variance

There are some proofs of this idea elsewhere but I am trying to demonstrate it to myself with a specific example so as to understand the derivation of the formula for the Standard Error of sample ...
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1answer
38 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 ...
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25 views

Statistical inference-wise, should I just worry about the standard error of the random part of my model?

I am modelling my real world system as: $$Y = f(x) + E$$ where $f$ is my deterministic model with some parameters $\theta_{1}$, $\theta_{2}$, ... and $E$ is the random part (stuff I can't explain, ...
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22 views

Definition of a priori and a posteriori Error Estimates for General PDE

My question will be written rather loosely because I can only imagine any answer will be very general. Given some PDE : $$ u'(t)= -\nabla \phi(u(t)),~~u(0)=u_0, $$ what do authors mean when they ...
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38 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?
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52 views

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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24 views

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 ...
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28 views

Statistics question on errors and probability with Coronavirus

Recently a survey in California suggested that considerably more people have been exposed to COVID-19 than previously thought. However, the testing equipment used apparently has a 1.7% false positive ...
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18 views

Best way to determine improvement knowing the mean, standard deviation and standard error of the measures

I have data of a study carried out on two groups of people, one of 13 and the other of 22. Each group was given two measurements, one at the start of the experiment and another one at the end. ...
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14 views

Wald Statistic from Odds Ratio & Standard Errors

Say I have a data frame, and I have the columns: "Species", "Odds Ratio" & "Standard Errors". I am asked to create the Wald test statistic for each species. How would I go about doing this? ...
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52 views

Standard deviation, standard error and confidence interval difference explanation

I write some code to generate random weights (I define low as 50Kg and high as 100Kg) of males, then generate 100 samples containing 100 measurements (weights per sample) i.e. 100 samples and each ...
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31 views

Uncertainty estimate of a sample of one

A monte-carlo approach to a problem produces many thousands of possible solutions, each ranked according to the total residue from observed data it implies, so that the solution with the lowest net ...
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1answer
17 views

Standard error and estimating intervals

I've been teaching myself some statistics and upon doing this problem I've stumbled at the very last part: I've had no problem reaching $\mu\approx x=220.1$ and $\sigma\approx y= \frac{1}{2\sqrt{5}}$,...
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29 views

Minimum iterations to guarantee a forward error of $\epsilon$

can anyone shed some light into this for me. I am asked to numerically solve $$x\arctan(x) = 1$$ and to ensure that the error $\epsilon$ is less than $10^{-3}$. Now I usually use Newton's method for ...
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22 views

When NOT to use Bessel's Correction for Standard Deviation

I can not find a clear explanation for when NOT to use Bessel's correction and use N instead of N-1. As I understand it, Bessel's correction would apply to things such as clinical trials, sampling ...
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41 views

How to calculate means and errors of intrinsically correlated runs?

I am currently simulating a molecule and need to calculate the global mean value and more specifically the error of the global mean of a parameter $r$ denoting its size. To do that I have a multiple ...
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28 views

Sampling error propagation

Imagine you have a population of size N, and a sample of size n. The population comes in three kinds ('red', 'black' and 'blue') and we want to know the proportions of each kind. For 'red' we would ...
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19 views

Root mean squared error (RMSE) vs Mean absolute error (MAE)

I have measurements from two different sensors. The one sensor is very accurate. The other sensor is sensitive to noise. I would like to calculate the error between these two sensors but I am not sure ...
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87 views

How do I calculate the uncertainty of this percentage difference?

So, I am working with a data set that is 'supposed to' follow a Poisson Distribution, so that $\langle N \rangle = \sigma^2$, where $\langle N \rangle$ is the mean of my measurements $\{n_i\}$ of the ...
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47 views

Linear Codes : Error detection

The code words of a linear code $C$ have the length $n=5$. Writing the code words into a matrix to get the linear independent ones, we get the following: \begin{equation*}\begin{pmatrix}0 & 0 &...
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25 views

Is it possible to infer the uncertainty of predictions for a time series model from the residuals distribution of a large representative sample?

Let me illustrate the question with an example: Imagine you construct a model to predict tomorrow's rainfall over London using some variables. Let's suppose that 300 years of data are available (1718-...
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56 views

Propagating Uncertainties on Interpolated Data

I have a data set of 2000 $[x, F(x), \delta F(x)]$ triples, where $x$ is exact and $F$ is a measured value with an uncertainty $\delta F$. I can interpolate/fit the function however needed, and this ...
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18 views

Nonlinear regression standard error for two parameters?

