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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Exact/Approximate Confidence Interval of Parameter Ratio from two Samples of iid Exponential

Suppose 2 independent samples $X_1,...,X_n \sim Exp(\lambda_1)$ and $Y_1,...,Y_m \sim Exp(\lambda_2)$, and are iid within samples. I am thinking about how to make an exact confidence interval for $\...
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Confidence intervals for variations of the standard nonparametric bootstrap

The standard nonparametric bootstrap (sometimes called the $n$-out-of-$n$ bootstrap) of Efron (1979) and others takes resamples of the same size $n$ as the original dataset. However, in certain cases, ...
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Why don’t we calculate the average of an entire given population instead of computing confidence interval to estimate the population mean?

We compute confidence intervals to estimate the true population mean of either a sample (when population standard deviation is unknown) or an entire population (when population standard deviation is ...
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Why do confidence intervals width increase when sample size increases "a bit"?

I'll try to explain better. I sampled a LogNormal random variate and I extracted 12001 and 12002 samples (with same initial seed for Random Number Generator). In the first case the half width of ...
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calculate confidence intervals of two metaestimates

I basically have two metaestimates ( incidence of ARI and RSV positivity) with 95% CI and want to multiply these two estimates for the final estimate and calculate its 95% CI. Can someone suggest how ...
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How do we interpret odds ration below 1 when the 95% confidence interval lies below 1? [closed]

I have done logistic regression and the odds ration got was below 1 and I have noticed that the 95% confidence interval for the effect estimate which I got lies below 1. The p-value is statistically ...
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How to construct a confidence interval for the coefficients of a multivariate regression with dependence between dependent variables?

Suppose we have two linear regression models $y_1=a+bx+\epsilon_1$ where $\mathbb[\epsilon_1]=\sigma_1$ and $y_2=c+dx+\epsilon_2$ where $\mathbb[\epsilon_2]=\sigma_2$. In other words, I am using the ...
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If I have two confidence intervals that overlap, what can I say about the two statistics?

Suppose I had two statistics and I were to construct confidence intervals off the two statistics, and that they overlap. From what I understand, we cannot make a statement about the difference between ...
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Why not always use CI's from LRT since they don't require symmetry?

I'm confused on why anyone would appeal to asymptotic normality of mle, $$\hat{\theta} - \theta_0 \rightarrow^D N(0,I^{-1}(\theta))$$ When we can simply invert the likelihood ratio test $$L(\hat{\...
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Reporting uncertainty from a Monte Carlo simulation

I am confused about the how to report uncertainty in Monte Carlo simulations. Take this simplified example: Say I want to model a system with the following system equations: ...
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Proving a result in maximum likelihood theory: accuracy of the quadratic approx. to loglikelihood

I need help proving a result shown in a paper. I am reading Assessing the Quadratic Approximation to the Log Likelihood Function in Nonnormal Linear Models by Salomon Minkin. The paper defines several ...
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Confidence Interval - small dataset (30 records)

I'm trying to calculate a confidence interval for data analyst salary population. I have a very small dataset from a job posting site that contains only 30 records. The dataset doesn't follow normal ...
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1 answer
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Post-hoc power analysis for null results: how to use 95% confidence interval instead?

My PI is having me run a post-hoc power analysis on our samples, with a treatment and control group and a binary outcome. I was using this website to start the process. However, at the end, the ...
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How to interpret a specific confidence interval? [duplicate]

I am curious is there a formal definition for an individual confidence interval? I am seeing 2 very different sets of definitions for individual confidence interval: Definition 1: According to this ...
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Determining direction of effect in Wilcoxon Test and interpreting pseudomedian in R

I originally posted this on Stack Overflow (https://stackoverflow.com/questions/72649894/determining-direction-of-effect-in-wilcox-test-and-interpreting-pseudomedian), but I realized it fits better ...
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Hypothesis testing for $\sigma^2$ in linear regression

I'm trying to figure out a way to test hypotheses about variance in the linear regression model. The hypotheses I want to test are: \begin{align*} &H_0:\sigma^2=1\\ &H_1:\sigma^2<1 \end{...
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What sources of uncertainty are included in a (95%) confidence interval?

