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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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Calculating Standard Error (SE) of a Nonlinear Function Using SE of Its Parameters

I'm working with a nonlinear function, specifically a beta weighting scheme, which generates weights that can vary in shape (e.g., decaying, hump-shaped, U-shaped). I have estimates for the parameters ...
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Standard error of mean from in varying sample size for batch simulations

I have three batches of simulations and I calculate a specific property from these (not important for the question). I want to calculate combined SEM for these three batches Batch | #samples | average ...
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Linear Combinations of Sample Mean Difference

What is the standard error of the mean difference between 2 variables (a & b)? I have the following data: $$ \sigma_{A} = 1.813529 \nonumber \\ \sigma_{B} = 1.932183 \nonumber \\ cov(A,B) = 2....
joelleoqiyi's user avatar
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Can a large error be calculated using logarithm?

For example: $$\begin{array}{l} y = {x^{11}}\\ \Delta x = 0.1 \cdot x\\ \Delta y =\sqrt {\left( {\frac{{dy}}{{dx}}\Delta x} \right)^2} = 1.1 \cdot {x^{10}}\\ y \pm \Delta y = {x^{10}} \pm 1.1 \cdot {x^...
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Confidence interval 100 coin tosses, 52 heads?

I am really confused about the confidence interval for n=100 tosses and k=52 heads. If I estimate the probability $\hat{p}$: $\hat{p} = \frac{52}{100} = 0.52$ $Var(\hat{p}) = pq = 0.52 * 0.48 = 0.2496$...
DamianoDantuono's user avatar
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1 answer
148 views

Lower bound on sample size to determine coin fairness

This is a conclusion I came to through very basic knowledge of statistics and error analysis. Suppose we want to determine the fairness of a coin. To do this, we need to determine the probability of ...
Phineas Nicolson's user avatar
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Estimation of std error using sample std dev. will result in diff. sample statistic distribution for diff. samples. Won't this affect our decision?

During hypothesis testing (say, comparison of sample mean to a hypothesised population mean), we calculate p-value using sample mean distribution. For constructing this sample mean distribution, we ...
Swapna Sarit's user avatar
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187 views

How is it Possible to Optimize the Shichman-Hodges Slope Parameters from the Left and Right using Least Square Linear Regression Approaches

The Shichman-Hodges equations model a curve that on the left-hand side has a slope that decreases as a function of the variable $x_i$. That is $x_0=0$, and $y_i$ is a function of $x_i$ for $i=0$, and ...
Stephen Elliott's user avatar
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How can I calculate the SD from the SE of a least square mean?

I am conducting a meta-analysis and I need to collect mean and standard deviations (SDs). In some studies the raw means are not available and least square means are provided instead. Is there a way to ...
alfaeneri's user avatar
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Cant find the error values correctly. Need Suggestions.

I have 6 observational data. $L_1,L_2,L_3,L_4,L_5 $ and $ L$. Each of them have seperate error values $\delta L_i$ and $\delta L$. All of these data are numbers such as $1.38e36, 3.45e33, 9.61e41$, ...
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How to find the margin of error of a value consisting of the sum of 5 values? [closed]

I have a $X$ value that is the sum of 5 different $x1,x2,x3,x4$, and $x5$ values. Eacn $x_i$ has their error in same scale. I want to calculate the error of X. How can i do that? Basically, i tried to ...
Ege Tunç's user avatar
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standard error of an estimate of fraction of objects with a known binary probability

Lets have a group of N people that can be either men M or women W (or in general objects that can be 0 or 1). For each person $i$ we have an estimate of probability $P_i$ from <0,1> that it is ...
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Compute Sample Size for Specific Margin of Error & Confidence Level

I have a population that is in size equals to 65,536. The population follows a uniform distribution and is composed of discrete, ordered integer numbers. From this population I wish to identify the ...
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Estimate standard error of population proportion based on one sample

There is a basket with unknown number of red balls ($N_r$) and green balls ($N_g$). I draw a random sample of $k$ balls without replacement and see that $P_r$ of the balls are red and $P_g$ of the ...
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Why does multicollinearity increase the standard error of regression coefficients?

I understand the intuition that it is difficult to distinguish the effect of two independent variables on the dependent variable when they are highly correlated, but I don't see how this works its way ...
Martin's user avatar
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Standard error on subsample

Suppose that I know that $N$ samples $(x_1, x_2,...,x_N)$ are iid drawn from a distribution with known variance $\sigma^2$. I also observe the first $k<<N$ samples, and estimate the mean on ...
max1993's user avatar
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Which error calculation is the correct one?

