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.

Filter by
Sorted by
Tagged with
1
vote
0answers
12 views

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 ...
0
votes
0answers
8 views

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 ...
0
votes
0answers
5 views

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 ...
-1
votes
1answer
17 views

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 ...
1
vote
2answers
35 views

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 ...
1
vote
0answers
7 views

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 ...
0
votes
0answers
13 views

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 ...
0
votes
0answers
7 views

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 ...
1
vote
1answer
30 views

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 ...
0
votes
0answers
51 views

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. ...
0
votes
0answers
11 views

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 ...
0
votes
0answers
15 views

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 ...
0
votes
0answers
26 views

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 ...
0
votes
1answer
11 views

confidence interval ~ minimum sample size with a maximum width

My task is: minimum sample size, which guarantees that the width of the resulting confidence interval is a maximum of W = 0.06. Is my way right? $$\ X1, ... , Xn ~ (iid) N(μ,σ²), σ=9, W= 0.06, α=0.10 ...
0
votes
0answers
16 views

Plotting confidence interval - graph showing odd results

Just wondering if anyone can help me analyse the following: I plotted my confidence intervals from a GLM, and found that a lot of the points don't overlap the C.I. What exactly does this mean ...
1
vote
1answer
14 views

How to estimate the confidence interval for a proportion of two estimated values?

I have estimated two values and confidence intervals (CIs), how can I estimate the CI of its ratio? For example, a new method has been developed claiming to reduce SO2 emission in power plants by 20%....
1
vote
1answer
16 views

Confidence interval as RV

Paraphrased question from textbook for my intro to prob. class, and just wanted to verify my intuitions: Consider 1000 95% CIs for independently-selected datasets. How many CIs do you expect to ...
0
votes
0answers
17 views

Stuck on confidence interval analysis for GLM

I'm really new to R, and sort of stats in general. I've been using a GLM to analyse a series of data, which is basically tracking how concentrations of DNA change over time, when different treatments ...
0
votes
0answers
24 views

Estimation of the Bias

I have an estimator $\hat{\mathbf{x}}$ of a quantity $\mathbf{x} \in \mathbb{R}^d$. The mean squared error $$\mathrm{MSE} = \mathbb{E}\left[(\hat{\mathbf{x}} - \mathbf{x})^\intercal(\hat{\mathbf{x}}...
1
vote
1answer
17 views

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 ...
0
votes
2answers
34 views

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 ...
0
votes
0answers
8 views

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 ...
0
votes
1answer
36 views

Find a $100(1-\alpha)\%$ confidence interval from a population $\sim$ Gamma$(5,\theta)$

For $$f(x|\theta)=\frac{1}{24}x^4\theta^{-5}\exp^{-\frac{x}{\theta}}I_{(0,\infty)}(x)\hspace{0.5cm}\theta\in\mathbb{R}^+$$ I want to find a $100(1-\alpha)\%$ confidence interval. I know $T(X_1,\...
2
votes
0answers
33 views

Hypotheses for likelihood-ratio confidence intervals

I'm working on a physics research project, and in the process I've managed to both firm up my understanding of statistical significance (I hope) and confuse myself somewhat. The question I'm looking ...
4
votes
1answer
80 views

Distribution-free confidence interval for IQR

I am looking for a way to calculate confidence intervals for the interquartile range IQR of a numerical variable. Of course, they can be found by the bootstrap, but I am explicitly looking for a ...
0
votes
0answers
8 views

Can you find the confidence interval with just percentages?

If you are given two relative risks, and you use them to find odds and odds ratio, however you are not given any numerical values. You are just given the risks, why is it not appropriate to create a ...
2
votes
1answer
41 views

The difference between approaches to find 95% interval in normal distribution

I ran across two very similar problems but each one's supposed answer is approached very differently. Problem 1: A large study of serum folate levels in a sample of women age 16-45 reveals that ...
1
vote
0answers
10 views

Bootstrap confidence intervals for betas in a linear mixed model

I am trying to calculate bootstrap intervals for my beta coefficients in linear mixed effect models. I used the lme()function from the ...
1
vote
0answers
18 views

Interpreting overlap of bootstrapped confidence intervals

Assuming two samples of numeric values for two groups of unequal group sizes (e.g. 100 opinion scores collected from group A and 15 opinion scores collected from group B), I understand that non-...
1
vote
0answers
32 views

What are the assumptions for estimating a confidence interval through bootstrapping?

Context I created a rule based classification model for flagging emails about a certain topic. The process for creating that model, was to look at contents and flagging the email if certain terms are ...
2
votes
0answers
100 views

K-fold cross validation based standard errors?