I've been tasked with finding the standard error for two parameters in an equation, but I have no idea about statistics. If my question is answered, please point me in that direction. Otherwise, ...
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1answer
40 views

Unbiased estimator of the standard deviation of the proportion

For the sample proportion $\hat{p}$, standard error is known as $\sqrt\frac{\hat{p}(1-\hat{p})}{n}$. I wonder whether this is the unbiased estimator for the standard deviation of the sample ...
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68 views

Estimated standard error vs standard error

My statistics text is trying to define "estimated standard error" by an example, but I'd like a real definition so I can mentally keep it distinguished from just "standard error." It reads: Let $...
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1answer
128 views

What is the variance of Z? if $Z = \frac{X}{Y}$ and X and Y are given.

We measure voltage across a resistor and find that the measured samples are distributed normally with mean $E[X]$ and variance $\sigma_X$, we measure current across a resistor and find that the ...
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1answer
628 views

Standard error of standard deviation, skewness and kurtosis

I want to use this formula (shown below) for my work (not math based) to calculate the uncertainty in the sample standard deviation (obtained from the link below): Calculating uncertainty in standard ...
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477 views

Explain about the Correlation of Error Terms in Linear Regression Models

I would like to ask for the interpretation, both mathematically and intuitively if possible, about the homoscedasticity of the variance of errors in linear regression models. If there is correlation ...
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139 views

Standard Error of Coefficients in simple Linear Regression

In the book "Introduction to Statistical Learning" page 66, there are formulas of the standard errors of the coefficient estimates $\hat{\beta}_0$ and $\hat{\beta}_1$. I know the proof of $SE(\hat{\...
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632 views

Correction factor for calculating standard error when drawing sample without replacement - derivation

When drawing a sample of size n from population of size N This relationship holds $$ SE\space when\space drawing\space sample\space without\space replacement\space =\space correction\space ...
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47 views

Quickly estimating the optimal bin size for the Jackknife re-sampling method

I am trying to apply the Jackknife method to compute confidence intervals for data collected from Monte Carlo simulations. My understanding is that to counter the effect of autocorrelations I should ...
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39 views

weighted means when weights don't sum up to 100%

I have a sample of tortillas from which I want to estimate the weighted mean (weighted according to market share) of sodium content in tortillas sold in the market. The way I collected this sample was ...
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73 views

Computing the standard error for an estimated probability

Each year, the maximum height $X$ of a river is measured. A value over $6\,\text{m}$ would be catastrophic. The distribution $X$ is supposed to be Rayleigh, i.e its density is $$f_{X}(x)=(x/a)e^{-x^{2}...
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44 views

Fundamental limit to accuracy

In any real experiment, Eventhough we conduct experiment with utmost accuracy some random errors are bound to occur. $$P\left(x\right)=\frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{\left(x-x_0\right)^2}{2\...
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73 views

Order of accuracy of least squares for computing gradients

This is more of a numerical methods question. Hopefully, this is the right stackexchange board to post this question. I am wondering if anyone is aware of the order of accuracy of using least ...
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23 views

Statistics What is the Standard Error?

Bookstores like education, because national data show that $71$% of college graduates have read a book in the past year, compared to $54$% of the general population age 18 and over. The data also show ...
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2k views

Statistical error associated with a bin count

I have a collection of data points. I have computed the histogram of this data to create the empirical distribution. How can estimated the error in the value at each bin. Based on the the total number ...
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41 views

Method to define a error in a sensefull way

I have two functions $A(t)$ und $B(t)$ (given as a set of values) and I want to quantify how similar they are. In context: I want to check how good some approximation regarding the solution of an ...
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410 views

How to estimate random error in a single measurement?

(from Jwan622's post here), This image was shown, where we've got: 19 samples (n = 19) Mean of 4.4. Sample standard deviation of 2.3 (s = 2.3) If the standard error of mean from the sample is SE = ...
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109 views

Finding the order of error - Confusion

I am confused because two ways of determining the order of error have been presented to me. Unless I am mistaken, the following are true: 1) The order of error can be found by finding the errors at $...
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53 views

Calculating the standard error of the slope of a simple linear regression

For a particular dataset, a simple linear regression of $y$ on $x$ was fitted and it yielded the following quantities: $n = 25$ $R^2= 0.7114$ $ \hat{\beta}_1 = 0.2355$ $F$-statistic $= 56.68$ ...
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112 views

What is the value of $ \int_{0}^{+\infty}e^{x^2(1-2\Phi(x\sqrt{2}))}dx$?

I have accrossed the below integral when i have tried to know more about relationship between error function and CDF of the normal distribution ,I plug this integral in wolfram alpha but no result , ...