I have a function $$ LogC= (LogA - 0.80 * LogB - 8.40)/0.50 $$ Here i have error values for LogA and LogB. So i want to calculate error of LogC. I'm using the formula: $$\Delta LogC=\sqrt{(\frac{\...
Ege Tunç's user avatar
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171 views

In a cube of nominal size $5$ inches, the uncertainty in the measurement of each side is $10\%.$ Find the uncertainty in the measurement of the volume

In the calculation of the volume of a cube of nominal size $5$ inches, the uncertainty in the measurement of each side is $10\%.$ Find the uncertainty in the measurement of the volume. I tried solving ...
Thomas Finley's user avatar
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How to calculate the error of an function?

I have a function: $$L_R=4*\pi*5*R^2*J$$ I have error values for this R and J. So I want to find the error of $$L_R$$ Should I go for:$$L_R=f$$ $$df=L_{R_{error}}=\frac{\partial{f}}{\partial{x}}dx+\...
Ege Tunç's user avatar
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2 answers
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Calculating with constants with tolerance

I have a formula. LogC= (LogA - 0.80 * LogB - 8.40)/0.50 However, all these constants 0.80, 8.40 and 0.50 have +/- tolerances which are not equal. Respectively, +0.13/-0.15, +4.55/-4.20, +0.12/-0.20. ...
Ege Tunç's user avatar
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1 answer
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Find the number of measurements so that our iuncertainty is less than 2%

The results of a certain experiment whose true value is about 10.0 cm, follow a normal distribution with standard deviation of 1.0 cm. How many measurements will we have to do so that our uncertainty ...
Acedium 20's user avatar
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Calculations of standard errors

Problem Let $Y_1 \sim N(μ_1,1),Y_2 \sim N(μ_2,1), Y_3 \sim N(μ_3,1)$ and also assume that these three random variables are mutually independent. The observed sample values are $y_1 = 2, y_2 = 0 \ \...
Hmmmmm's user avatar
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Measuring a margin of error for an axis of symmetry

Typically when using an axis of symmetry, it proposes a theoretically perfect axis. What measurement could be used as a +/- margin of error when looking at such an axis in an applied situation? For ...
Jesse Williams's user avatar
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132 views

Relative and absolute error $\sin(x)$

Estimate the absolute error in determining $\sin(x)$. Estimate the relative error in determining $\sin(x)$. I know how to calculate these for a specific $x$ with the formula \begin{align} \textrm{...
Willem's user avatar
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Can the variance of the sample variance be negative?

In this answer is shown that the variance of the sample variance is $$ \text{Var}(S^2) = \frac{1}{n} \left(\mu_4 - \frac{n-3}{n-1}\sigma^4\right) $$ where $\mu_4$ is the fourth central moment, ie $E[(...
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Confusion about the import of the standard error

The standard error is defined: $$ SD(\bar{X}) = \frac{\sigma}{\sqrt{n}} $$ where $\sigma$ is the standard deviation of the population and $n$ is the sample size. In the book I'm reading, it seems to ...
Dan Öz's user avatar
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$\varepsilon_{ij} \in \mathcal{N}(0,\sigma^2)$. What can we say about the third moment?

the errors $\varepsilon_{ij}$ are independent $\mathcal{N}(0,\sigma^2)$ random variables. What can we say about the third moment? For example, is $\mathbb{E}(\varepsilon_{ij}^3)$ bounded? I really ...
wjc's user avatar
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Ridge regresssion on a Echo State network

I am working with this article:http://www.scholarpedia.org/article/Echo_state_network on echo state networks. Here they speak about a ridge regression for the ESN. Normally the outputweight matrix ...
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Getting the wrong expression for standard error

Here is the question: To estimate the proportion $p_1$ of male voters who are in favor of expanding the use of solar energy, take a random sample of size $m$ and set $X$ for the number in favor. To ...
seasonedfish's user avatar
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Average of Relative Error (Relative Error of a Sequence)

I have a sequence of ground truth and a sequence of measured values. Ground truth sequence: 4,5,3 Measured values sequence: 5,4,5 I would like to ...
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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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263 views

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 ...
Maroon Racoon's user avatar
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106 views

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 ...
MOOSE's user avatar
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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....
Zhao Dazhuang's user avatar
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42 views

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% ...
flienky's user avatar
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2 answers
64 views

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. ...
Bobasheto's user avatar
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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 ...
mng's user avatar
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1 answer
164 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 ...
Working dollar's user avatar
1 vote
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30 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 ...
Cris's user avatar
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1 answer
439 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 ...
Mina's user avatar
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259 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 ...
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279 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 ...
imbAF's user avatar
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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 ...
K A's user avatar
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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 ...
Snakeryan's user avatar
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69 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 ...
Alex Marshall's user avatar
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372 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 ...
Archana Dash's user avatar
3 votes
1 answer
1k 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 $...
HWIK's user avatar
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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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