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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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Why do you use n-1 in Standard error of the mean but n in hypothesis testing

When you divide in hypothesis testing you use the formula: $$ \frac{\bar X-\mu}{s/\sqrt n} $$ but the standard error of the mean is: $$ \frac s{\sqrt {n-1}} $$ Why don't you use $n-1$ when ...
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293 views

Error propagation for bitwise operators

When input quantities contain uncertainty, how those uncertainties are propagated to the output for operations of addition, subtraction, multiplication and division can be found in literature defined ...
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93 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 , ...
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1answer
319 views

Intuition for Standard Deviation

I've been studying descriptive statistics and am having a hard time understanding the actual intuition behind standard deviation. I'm trying to get a practical feeling for it and so I'm trying to draw ...
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163 views

Are the statements about the confidence interval correct?

We have a 90%-confidence interval. I want to check if the following statements are correct. If double the sample, the possibility that the value that we are looking for is out of the confidence ...
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1answer
80 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
267 views

Statistics. How are standard error and confidence intervals useful without knowing population size?

I understand standard error and confidence intervals as formulas, but not as concepts. Can you help me understand them better? A smaller standard deviation (smaller spread of your data) and a larger ...
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342 views

Standard Error of weighted mean estimate

$X$ is a random variable with unknown distribution. A number of experiments are conducted to estimate $X$. Each experiment has a different reliability measure in estimating $X$. These $n$ experiments ...
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2answers
39 views

Where is the mistake in this attempt to find the standard error of an estimator?

I'm reading a paper: Bect et al 2012, Sequential design of computer experiments for the estimation of a probability of failure. I'm looking at page 2, but the details of the paper don't matter. What ...
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1answer
67 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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1answer
535 views

Error Bound using Stirling's approximation

Using Stirling's formula, how can we bound the absolute error of $$e^x-\sum_{n=0}^N \frac{x^n}{n!}$$ on the interval $|x|\leq R$ where $R\leq N/2e$
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1answer
291 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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1answer
418 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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1answer
48 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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1answer
55 views

Can the margin of error be used in this kind of problem?

I've recently been learning about margin of error, i.e. $E=\frac{1}{\sqrt{n}}$. I met this problem which doesn't ask to find any margin of error but I wonder can it be used in this situation. Nails ...
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1answer
80 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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61 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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247 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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31 views

Standard error for different distributions

I'm trying to estimate the standard error of the mean for measurements sampled from an unknown distribution. Wikipedia says: The standard error of the mean (SEM) can be expressed as: $$ \bar{\...
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82 views

estimation of variance of slope and intercept in logistic regression

let us suppose we have following data i would like to test whether number of hours of studying helps me to predict student will pass or not, i used following step, initially i give some values to ...
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63 views

Standard Error - Why the calculation works

I'm new to statistics, and in an effort to understand how Standard Error works I've put together a small data set to try and get my head round it and would be really grateful if you could answer a ...
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1answer
46 views

What is the best measure of error for a data set where each point is the mean of 3 quick readings?

I have an experiment that relies on measuring temperature as a function of a given condition. I change the condition, allow the temperature to stabilize as much as possible, then take 3 measurements ...
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Should I use $\sigma_x^{-2}$ or $\left(\sigma_x/x\right)^{-2}$ as my weights when fitting simulation data? My intuition tells me to use the latter.

I have simulated a set of probabilities $\{p_n\}$ by the hit-or-miss Monte Carlo method. Specifically, my program checks whether or not an $n\times n$ matrix has a certain feature or not; say that, ...
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2answers
62 views

How to obtain the standard error of measurements that already have error bars?

Suppose I make three measurements: 9, 10 and 11. Let's say there is no uncertainty associated with these values because they are counts. Numbers of children in a class say. I want to know the average ...
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3answers
78 views

Standard error. Why does it get more accurate as N gets bigger?

