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Questions tagged [confidence-interval]

A confidence interval is an interval that covers an unknown parameter with $100(1-\alpha)\%$ confidence. Confidence intervals are a frequentist concept. They are often confused with credible intervals which is the Bayesian analog.

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Concentration bounds for a mixture of a fixed value and a uniform distribution

Suppose we have a mixed random variable $R= (1-p)X + pU$, where $X$ is just a single value $X \in [-\pi, \pi]$, $0 \leq p \leq 1$, and $U \sim \text{Uniform}[-\pi, \pi]$. I.e. a single trial returns $...
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How to construct class proportion confidence interval for an LLM classifier with known bias and precision and recall?

Let's say I have a dataset, $D$, with known ground truth labels. I nonetheless use a few-shot LLM classifier on this dataset to predict $k$ classes for each label. From the LLM results, I get ...
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How to generate 95% prediction interval around predictions from ML model?

I have predictions from an ML model and would like to generate 95% prediction intervals around each prediction generated from the model such that I can claim that these are the plausible range of ...
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My questions are related to the outputs of model built with npmlt function [closed]

I fitted (using npmlt function) a mixte multinomial regression model which ran without errors. I expecting that the outputs of the model includes p-values that I didn't find. My need now is that ...
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Probability of fixing error in application, given successful and unsuccessful runs before fix

An application communicating with a database started to fail with network errors. The errors occur only during some runs, and at random times when running the application. If a network error occurs, ...
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Why are confidence intervals valid? [duplicate]

Recently, I began my statistics journey to understand the field better. Previously, my experience with statistics consisted of memorizing formulas, conditions, and applications of the latter. While ...
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confidence intervals for proportions containing a theoretically impossible value (zero)

This is really a hypothetical question not related to an actual issue I have, so this question is just out of curiosity. I'm aware of this other related question What should I do when a confidence ...
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confidence interval and rejection

Assume I have a data sample $X_{1}, \dots X_{n}$ from a normal distribution. Then, we consider the following hypothesis $$ H_0: \quad \mu = \mu_{0} $$ and alternative $$ H_1: \quad \mu \neq \mu_{0} $$ ...
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Confidence intervals when using stratified proportionate random sampling

I have hypergeometric distribution with population size N. I need to estimate population proportion p. I would like to use confidence interval. I have also three non-overlapped groups in my population....
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Worst-case analysis using confidence intervals

I need to state something about the minimum expected value of the population with a certain confidence, and I'm not sure if I understand the process correctly. Say I have a process with a strict ...
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How to calculate confidence interval using the delta method in R?

I'm trying (struggling) to calculate the delta method for a confidence method in R. Does anyone know how to do it? Any advice would be most welcome. In the literature, there's a simple IV/2SLS model ...
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Notation to report the measurement of a parameter

The estimation of a parameter ($p$) is customary reported in Physics and other fields with, $ p = \hat{p} \pm \Delta p$, where $\hat{p}$ is an estimator, and $[\hat{p} - \Delta p, \hat{p} + \Delta p]$ ...
Diego Ravignani's user avatar
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How to actually use the Empirical Influence Function for BCa Bootstrap Intervals?

In the course of seeking reassurance for another part of a hobby analysis* I found a stack answer which mentioned The Jackknife, the Bootstrap and Other Resampling Plans (Efron, 1980). Having managed ...
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Interpreting differences between confidence intervals with and without adjustment for clustering. Should those from adjustment be wider?

I am trying to interpret an article involving data from a cluster randomised trial, where the confidence intervals for effect sizes are said to have been adjusted 'using the standard errors of the ...
Roger Gomm's user avatar
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How to express the uncertainty in the OR of a right-tailed Fisher's exact test?

Many OR (odds ratio) visualizations show 95% confidence intervals expressing uncertainty like on the left panel in figure below. However, in genomic overrepresentation analysis right tailed Fisher ...
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Intercept significant, but confidence intervals around its standardized β include 0

I ran a HC (‘robust’) regression. The intercept is significant, which is reflected in the confidence intervals around the unstandardized betas. However, the CIs around the standardized β are quite ...
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Prediction bands for weighted linear regression

For a linear regression of $x_i, y_i,$ we know that the confidence intervals are: $$\hat{y} \pm t \cdot s \sqrt{ \frac{1}{n} + \frac{(x - \bar{x})^2}{\sum (x_i - \bar{x})^2} }$$ and prediction bands: $...
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Extract credible/confidence interval of a threshold in a Bayesian posterior draws distribution [closed]