Today, I came across an interpretation of 95% confidence interval (thereafter "CI"). The text has been written from education science perpective saying that, beside a (1.) random sampling ...
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Calculating confidence intervals for gamm4 models [closed]

I am working with gamm4 models in my research and am having trouble understanding how to go about calculating confidence intervals for my models. EX model: m<-gamm4(turbidity~ year+discharge,data=...
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Predict future values of a variable from historical data

Thanks in advance I have a problem statement at hand that requires me to predict the lead time for a supplier-material combination. the historical lead times are erratic and continuous in nature and ...
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2 votes
1 answer
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Can the confidence interval assess the goodness of fit of fitted regression line?

I understand that the confidence interval for the mean is completely different from the confidence interval band for the regression model. I also understand that the confidence interval bad represents ...
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Confidence Intervals for ICC

I was wondering if anyone might know of a way to calculate confidence intervals around an ICC(1) value? I'm running a multilevel model using the lmer() function in lme4 where I'm interested in seeing ...
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1 vote
1 answer
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Confidence interval for a rate ratio

My question is easy, but I really got stuck here ... Say I have 500 people, among them, 200 likes eating ice cream. Among these 200, 60 likes strawberry ice cream. So the rate ratio of ice cream vs ...
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Inter-laboratory results comparison

Having sampled nitrogen at several points on the fields, we sent the samples to three different institutes. The results for the same point should be comparable but it seems that the values measured by ...
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Meta-analysis of paired count data

I have data from 70 studies reporting number of observed events in two time periods, one before Covid and one during the Covid pandemic. The duration of the timeperiods and the size of the population ...
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How to construct a confidence interval for the difference between two means of a two normally distributed RV $X,Y$, that are dependent on one another

How to construct a confidence interval for the difference between two means of a two normally distributed RV $X,Y$, that are dependent on one another. The variance is known So we have: $$X \sim N(\...
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Error in Faraway "Linear Models with R" treatment of confidence intervals?

I have recently been reading Faraway "Linear Models with R" and I am particularly interested in the section for computing and plotting confidence intervals. On page 45, he provides the ...
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Schemes for increasing the joint coverage probability of confidence intervals with sample size

I'm estimating a fixed number of parameters and I want to have joint confidence intervals for them. However, for reasons that would take most of a paper to describe, I'm looking for a scheme that ...
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Trying to understand how to calculate a hotelling's T2 Confidence Ellipse

I have read probably too many things and maybe confused myself along the way :) Anyway, let's say I had a data set that I have performed PCA analysis on. Let's say a spectral dataset 100 observations ...
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1 vote
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How to find an intersection of confidence intervals [closed]

I need to calculate the uncertainty level of the intersection point of two lines given that we know the confidence intervals (CI) for both lines. Is the intersection of lines CIs would be a ...
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1 vote
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Standard error for a difference-in-difference estimate

I am trying to calculate a difference-in-difference estimate. I have a binary outcome variable, and have estimated risk differences for my intervention and control groups. If we take an example where: ...
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How to Calculate the Variance of the Aggregate of a Bernoulli Process Given Known False Positive and False Negative Rates

I have $n$ sensors which output either $0$ or $1$. These sensors have known measurement error reflected by a false positive rate, $fpr$ and false negative rate, $fnr$. In my case, $fnr > fpr$. ...
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Confidence interval for multiple mutual information values / G-test values

I have a dataset with N observations and I have expected labels for those. By putting disturbances on the observations (noise, introducing missing values and such) I created 8 new datasets (new ...
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Demonstrate discrepancy between proper and improper confidence intervals of a sum of variables

In my company, someone fitted regression models for the sales of 100 independent stores over a 52-week period. He then calculated the sum of the sales by adding the estimated means together. This is ...
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2 answers
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How is a 50% confidence level analogous to flipping a coin?

