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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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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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17 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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2answers
17 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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20 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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74 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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17 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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92 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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74 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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30 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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15 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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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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68 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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68 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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239 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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21 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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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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42 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 ...
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How is the Standard Deviation affected when more (bounded) random numbers are included in a sample?

If I generate random numbers between two bounds, e.g. $0$ to $100$, will the standard deviation converge to a particular value the more random numbers I generate?
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31 views

Error of the intersection of two linear functions

I have the following linear fits of two data sets $L_1: y=(a_{1}\pm e_{1})x + (b_{1} \pm f_{1})$ $L_2: y=(a_{2}\pm e_{2})x + (b_{2} \pm f_{2})$ How do I calculate the intersection of $L_1$ and $L_2$...
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66 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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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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56 views

Gauss-Legendre and Gauss-Chebyshev error estimates

I would like to estimate the error when calculating the value of the integral $$\int_{-1}^1\frac{e^{-x^2}}{\sqrt{1-x^2}}$$ an 8-point Gauss-Legendre quadrature and an 8-point Gauss-Chebyshev ...
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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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Derive a formula of the following form that is accurate for polynomials of as high a degree as possible.

I'm being asked to derive a formula of the form $$ y(t+h) = ay(t) +by(t-h) +h[cy'(t)+dy'(t-h)]$$ that is accurate for polynomials of as high a degree as possible. I believe I need to use ...
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67 views

Calculate of p-value in t-test seems contradictory in Stata and Excel?

As we know, in a t-test the t-value is given by $t = \frac{\bar{x}-x^{*}}{s_x}$, where $\bar{x}$ and $s_x$ are the sample mean and sample standard deviation calculated from the observed data, while $x^...
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20 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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1answer
311 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
37 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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234 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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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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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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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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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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528 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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53 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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258 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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44 views

Standard error of estimate

In order to estimate total weight of rice of 100 bags, a sample of 25 bags was weighted giving the average weight of 50 kg. If the population standard deviation is 1.5 kg, estimate the total weight of ...
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1answer
303 views

Uncertainty in Standard Deviation

I am attempting to find the uncertainty of the standard deviation. In the experiment I performed, I took 50 trials where I recorded the disintegrations over a period of time as counts. Now, I want to ...
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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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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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291 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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271 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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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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149 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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127 views

Gap correction between two curves

I have two curves like this : I would like to be able to calculate the gap between these two curves according to the Y value. For example: In my example Y < 5, error between the two curves is ...
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1answer
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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, ...