I have a Bayesian model created through bayer package in R on which I need to calculate confidence/credible intervals for a ...
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2 votes
1 answer
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Predicting cost for several options and then choosing the cheapest option

I created an ML model that predicts the cost of shipping an order in our online store. For each order placed, there is a variable number of methods (up to 10) available to ship. So for one order, ...
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Expected Value Chi Square distribution

I'm trying to simulate the distribution from the sample variance $s^2$ and compare it with the theoretical distribution. Therefore, I perform a fairly simple simulation (upfront, I'm not a ...
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How to implement an Anderson-Rubin test and calculate confidence intervals for an iv model set up with plm in r?

I have run an IV model using the plm-package in r. The underlying data is panel data. My instrument is "weak", i.e. the F-statistic lies below 10. How can I implement an Anderson-Rubin test ...
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How to determine the confidence intervals for the principal axes of a second-rank tensor?

The question in short: How does one estimate the confidence intervals for the principal axes of a second-rank symmetric tensor when the measurement errors are themselves a function of the values of ...
Armadillo's user avatar
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In Regression Through the Origin, why do the CIs of the slope depend on datapoints with zero x value?

I'm working with a Regression Through the Origin model as described in this reference. The model is $Y_i = \beta X_i + \epsilon$ and the least squares estimate of $\beta$ is $\hat\beta = \frac{\sum ...
Ryan Moulton's user avatar
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Updating population variance assumption after sampling

I'm trying to get my head around how to think about a situation where an assumption on the population variance in the sample sizing stage of an experiment goes wrong. Let's say I'm estimating a ...
Nils Gudat's user avatar
11 votes
2 answers
160 views

Confidence int. expands much more rapidly than prediction int. as we depart from $\bar X$

In this post we see a regression plot (pasted below) with a confidence interval (CI) and a prediction interval (PI). The CI is expanding fairly noticeably as we get further away from the mean of $X$ (...
Richard Hardy's user avatar
1 vote
2 answers
40 views

Calculate combined confidence interval of two variables in a negative binomial model (in R) [closed]

I have a multivariable negative binomial model in R for which I want to combine two variables: Variable 1: binary variable (no/yes) Variable 2: continuous variable (0-3) I want to calculate ...
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Using Predictive Value Confidence Intervals to "Predict" Outcomes

Here's the quick version: Say I have a confusion matrix with the following data based on a proficiency cut score on a pretest and outcomes on (passing/failing) a class. The cut score was determined ...
jacev123's user avatar
2 votes
1 answer
42 views

Why is it recommended to keep use.u=T (in bootMer) when doing parametric bootstrap for lmer models?

I am performing a parametric bootstrap with the intention of using the simulated values to create confidence intervals for my coefficients in a mixed model. I saw that it was generally recommended to ...
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How to compute the confidence interval of root mean square (e.g., ci of the RMS of the alternating current signal)

If $\bf x$ are $N$ measurement of alternating current signal (sinusoidal), its root mean square is computed using $RMS=\sqrt{\frac{\sum{x_i^2}}{N}}$. My question is: Does the confidence interval exist ...
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Why Do AR-NN Models Have Tighter Confidence Intervals Compared to Linear AR Models?

I have conducted a forecast for the following data series using different autoregressive models: Intercept-only, AR1, AR2, ARIMA BIC, ARIMA AIC, and AR-NN. Using the point forecasts, the AR1 model is ...
george1994's user avatar
1 vote
1 answer
66 views

Calculating confidence intervals for proportion data (multiple data points)

Folks - I am looking for a way to calculate a confidence interval (e.g. 95%) or other metric of variability for a data series (a sample of multiple data points) in which the data are all proportions (...
Alex H's user avatar
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Statistical test for variability among more than one group

I am very new to statistics and still learning. Below are the funnel graphs which shows the effect/percentage of polypharmacy(patients with two or more drugs) against practice/hospital population size....
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How were the asymmetric recovery ranges in Table A5 of Appendix F from AOAC determined?