I have an expensive model (or class of models). My baseline approach to quantify uncertainty re the model parameters are hessian based standard errors, and I use k-fold cross validation for model ...
1
vote
1answer
58 views

Calculating the Standard Error and Confidence Interval for Cohen's Quadratic Kappa

I need to evaluate the performance of a machine learning application. One of the evaluation metrics chosen is Cohen's Quadratic Kappa. I found this Python tutorial on how to calculate Cohen's ...
1
vote
0answers
17 views

How to determine if updating a variable will result in a target output within some confidence interval?

I'm trying to optimize a manufacturing process for work, and was stuck when trying to estimate our confidence in a settings update procedure. We are trying to configure an instrument setting (x) from ...
1
vote
1answer
17 views

Is this 95% Confidence Interval Based on the Corrected Correlation or Uncorrected Correlation in Meta-Analysis

My questions are: Is the 95% CI in a meta-analysis based on the uncorrected correlation or corrected correlation? Can a 95% CI have an upper limit that is smaller than the lower limit? Context: I'...
0
votes
0answers
7 views

Minimum variance vs. Value at risk

When computing Minimum Variance Hedge Ratios as explained f.e. in Hull (2012) the goal is to select a hedge ratio such that the variance of the portfolio is minimized. My question is now what are the ...
1
vote
1answer
24 views

Quantiles from Lognormal distribution

Is there a closed form solution for the quantiles of the lognormal distribution. And if so can they also be interpreted as Value at Risk measures? F.e. is the 5% quantile of a lognormal PDF equivalent ...
1
vote
1answer
14 views

What is the confidence interval formula that RMISC package in R uses? [closed]

I tried figuring out the formula that the RMISC package uses but I wasn't sure, I couldn't find the documentation on it? I tried using the t, and Z statistic but it wasn't giving me the same answer as ...
1
vote
2answers
36 views

Confidence interval of the proportion in case of 0 [duplicate]

I am trying to estimate the (say 95%) confidence interval of a proportion. For instance, I want to estimate how many students will take a particular course next year. There are N1 students in total. ...
1
vote
0answers
46 views

How to calculate coverage probability from binomial confidence intervals?

For a given alpha I have been calculating various confidence intervals for a binomial distribution(Wald, Wilson, Agrest-Coulla etc.): ...
0
votes
1answer
25 views

Which reference could I cite for using confidence intervals instead of P-values when using robust linear mixed models (R package: robustlmm)?

I am using the R package robustlmm for some analysis due to its characteristics. I have read in posts like this one that with this type of models is better to use confidence intervals than $p$-values, ...
0
votes
1answer
21 views

Expected outcome and its confidence interval

Recently I was asked about this issue in an interview and I am curious about the result. We have a coin, fair or not, and we toss it 100 times. As a result, we get 20 Heads and 80 Tails. A) What is ...
0
votes
0answers
15 views

Confidence interval for categorical samples as a percentage

I have some randomly sampled data and I'm looking to slice the data into subgroups and present an attribute as a percentage of several categories (e.g. attr == A | B...
2
votes
0answers
45 views

Confidence intervals for sum of n rolls of a biased k-sided die

I have a distribution that is similar to taking the sum of rolling a possibly biased k-sided die n times. For simplicity, let the die be three sided and let the numbers of the faces of the die be 1, 2 ...
0
votes
0answers
6 views

Prediction band for linear regression with multiple parameters

I found the following equations for computing the prediction interval of a simple linear regression: $s_{\hat{Y}_{X}} = s_{Y|X}\sqrt{\frac{1}{n}+\frac{\left(X-\bar{X}\right)^{2}}{\sum_{i=1}^{n}{\left(...
1
vote
0answers
13 views

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 ...
1
vote
0answers
26 views

Estimating Cost of Querying a System and Developing Distributions

Okay so, Pretend you have a gum ball machine with many different colors. It cost $X to get a gum ball out of the machine. You want to take a sample to produce good distributions of the diameters of ...
0
votes
1answer
26 views

confidence interval for arbitrary distribution

Let's say I have some random variable $X$ whose CDF can be evaluated exactly but cannot be Inverted .Can someone given me an algorithm or some pointer to relevant source which talks about this.Every ...
2
votes
0answers
19 views

Calculating 95% confidence Interval, without R

For my exam we are given extracts of data from R, usually with a summary and ANOVA table. From there a question that often comes up is to calculate a 95% confidence interval for a given variable. I ...
2
votes
1answer
16 views

It is possible to find point estimate of population mean and population variance when confidence interval of population mean is given?

Let's say that somehow $100(1-\alpha)\%$ confidence interval of population mean $\mu$ is known as $(a,b)$ and the number of samples is $n$. Is it possible to infer point estimates of population mean ...
0
votes
0answers
5 views

Get confidence bound for dependent observations

I have created a metric which is basically a way of assessing performance of an individual by looking daily at the performance and compare to the performance level before the individual started. So ...

1
2 3 4 5
68