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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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 ...
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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 ...
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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 ...
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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: $$\Delta LogC=\sqrt{(\frac{\...
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In a cube of nominal size $5$ inches, the uncertainty in the measurement of each side is $10\%.$ Find the uncertainty in the measurement of the volume
In the calculation of the volume of a cube of nominal size $5$ inches, the uncertainty in the measurement of each side is $10\%.$ Find the uncertainty in the measurement of the volume.
I tried solving ...
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How to calculate the error of an function?
I have a function: $$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+\...
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How can I calculate p-values, t-statistics, and Standard Error for multiple regression by hand?
I'm attempting to calculate p-values and t-statistics for multiple regression, but all the resources I've been finding on the topic have confusing or inconsistent information. The best resource I've ...
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2
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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. ...
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Find between which values the 20% central will be at.
The measurements of the times of a group of children competing in a race of
The 100-m dash follows a normal distribution with a mean of 13.4 s and a standard deviation of 1.2 s. Among which values ...
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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 ...
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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 \ \...
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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 ...
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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{...
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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 ...
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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 ...
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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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1
answer
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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 ...
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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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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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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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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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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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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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1
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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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63
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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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220
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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 ...
3
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1
answer
703
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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 ...
0
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1
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249
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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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