I am trying to understand how the recovery ranges in Table A5 of Appendix F from AOAC (https://www.aoac.org/wp-content/uploads/2019/08/app_f.pdf) were determined. I did not understand how the ...
Éderson D'Martin Costa's user avatar
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Confidence intervals ODE ridge regression

i want to find confidence intervals for a least squares loss which is L2 regularized. I have only found something for linear problems, but in my case i want to estimate ordinary differential equation ...
LH44Stat's user avatar
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0 answers
21 views

Confidence intervals for distance correlation in R

I've been trying to calculate the confidence interval for a distance correlation (energy::dcor) between two variables, and its p value. The data is: ...
Capi Bara's user avatar
6 votes
1 answer
112 views

Valid confidence intervals in GAM’s using shrinkage estimation

In this blog article: https://www.fharrell.com/post/improve-research/ it states: “The frequentist paradigm does not provide confidence intervals or p-values when parameters are penalized”. I was ...
user167591's user avatar
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2 answers
37 views

How to estimate the confidence interval of a very small proportion? [duplicate]

I want to the estimate the confidence interval of a very small proportion. Let's say I have simple random sample of 1000 and 4 people answered the question with yes. One might want to make use of the ...
as_meth's user avatar
4 votes
1 answer
249 views

Comparing coefficients and confidence intervals when some categories have very few observations (logistic regression)

I'm fitting a logistic regression model (with multiple predictors) to data where the outcome is a success or failure. My data points are in the range of 100,000. Most of my variables are categorical, ...
Myungjin Hyun's user avatar
3 votes
1 answer
31 views

Can/should a scientific paper simultaneously perform one-sided hypothesis testing and a two-sided confidence interval?

Let's say you wish to perform a one-sided hypothesis test in which you want to reject $H_0: \Delta \leq 0$ in favor of $H_1: \Delta >0$. You select this hypothesis test specifically because you are ...
NovicePatience's user avatar
2 votes
1 answer
63 views

Confidence interval for GLMM

I am conducting a GLMM for my bachelors thesis and I am wondering, how I can calculate and whether it is common to report confidence intervals for the models' estimates. This is the model I fitted on ...
Johanne's user avatar
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6 votes
2 answers
313 views

Highest-density vs equal-tailed confidence interval

When a sampling distribution is symmetric (and I'm okay assuming unimodal too, if necessary), it's natural to center confidence intervals around the point estimate. But for a skewed distribution (e.g. ...
Quinn Culver's user avatar
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0 answers
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How do I find confidence interval and what do I do with confirmation points?

I'm running a face-centered composite design with confirmation points. Am I correct in my assumption that the "S" I get from Minitab can be used to calculate CI? If not, how do I get the CI? ...
Ladislav Révay's user avatar
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1 answer
38 views

Standard error and confidence intervals [duplicate]

About theoretical concepts... We use confidence intervals to do an inference to extrapolate results from study to similar sample. Is this true? Which is the difference between a confidence interval, ...
mdscience's user avatar
6 votes
4 answers
991 views

Is it incorrect terminology to say "confidence interval of a random variable"?

I have seen claims that "population paramter is not a random variable" when discussing confidence intervals. eg here Be sure to note that the population parameter is not a random variable. ...
Shreyans's user avatar
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6 votes
1 answer
168 views

Gaussian Process: confidence interval vs prediction interval vs credible interval

Let a distribution over functions be described by a Gaussian Process (GP) prior, following the notation of Rasmussen and Williams: $$ f(\mathbf{x})\sim\mathcal{GP}(m(\mathbf{x}), k(\mathbf{x},\mathbf{...
abc's user avatar
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1 vote
0 answers
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Why confidence interval for proportion uses z instead of t score? [duplicate]

The confidence interval (Wald interval) for the parameter $p$ of a binomial distribution is computed from the approximation by a Normal distribution: $$ \ p ~~ \approx ~~ \hat p \pm \frac{\; z_\alpha\ ...
luchonacho's user avatar
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3 votes
1 answer
62 views

P-value vs confidence interval interpretation

Refreshing on hypothesis testing. A p-value is defined as "the probability that an observation would be as or more extreme than observed given that the null hypothesis is true." The null ...
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1 vote
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Help with sequencing topics in undergrad stats course

For several years I sequenced my stats course so that estimation theory came before sampling theory. Seemed to make sense—you need a couple of estimators in hand to talk about their distributions. But ...
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0 answers
22 views

What is the meaning of confidence intervals when NOT using sample data and instead have data on the whole population? [duplicate]

I'm trying to understand why you would need confidence intervals or compute statistical tests (for comparing proportions) when your data is NOT from a sample and you have data on the whole population. ...
Jam.Wil's user avatar
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0 answers
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Start of instantaneous hazard rate

I'm looking at survival of organizations, with survival in years. I want to produce an instantaneous hazard plot with a confidence interval. I first used pehaz from ...
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