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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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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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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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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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45 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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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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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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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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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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58 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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241 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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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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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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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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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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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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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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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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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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122 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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96 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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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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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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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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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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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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46 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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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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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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128 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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149 views

Bivariate Normal Distribution Standard Error

Data from a large population indicate that the heights of mothers and daughters in this population follow a bivariate normal distribution with correlation 0.5. Both the mothers and daughters have a ...
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derivation of standard error - Why can we assume all variances can be the same?

I'm learning how to derive standard error of the mean mathematically. I understand that standard error is the square root of the variance of the mean: $SE =\sqrt {Var((x_1+x_2+...+x_n)/n}$ And ...