# 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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21 views

### Confidence Interval of linear regression model - Standard Deviation vs Standard Error

For a (large) experimental dataset I am assuming a quadratic model and perform a regression analysis. Then I'd like to have some information about the accuracy of my model parameters, so I'm ...
16 views

### Standard error in Data for regression

I am working on my thesis and there I need to approximate a function in the sense of sum of the square differences, i.e. $$\min \sum_{i=1}^{n} (y_i-\eta_i)^2$$ for the function $y$ and Data $\eta$....
22 views

### Standard Error propagation for correlated variables

The following is a toy problem to illustrate my question. Let $[A_{1}, ... ,A_{n}]$ be a series of $n$ random variables. Each variable has $m$ observation under two experimental conditions resulting ...
34 views

### Statistics 101: T test vs Z test. Sample proportion vs Sample mean

Sorry, I'm just on Khan academy and can't seem to grasp the essence of statistics. Hope to find some help out here. Both are samples, but why when looking for confidence interval of a: sample ...
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### What is suitable error measurement to find time error that cause from different values of parameter?

This is the figure I obtained from Maple software. Now I need to find time error from this figure. The exact solution is in blue line and the other line are approximated solutions. Can someone suggest ...
34 views

### Calculating a confidence interval

In a random sample of $n=400$ people, 136 said they liked the product. Construct a $95\%$ confidence interval for the population proportion who might like the product. The sample proportion $\hat p$ ...
36 views

### How to calculate the threshold value to change the Welch's T-Test? [closed]

Given I have two samples where for each sample I know: Number of Values: $n_1, n_2$. The means: $m_1, m_2$. Standard Deviation: $s_1, s_2$. Also each sample share a min and max value that it can ...
27 views

### How to incrementally update a Welch's $t$-Test?

Say I have two sample distributions where for each distribution I know: Number of Values: $n_1, n_2$. The means: $m_1, m_2$. Standard Deviation: $s_1, s_2$. With this information I am able to ...
27 views

### Variance of Sum to Sum of Variance

There are some proofs of this idea elsewhere but I am trying to demonstrate it to myself with a specific example so as to understand the derivation of the formula for the Standard Error of sample ...
38 views

### What's the difference between 'standard error' and 'estimated standard error'?

100 people are given a standard antibiotic to treat an infection and another 100 are given a new antibiotic. In the first group, 90 people recover; in the second group, 80 people recover. Let $p_1$ be ...
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### Statistical inference-wise, should I just worry about the standard error of the random part of my model?

I am modelling my real world system as: $$Y = f(x) + E$$ where $f$ is my deterministic model with some parameters $\theta_{1}$, $\theta_{2}$, ... and $E$ is the random part (stuff I can't explain, ...
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### Definition of a priori and a posteriori Error Estimates for General PDE

My question will be written rather loosely because I can only imagine any answer will be very general. Given some PDE : $$u'(t)= -\nabla \phi(u(t)),~~u(0)=u_0,$$ what do authors mean when they ...
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### Estimation of the standard deviation for Power Law distribution

I've understood everything in the picture (source) below except for this equality: $$\hat{\sigma} = \frac{\hat{\alpha} - 1}{\sqrt n}$$ Can someone please explain where does it come from?
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### AP STATISTICS 2008 EXAM Question on standard error of estimated proportion

This question is taken from the 2008 AP Statistics free-response question 4) An experiment was conducted to study the effect of temperature on the reliability of an electronic device used in an ...
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### Uncertainty in Grabbing Colored Coins

Suppose I have a source of red and blue coins that have a red composition of absolute percentage $a_r$ with uncertainty $\sigma_r$, and similar measures for blue. If I take $N$ coins randomly from the ...
28 views

### Statistics question on errors and probability with Coronavirus

Recently a survey in California suggested that considerably more people have been exposed to COVID-19 than previously thought. However, the testing equipment used apparently has a 1.7% false positive ...
18 views

### Best way to determine improvement knowing the mean, standard deviation and standard error of the measures

I have data of a study carried out on two groups of people, one of 13 and the other of 22. Each group was given two measurements, one at the start of the experiment and another one at the end. ...
14 views

### Wald Statistic from Odds Ratio & Standard Errors

Say I have a data frame, and I have the columns: "Species", "Odds Ratio" & "Standard Errors". I am asked to create the Wald test statistic for each species. How would I go about doing this? ...
52 views

### Standard deviation, standard error and confidence interval difference explanation

I write some code to generate random weights (I define low as 50Kg and high as 100Kg) of males, then generate 100 samples containing 100 measurements (weights per sample) i.e. 100 samples and each ...
31 views

### Uncertainty estimate of a sample of one

A monte-carlo approach to a problem produces many thousands of possible solutions, each ranked according to the total residue from observed data it implies, so that the solution with the lowest net ...
17 views

### Standard error and estimating intervals

I've been teaching myself some statistics and upon doing this problem I've stumbled at the very last part: I've had no problem reaching $\mu\approx x=220.1$ and $\sigma\approx y= \frac{1}{2\sqrt{5}}$,...
29 views

### Minimum iterations to guarantee a forward error of $\epsilon$

can anyone shed some light into this for me. I am asked to numerically solve $$x\arctan(x) = 1$$ and to ensure that the error $\epsilon$ is less than $10^{-3}$. Now I usually use Newton's method for ...
22 views

### When NOT to use Bessel's Correction for Standard Deviation

I can not find a clear explanation for when NOT to use Bessel's correction and use N instead of N-1. As I understand it, Bessel's correction would apply to things such as clinical trials, sampling ...
41 views

### How to calculate means and errors of intrinsically correlated runs?

I am currently simulating a molecule and need to calculate the global mean value and more specifically the error of the global mean of a parameter $r$ denoting its size. To do that I have a multiple ...
28 views

### Sampling error propagation

Imagine you have a population of size N, and a sample of size n. The population comes in three kinds ('red', 'black' and 'blue') and we want to know the proportions of each kind. For 'red' we would ...
19 views

### Root mean squared error (RMSE) vs Mean absolute error (MAE)

I have measurements from two different sensors. The one sensor is very accurate. The other sensor is sensitive to noise. I would like to calculate the error between these two sensors but I am not sure ...
87 views

### How do I calculate the uncertainty of this percentage difference?

So, I am working with a data set that is 'supposed to' follow a Poisson Distribution, so that $\langle N \rangle = \sigma^2$, where $\langle N \rangle$ is the mean of my measurements $\{n_i\}$ of the ...
47 views

### Linear Codes : Error detection

The code words of a linear code $C$ have the length $n=5$. Writing the code words into a matrix to get the linear independent ones, we get the following: \begin{equation*}\begin{pmatrix}0 & 0 &...
25 views

### Is it possible to infer the uncertainty of predictions for a time series model from the residuals distribution of a large representative sample?

Let me illustrate the question with an example: Imagine you construct a model to predict tomorrow's rainfall over London using some variables. Let's suppose that 300 years of data are available (1718-...
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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 ...
18 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, ...
40 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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### 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\...
73 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 ...
23 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 ...
2k 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 ...
41 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 ...