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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What is the relationship between OR, se, and CI
Apologies if this is a duplicate question, but I have been unable to find a clear answer.
What is the relationship between Odds Ratio, standard error, and confidence intervals?
I try to do a meta-...
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Binomial confidence interval over the number of trials
I have a process which succeeds with known probability $p$, and fails with probability $q = 1-p$. The process is repeated a finite, but unknown, number of times $n$.
Given a number of successes $r$ (...
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Estimation of pooled prevalence (with 95%CI) in imputed and weighted data in R
I am trying to estimate the prevalence of a binary variable "x" and its confidence interval after multiple imputations (using mice) and applying weights in R. I use Rubin's rules for the ...
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How to compute a confidence interval with an inaccurate evaluator?
Let's consider the following prompt for an LLM:
System prompt: You are an expert in Python language. Your role is to answer to any Python related question.
User prompt: <User query>
I want to ...
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How to compute confidence and uncertainity of model without ground truth from softmax output?
Suppose I have 3 classes A,B,C.
Performing:
y_pred = model.predict(X) # suppose X only two sampel
Returning vector with length ...
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How does the variance of the mean enters the theory of confidence intervals?
This semester I'm taking an elementary Physics laboratory class. We're discussing basic probability and statistics and we're interested to apply them to the study of physical measurements. I'm a bit ...
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Fixed-Length Confidence Interval for Gaussian iid Mean [closed]
I have a question on an exercise where the goal is to find a bounded length confidence interval for the mean of Gaussian random variables. More precisely, my question is on part a) of the exercise ...
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Number of subjects for test-retest reliability estimates
I am designing a study aimed at evaluating the test-retest reliability of a certain sports endurance test, which I will calculate using an ICC(3,1) following Weir (2005).
I would like to have a rough ...
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How to aggregate confidence interval from spline into intervals correctly for Cox model?
Currently i'm estimating HR splines using mgcv::gam::coxph. My spline is nonlinear and has one turn, so i'd like to divide my spline into two sections given the turn and get conditional estimates for ...
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Comparing two identical surveys with different samples sizes and response levels
Silly question, but my mind has gone blank. I’m trying to undertake a simple comparison between two samples (organisational performance) using an online survey. To obtain a CI of 80% with a margin of ...
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Why a 95%CI for difference of proportions and a 2x2 Chi-square test of independence don't agree
A 95% confidence interval for a difference of proportions and a 2x2 Chi-square test of independence both try to answer the same question, in an elementary situation, using the same distribution (...
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Interpret p-value in A/B test results
I need to interpret the A/B test results. So, I have the control cohort named Baseline and also I have two other cohorts named ...
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Confidence interval for a slope in a linear model with an interaction
lm(y ~ x + gender + x*gender)
Suppose the experimental units are 15 males and 17 females. It appears that what R does in response to the command above is that it ...
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Calculating confidence intervals with a change in the instrument
In an instrumental variable study, I have the point estimate of the outcome (a health outcome) and the corresponding confidence interval. I also have the mean of the instrument and the range (number ...
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Confidence interval - CLT , beginner level
I'm taking an online course about statistics and more precisely about the confidence interval.
Below is an exercise in which they are trying to estimate the number of shoes that can be sold for each ...
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Confidence interval with an infinity upper limit
So, I want to try finding a variance confidence interval of a unknown distribution with a known mean (With n very large). So, I first used Central Limit Theorem so that an distribution X with mean $\...
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Understanding the Interpretation of Confidence Intervals in Repeated Experiments
I understand that the interpretation of a 95% confidence interval (CI) is that, in the long run, 95% of such intervals computed from repeated experiments will contain the true parameter. I also know ...
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Find the confidence interval of ratio of variance with unknown distribution but known mean [closed]
From the previous question, I'm going to assume that for a random sample $X_1,X_2,\dots,X_n$ and $Y_1,Y_2,\dots,Y_n$, that $\frac{\bar{X}-\mu}{\frac{\sigma}{\sqrt{n}}} \xrightarrow{D} N(0,1)$ by ...
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Determining number of observations be within confidence threshold
I have a model which has an accuracy of $A$. It makes a prediction with $Y$ confidence about a number of samples. Samples are observed many times, but not all are observed equally. So my data looks ...
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Confidence interval for the range using bootstrapping
I have a machine producing parts with a variance in their lengths, each pack consists of 5 of said parts ( they are supposed to be identical ) , a pack is considered refused if the range between the ...
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Learning to do the parametric bootstrap
I learned about the parametric bootstrap (Can we bootstrap regression coefficients instead of data?) and I am interested in applying this method to determine the confidence interval on the ratio of ...
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Confidence regions for (mu,sigma) normal distribution
At the normal distribution, I want to find a confidence region for the bidimensional parameter $(\mu,\sigma)$. Is there a better way of doing so than calculating the Cartesian product of the two ...
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Drawbacks of stratified test set bootstrapping for metric UQ
I am using test-set (percentile) bootstrapping to quantify the uncertainty of various model performance metrics, such as AUROC, AUPR, etc.
To avoid any confusion, the approach is simply:
bootstrap ...
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Can we bootstrap regression coefficients instead of data?
I have a question about using the bootstrap in situations (e.g. Confidence intervals for the ratio of marginal effects? (GAM Regression)) where the traditional bootstrap method might be complicated (e....
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Confidence intervals for the ratio of marginal effects? (GAM Regression)
I have a question on how to adapt confidence intervals for marginal effects.
I have some data in R (response is between 0 and 1, t is a time variable, predictors are continuous and greater than 0):
<...
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Examples of Concentration inequalities
I'm looking for relations of the form
$$
P[X\leq \mu_N-\delta_{N,n,\epsilon}]\geq \epsilon
$$
where the random variable $X$ is the fraction of successes in $n$ samples from a binary population of size ...
