# Questions tagged [confidence-interval]

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

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### Wilson confidence interval - question on conventions

Is there a convention when using the Wilson interval and all observations are successes (or failures) to artificially increase or decrease the lower bound of your CI estimate to encompass the ...
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### Errors on 'Profiling Confidence Interval' after Maximum Likelihood Estimation in R

I'm practicing a cancer treatment model using Maximum Likelihood Estimation with 'bbmle' packages in R. Step 1. I generated a virtual dataset ...
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### How to handle multiple test correction between conventional p values and bootstrapped confidence intervals?

I have a correlation matrix and point estimates from mediation analyses all for a single research paper. I'm treating this paper as a single family of tests. The data is not normally distributed so ...
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### Are the confidence intervals and p-value for this risk consistent?

I'm trying to calculate a risk ratio with the following 2x2 contingency table, where the rows are exposure groups and the columns are disease status. The first row of the matrix shows that 1/38 ...
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### Pivotal Quantities for confidence intervals - Why does it work?

I try to get an intuition on, why pivotal quantities are used to construct confidence intervals. First, I show how I understand the algorithm: For example let $x_1,...,x_n \in \mathbb{R}$ be ...
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### Interval Estimation for a Binomial Proportion Given a Specific Test Outcome

Imagine that I had a coin, I tossed it 10 times (n) and it came up heads each time (x). What proportion heads I would get if I tossed it infinity times? A point estimate is 100%. I can get the ...
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### Confidence Intervals on Predicted Values

Here is a distillation of the problem: There are 100,000 trials. On each trial, a model predicts a number between 0 and 6. The model that makes these predictions has been shown to be 90% accurate on ...
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### Calculating a Weighted Standard Error of the Fit for Nonlinear Regression

I have a data set of $N$ points to which I have fit an equation of $n$ parameters $\theta_{1..n}$ such that $y_i \sim f(x_i; \theta_{1..n})$. These data $(x_{1..N},y_{1..N})$ have been provided with ...
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### Understanding confidence intervals with coefficients

maybe someone can put me in the right direction. I already read some of the "understand confidence intervals" posts, but none of them seem to give me the information I need. I am a student and I am ...
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### Pooled samples: estimating prevalence of disease

Struggling to understand the concept of pooled sampling and estimation of prevalence. Would really appreciate some help to understand this. Example: 0.5% of the population has a specific disease. ...
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### Std error of measurement and CIs for inter-rater observations

Reliability is often reported somewhat abstractly and can be difficult to interpret (e.g., ICC = 0.9). For test-retest reliability, it can be helpful to express measurement error in the scale of the ...
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### Confidence Interval for a sampling P95 in unknown distribution

TLDR: I need to estimate what is the minimum sample size to get a W-wide confidence interval of daily Response Time's P95 of which I only get a sample of events. Detailed: Due to a Service Level ...
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### Odds ratio and confidence interval with IQR increase

I am fitting a logistic regression model and I have an IQR increase of exposure. As I want to get the 95% confidence interval when one IQR increase is applied, I feel I am a little bit confused. I ...
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### Calculating confidence interval for cross-sectional study with dichotomous variables

I am conducting an epidemiological study and will have results that tell me which proportion of my population will have immunity to a certain disease. The results here will be immune / not immune with ...
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### Precise definition of the confidence interval - sources?

I always thought that the CI is defined as the set of parameter values corresponding to hypotheses which we can retain. But I struggle to find a source for this definition. Is it not correct? Most ...
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### Simmetry confidence intervals [duplicate]

I am reviewing the construction of confidence intervals for a random sample with Bernoulli distribution. The book uses the statistics of the central limit theorem that distributes $N(0,1)$ to estimate ...
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### How to (easily) calculate confidence & prediction intervals AFTER a model selection procedure?

First of all, this question refers mostly to linear regression. When someone uses a model selection procedure, for example, choosing the optimal dimensionality of the predictor space via best subset ...