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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16 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$ ...
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14 views

FFT error analysis

When I do a FFT for a signal with the computer program of my choice I usually get a complex array from which I can extract the amplitude and phase as a function of frequency. What is the standard way ...
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34 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 ...
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33 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 ...
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18 views

Standard Error interpretation for the Monte Carlo estimate of the mean differences.

I am estimating the Monte Carlo mean difference of two idd uniformly distributed $X_{1}$ and $X_{2}$ and its standard error. $$\hat{\theta} = E|X_1 - X_2| \quad \text{ and } \quad \hat{se}|X_1 - X_2| ...
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12 views

About standard error

I knew that that we can calculate the standard error of I^th regression coefficient in an MLR by using VIF via the following formulae: $$S_{b_i}=s*\frac{VIF_i}{s_{x_i}\sqrt{n-1}}$$ May I know in this ...
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1answer
54 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 ...
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8 views

Question about confidence intervals and prediction intervals

Considering following linear multiple regression model: \begin{equation} y=X\beta + e, \end{equation} where observations $y\in\Re^n$, coefficents $\beta\in\Re^p$ and $e\sim N(0,\sigma I)$ is a white ...
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44 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 ...
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7 views

What is the error difference between an expected value and random sample?

If take a single random sample from a known distribution (uniform distribution) with an expected value of 5, how do I calculate the error associated with this sample as obviously the value could range ...
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33 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 $1$)? ...
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7 views

Simulated standard error in fit parameters not matching the diagonal elements of covariance matrix

My function is a Gaussian: $$ y(x_i,\mathbf{a})=a_1 e^{-(x_i-a_2)^2/(2a_3)^2} $$ which is sampled at discrete locations $x_i.$ According to the definitionm the covariance matrix $C$, can be obtained ...
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18 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 ...
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44 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 ...
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24 views

How to calculate error for random sampling?

I am currently completing a project where a value of a "resource" is randomly sampled from a uniform distribution. This value is then used as part of another calculation. This particular ...
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144 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}\...
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20 views

Standard error of the difference of two means which are derived from variably-sized sets

Let's say we have a pool of N individuals who try to shoot targets at a distance of 10m and at a distance of 20m. They are encouraged to shoot M times, but many stop before reaching that goal - this ...
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48 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 ...
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34 views

understanding 2 equivalent formulations of both data set measures with expectation and relative error

I have two independant experiments have measured $\tau_{1},\sigma_{1}$ and $\tau_{2},\sigma_{2}$ with $\sigma_{i}$ representing errors on measures. From these two measures, assuming errors are ...
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40 views

How do you find standard error if the probability is 0 or 1?

Say I have an experiment that has $700$ cases, $40$ have property $X$ and $350$ have property $Y$. It just so happens that $P(X|Y) = 0$. How do I find the SE of this proportion? I have been using the ...
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26 views

How to evaluate error of a quantity taken as the integral of a part of a distribution

I am having trouble - given my very limited knowledge of statistics - to know how I can evaluate the error in the following situation: I have a large number of points (1 or 2 millions) and have ...
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7 views

Standard error for difference of standard deviation

Since under the Null hypothesis, $\sigma_1=\sigma_2$, why is this not applied in the standard error formula? Shouldn’t it be $\sigma_1=\sigma_2=\sigma$?
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58 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: $e = y - \hat{y} = (I-H)y$ ...
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18 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 ...
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20 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 ...
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31 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 ...
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74 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?
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67 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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1answer
55 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
52 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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181 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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270 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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1answer
25 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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34 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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93 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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22 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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1answer
50 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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43 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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1answer
103 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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2answers
26 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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1answer
92 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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22 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
67 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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2answers
117 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
256 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
1k 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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2k 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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1answer
292 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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933 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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95 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 ...