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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17 views

Deriving confidence interval for random-effect model

In R, when using the usual linear regression functions, such as lm(), deriving and plotting confidence bands are easily done with the ...
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Why is binning in Expected Calibration Error done the way it is?

I see the definition of expected calibration error being $$\sum_{m=1}^{M}\frac{|B_m|}{n}|accuracy(B_m)-confidence(B_m)|$$ Where $B_m$ represents a outputs of the model that predicted class $m$ in a ...
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How to obtain the covariance matrix from two regression model (for estimating 95% CI using delta method)?

I am trying to estimate the 95% CI for a function using delta method. Let say this function is t1/t2 In the case that t1 and t2 come from the same regression model, I can estimate the 95% CI using the ...
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115 views

Confidence Intervals guaranteed to be centered at 0?

With most pivotal quantities that I'm thinking of, after we rearrange stuff to get an interval, the interval's "location" depends on a random point estimate. The example below has an ...
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26 views

How do I choose which confident interval for proportion difference to use in SAS?

In SAS, there are different CIs for proportion difference ($\pi_1-\pi_2$) to choose? 1.Continuity-corrected Wald CIs based on normal approximation 2.exact method 3.Miettinen-Nurminen CIs based on ...
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Given a regression model, is there a way to evaluate confidence of a prediction?

What are methods for evaluating the predictive probability or something equivalent in a regression problem? In classification problems a predictive probability will be outputted given an input. For ...
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How to obtain an odds ratio and 95% CI between two specific clusters in a multilevel logistic model?

I was wondering how one would estimate an odds ratio (OR) and its 95% confidence interval (CI) for the difference between two specific clusters/groups in a two-level multilevel logistic model? I ...
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Is this the correct way to compute confidence intervals on the original scale for GLM(M)s?

Suppose I have fitted a GLM and want to produce a confidence interval (or a prediction interval) on the original scale of the outcome. What I would do is estimate it on the link scale and then inverse ...
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54 views

In R, trying to find the confidence interval for the difference in proportions

I am comparing two different groups based on working status. For this instance I am looking at occupation so I have a table that looks like so: ...
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26 views

How to combine population proportions and confidence intervals?

Say I've looked at three random samples, one each from three populations of students. I found that a few students in each sample didn't turn in a fieldtrip permission slip, leaving me with the ...
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Does the bootstrap confidence interval rely on assumptions about the null distribution?

My question is based on the notes from the relevant lectures. When deriving confidence intervals (CI) from the null hypothesis significance test, we invoke the assumption that the data comes from the ...
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Confidence interval calculation: why sometimes the SD is dividted by the sqrt of sample size, and sometimes not?

I have trouble understanding the following: Looking how reference ranges for laboratory values are calculated, I found the following: In our sample of 72 printers, the standard error of the mean was ...
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Is the ratio of two sums normally distributed?

I've encountered this problem and I'm not sure whether my logic is correct. Suppose I have a random sample of customer spending and I want to estimate the market share of a given store in a given ...
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Univariate and multivariate logistic regression analyses that show a very different significative trends in odd ratios in R

I have a question about logistic analyses. I want to see weather two variables are associated to the variable response. To do that, I did univariate and multivariate logistic regression analyses. I ...
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27 views

Confidence intervals for discrete distributions

Let $X$ be a discrete r.v. whose p.m.f. depends on some parameter $\theta$. Define $F_X(x|\theta) = P(X \le x|\theta)$ and $\overline{F}_X(x|\theta) = P(X \ge x|\theta)$. Let $\epsilon_1 + \epsilon_2 =...
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R function for conducting multiple comparisons corrections on p-values and confidence intervals

I have conducted 5 different logistic regressions on behavioural data, as there are 5 outcome (dependent) measures. The independent variable is always Group (Patient vs Control). I have used the glm ...
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Pivoting a discrete cdf? A method for interval estimation

I am studying the following theorem from "Inferential Statistic" by Casella. With reference to the picture below, there were some mistakes in the proof, which I corrected using a pencil : ...
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How to use bootstrap method to compute confidence interval for HMM parameters?