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Is being "a 95% confidence interval" a property of an estimatOR, not a property of an estimatE? [duplicate]
It seems to be agreed upon that "X% confidence interval" means the following:
If I obtain an infinite amount of size $N$ samples from the same distribution and use the same procedure (...
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False interpretation of 95% confidence interval? [duplicate]
Disclaimer: I come from a science background and recently started a Master's degree in Statistics, so my current statistical knowledge comes from introductory university courses and the occassional ...
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Opposite results between one-side confidence interval and one-side hypothesis test for one proportion each other?
I'm trying an example in PennState STAT 415 (Example 9-2)
Method 1: a right-tailed hypothesis test
In short, the observed sample proportion is $\hat{p}=\dfrac{104}{590}=0.176$. The null hypothesis ...
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Compare frequencies - which approach? (Excel-based)
I'd like to check if two groups differ significantly in proportions.
To make this more concrete: I have sub-group A that represents X% of group 1, and sub-group B that represents Y% of another group 2....
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How can I properly set up a before and after analysis to determine a correlation of voter turnout?
For my own understanding, I'm interested in analyzing whether or not an increase or decrease in the lobbying of a specific industry, in a wide variation of cities, had an increase or decrease in the ...
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Contradiction when estimating uncertainties with chi2 distribution
I have a contradiction when estimating parameter uncertainties using a likelihood function with independent Gaussian errors i.e.
log L ~ exp(-0.5 chi^2)
where chi^2 is the sum of the squared residuals....
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Confidence interval for entropy from Basharin’s asymptotic normality result
Setup:
Say we have i.i.d. observations $X_1, \dots, X_N$ from the distribution given by
$$
0 < p_i := \mathbb P(X_j = i) < 1, \quad i = 1, \dots, s, \quad \text{and} \quad \sum_{i = 1}^s p_i = 1....
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Transform sample data from different populations to increase sample size
I have n = 6 for each of six different normal distributions with different means and possibly same (or similar) stdev. So the distributions have similar shape with different position of center. I ...
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Confidence interval for the difference of 2 poisson means
I have 2 samples drawn from 2 poisson distributions. My null hypothesis was that the 2nd distribution had a mean that is equal or greater than the 1st distribution. I tested this hypothesis at the 95% ...
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Problem with confidence level in GLMM with zero-inflation and zigamma family
I am evaluating which treatment promotes greater root length in a root growth analysis. I have five different treatments, each with four samples, evaluated over nine days across three independent ...
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I have got two different confidence intervals. What am I doing wrong?
I calculated a 90% confidence interval for the intercept of an OLS regression using R. When I used confint(model, '(Intercept)', level=0.90), I got a different CI from the one I calculated with [beta0-...
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Confidence bands for binary time series data
Context: I have binary data $x_{it}\in\{0,1\}$ where $i\in\{1,...,N\}$ indexes trials and $t\in\{1,...,T\}$ indexes time (independent across trials; not independent across time). It's from a ...
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Calculate confidence interval in multiple dimensions
I would like to calculate the confidence interval of a multidimensional probability vector X ($p$ dimensions, r realizations). I feel like I got pretty far already but somehow the last step seems to ...
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Wilks' theorem, confidence regions on a projected subspace?
Background
My context is I am thinking about maximum likelihood estimation of a parameter $\theta\in \mathbb{R}^r$ by drawing samples $\{x_i\}$ from a distribution which depends on $\theta$. I know ...
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BCa Bootstrap Confidence Intervals for Clustered Data
I want to compute a confidence interval for the F1-score of a machine learning model for the classification of blood cells on test data. The data is clustered, as I have multiple cells for every ...
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Looking for a book regarding outlier/anomaly detection in time series using confidence or prediction interval
I read a book/paper long time ago where the author describes how to use model and its confidence/prediction interval to detect outliers and replace them with the forecasting value.
It had a nice time ...
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Computing confidence intervals for fenegbin object when predicting predicted probabilities
I would be grateful for some help computing confidence intervals for predicted probabilities of a negative binomial model estimated through fixest::fenegbin given a ...
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Difference Between Confidence Bands and Confidence Intervals
I've read other answers on this stackexchange for this topic, but I have a few questions I would like clarified:
Confidence bands are usually visualized as the connected lines ('bands') formed from ...
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Multiple regression confidence intervals for slope coefficient of a covariate
When constructing such a confidence interval and evaluating whether it contains 0 (for the t test to see if the covariate is of relevance in the regression) are the other variables being controlled or ...
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Looking for a test on the quality of an approximated CDF
I have a $C^1$ function, $\mathcal{E}_n(x)$ that stands as an approximation of a CDF, $F(x)$ of a continuous random variable $X$, derived using $n$ sampled points, $X_1,X_2,...,X_n \sim f$. The PDF, $...
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Can the lower (or upper, for that matter) limit of a confidence interval be chosen as a parameter rather than the central value?
To create a counterfactual measure in a study on policy interventions to reduce the effect of outside temperature on mortality in later life, I would like to use the lower bound of confidence ...
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Estimating the standard deviation from only the mean and 95% CI
I need to generate a population of a variable which I can sample from in a Monte Carlo simulation. The only information I have on this variable is from a published paper in which the mean and 95% ...
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Estimate standard deviation and get a confidence probability
I have no background in statistics so please be nice. With my little knowledge, I also did not find any similar posts or at least posts that I could understand.
Here is my problem, I have a variety of ...
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Interpreting parameter distributions and 95% confidence intervals from Monte Carlo sampling
I have fit two datasets with a model (multiparametric biochemical network models) and these fits give estimates of many parameters, including one that I'll call A. The best-fit values for parameter A ...
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