I'm rather new to statistics. I'm learning on my own and I'm trying to understand confidence levels. I read, "How Confident Do You Need to be in Your Research?" by Jeff Sauro, Ph.D., 5 Jan ...
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1 vote
1 answer
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Bootstrapping (aleatoric and epistemic) risk score uncertainty

I am working on various risk score estimation problems. I assume individual subjects are associated with a true risk $$r_i = f(x_i; \epsilon_i), \quad 0 \leq r_i \leq 1,$$ where $x_i$ is some ...
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1 vote
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T-distribution problem

I am working through the exercises of Martin Sternstein's Statistics (Barron's College Review Series) ... struggling with Exercise 4 in Chapter 14. Given are the weight lifting strengths of 9 people ...
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Can confidence intervals be found for the difference in marginal probabilities from two different logistic models of the same sample?

So, I have two multivariable logistic regressions for the same sample. They differ in one independent variable: Model A has a dummy variable for membership in the top 50% (compared to the bottom 50%) ...
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1 vote
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SUR regression (which fails for too big in R) has identical variables, so is mostly multiple OLS; does error term effects matter?

I originally posted this to stackoverflow, and was advised by I_O that the question would be appreciated more here. I am not sure how to reformat this to be appropriate here, so I am copying it over ...
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1 vote
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Confidence interval for normals of normal model

Suppose $X$ is a normally distributed random variable with unknown mean $\theta$ and known variance $\sigma_{X}^{2}$. Suppose that $Y_{1}, \ldots, Y_{n}$ are random variables that, conditioned on $X$, ...
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1 vote
1 answer
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Finding confidence interval given z-score and null hypothesis

I am working on a homework question and got stumped on this question. Suppose researchers perform a large-sample test of a population proportion where the null hypothesis is that the population ...
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2 votes
1 answer
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How to get most likely value with confidence interval or expected value from a set of observations

lets say I have a set of values (R-code below for creating a vector) ...
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Ratio Confidence Interval for Proportions

Wondering if Fieller's theorem is used for the 'ratio' value in the compare argument in ...
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0 answers
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How can generate 95%CI for GAM model in Stata?

I am analyzing a dataset with generalised additive models(GAM) in Stata. I want to obtain 95% confidence interval(95%CI) for my result. I have read the documentation in Stata ("Help gam") ...
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3 votes
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Do asymptotic statistics "solve" the Behrens-Fisher problem?

The Behrens-Fisher problem concerns comparing two means from independent (maybe multivariate) samples in a way robust to heteroskedasticity in the populations being compared. It seems that if one ...
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Do confidence intervals make sense for win rates in sport?

Imagine we have 2 teams play 10 matches against each other with team A winning 6 of them I.e. 60%. In this setting do confidence intervals for the probability of winning make sense? On one hand I ...
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How can I compute rectangular confidence regions for parameters using R?

Simultaneous confidence regions for multivariate parameters (say, a confidence region for multivariate mean, or for regression parameters) usually find an elliptical region when the parameters' ...
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Proper way to report on Confidence Intervals for 2 Proportions means

Disclaimer: Stat noob Context: I'm trying to figure out the best way to report CI to a non-data/stat/math savy audience. I'm performing a two proportion z test for an experiment. Control: 0.3097 ...
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1 answer
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Confidence intervals, doesn't the definition suggest that it has a probability of e.g. 95% of containing the true value of the parameter? [duplicate]

I'm learning about confidence intervals and it explicitly states that the confidence interval is not to be interpreted as that it has 95% probability of containing the true value of the parameter. ...
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Does the "type" of standard error affect the relationship between the standard errors of standardized vs. unstandardized estimates?

While previous answers explain how to convert between standardized and unstandardized coefficients and their standard errors, it is not clear if this formula applies across different types of standard ...
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Error bars or standard deviation around means from zero-inflated heterogenous data?

I've constructed a plot of mean values per group (year) solely for the purpose of examining my data and have been told to always include either standard error (S.E.) or confidence intervals (C.I.'s). ...
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