I came across this quote about the Standard Error in the OpenIntro Statistics book: We required a large sample in Chapter 4 for two reasons: 1. The sampling distribution of x tends to be more ...
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18 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
34 views

Error term in an infinite series

Well, I've the following series: $$\frac{1}{\left(1+\epsilon\cos\left(x\right)\right)^2}=\sum_{\text{k}=0}^\infty\epsilon^\text{k}\left(1+\text{k}\right)\cos^\text{k}\left(x\right)\tag1$$ This ...
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1answer
29 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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1answer
82 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
21 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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2answers
161 views

Question about standard error of sample standard deviation

I have a question regarding one formula (3.8) on page 84 of the sixth edition of financial risk manager handbook. For convenience, I will rephrase the problem as below. Define $X$ as the random ...
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1answer
2k views

How can we calculate the standard error from a single sample?

Say we sample 19 dolphins for mercury levels. Say the summary of the sample is here: So the mean is 4.4 and the sample's standard deviation is 2.3 From this, why do we say the standard error (which ...
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17 views

How do you calculate error bars on elo rating?

In season 14 of the Top Chess Engine Championship, Stockfish defeated Leela 50.5-49.5 in a 100-game match (the closest possible winning margin). Using an elo calculator such as this one, we can see ...
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Accuracy of Euler Monte Carlo discretization without knowing exact solution?

By using Euler Monte Carlo discretization (for a Hull-White model) we simulate $$r(t+\Delta t)=r(t)+\lambda(\theta(t)-r(t))\Delta t+\eta\sqrt{\Delta t}Z$$ with $Z\sim N(0,1)$, $\lambda$, $\eta$ ...
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1answer
18 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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What is the relation between standard error and power, and unequal randomization?

If you are doing some kind of hypothesis testing (superiority or equivalence) for the difference of two means/proportions, the standard error is: Square root of (Standard deviation of sample A / nA + ...
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1answer
16 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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18 views

Uncertainty associated with area under curve (integrated) estimates

Say I have a set of data points ($y$) measured at different times (hence a time series) which I know the uncertainties of the individual data points (in standard error). I connect them to form a line ...
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25 views

What is the minimum variance band of Poisson Distribution?

I am trying to calculate the minimum variance bound of Poisson Distribution. poisson distribution: P(X=x)=(λ^x)/x! e^-λ, were λ is the mean. I got λ/(sum of x), but I am not sure if this is right. ...
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19 views

How to calculate Measurement error of n measurements based on standard error and the quantile funcion

Let's say I have $n$ measurements $x$ sampled from a normal distribution X and I would like to estimate the mean with errors. Is the belove method correct? I'm mostly concerned about if I'm wording ...
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146 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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110 views

Sampling uncertainty (uncertainty in standard deviation)

Say I took twenty measurements of the wind velocity at a point. This is a sample of the infinite number of measurements I would need to get the true velocity at that point. I then calculate the mean ...
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10 views

Standard errors from poisson data

I am trying to fit some data to a poisson model and have got an MLE estimate (sample mean) of 0.465 from a sample size of 647. How do I calculate my standard error?
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35 views

Standard error of the variance of Uniformly distributed data

I would like to derive the standard error of the variance for a sample taken from a Uniform distribution with bounds $a$ and $b$. The standard error of the mean of that sample is straigtforward: $SE_{...
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17 views

Error Calculation on an Average of Errors

Recently I have done an experiment with diffraction grating. I had to calculate 'N' (number of lines per meter) from the equation sin(${\theta}$)=pN${\lambda}$. I then required an average N to use in ...
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19 views

Variance vs. asymptotic variance of OLS estimators?

I immediately assumed that all three were true. Which one is false, and why?
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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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0answers
10 views

What is standard error (any approximation) in a variable when only Mean value and percentiles (16th and 84th) of the PDF over variable are known?

I have variable 'X' for which I know only the MEAN value along with 16th and 84th percentile of its PDF. Now this variable (X) is used in another variable calculation (let's say 'Y') for which I have ...
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24 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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49 views

How do I calculate Cp and Cpk (Capability) on Mean and Range Charts?

so I've been working on a question involving constructing a mean and range chart with upper and lower action and warning limits, I've got the first part of the question right (I've plotted the chart ...