I have known how to estimate parameters in hidden Markov model by Baum-Welch algorithm. And then I was curious about how to compute the confidence interval, but I found that few articles discuss about ...
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One-tailed vs Two-tailed Confidence Interval

I have a question that asks: e) Use the output and the t table to find a 95% upper confidence bound on the difference in means. $H_0: \mu_1 - \mu_2 = 0$, $H_a: \mu_1 - \mu_2 \neq 0$ The answer uses a ...
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38 views

Why do 95% confidence intervals contain the unknown population mean 95% of the time?

I am learning about the Central Limit Theorem (CLT) and confidence intervals from this online course. I have learnt that that the CLT states that the theoretical sampling distribution of a sample ...
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23 views

Calculation of 95% Confidence Interval for an Incidence Rate Difference

Suppose that I have two pre-computed Incidence Rates with 95% CI, calculated from the same sample. Let's say IR1: 10.0% [8.0-12.0%] IR2: 21.0% [15.0-27.0%]. If I want to calculate an IR difference, ...
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Is it normal to get very high odds ratios and confidence interval?

I am performing a logistic regression with different variables by R. The code used has been this one: ...
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Handle numerical error in bootstrapping to compute Wald confidence interval

Let $f(\theta|x)$ be the likelihood function of a random variable $x$ with parameter $\theta$. Due to complexity, I have maximized $f$ using a Newton-Raphson method with a bounded interval. This ...
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Where does (co)variance come from in a linear (OLS) regression?

Given that linear models can be solved exactly via calculus, how is it possible to define a variance for the parameters ($\mathbf{a}$) which minimize some error function? say $Err=(o_i-f(x_i; \mathbf{...
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How to estimate minimum sample size to achieve a certain confidence interval?

The title of this question is a bit general. Allow me to elaborate. Context I'm measuring a biological parameter (BP) of different subjects. For each subject, BP follows a normal distribution, with ...
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Autocorrelation Confidence Interval Derivation and Ljung-Box Test

It seems to be a rule of thumb to use $\frac{1}{\sqrt n}$ as a standard error for an autocorrelation estimate of a time series, which then allows one to construct a confidence interval for sample ...
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Ratio between two values with confidence intervals

I have two integer values, each with confidence intervals, and I want to calculate the ratio between the two values. My strategy would be to find all the pairs of integer values within the CIs and ...
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find a Confidence Interval for several given probability mass functions

What's the difference between a confidence interval and a credible interval? In this answer to the above question, the users gives a toy example of finding the confidence interval for a parameter ...
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41 views

Can confidence intervals or uncertainty intervals provide information on replication? [duplicate]

Let's say I'm looking at a forest plot from a meta-analysis. I notice that most of the width of the confidence intervals are fairly consistent and the point estimates are all on one side (showing a ...
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How to compute the confidence interval of a correlation function

What is the best way to compute confidence intervals of a (cross) correlation (function value at lag time $\tau$) $c(\tau)$? Typically one estimates the value $\hat{c}(\tau)$ but the question is what ...
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55 views

Why do we use %95 confidence interval when it does not mean the likelihood of containing the true parameter?

When I was an undergrad student, it was stated that because the point estimation does not exactly match the true parameter, we use confidence intervals. Then, they told that with a %95 confidence ...
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Determining sample size for comparing rate of occurrence between two groups

Scenario: You are running a comparative clinical study. A test product is being used by one portion of the population (Group T) and a control product is being used by another (Group C). The Question: ...
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Calculating the confidence interval for the mean value from a sample

The central limit theorem states that the means of many different samples with n>30 from a population that follows an arbitrary distribution are normally distributed. If you now have the ...
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Compute interaction from mean and confidence interval of a 2 x 2 design

Is there a way to compute the interaction effect and its p value of a 2 by 2 design if I only know their estimated mean and confidence interval: Time 1 Time 2 Condition1 19 [16, 21] 22 [20, 25] ...
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Coverage for confidence intervals

I would like to know if my simulation approach to find the coverage for a confidence interval of a prediction $\boldsymbol{\beta}^T\boldsymbol{X}_N$ is correct I generated a dataset of $n$ samples of ...
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37 views

Determining bootstrap confidence interval

I'm using bootstrapping for the first time. I need to define a confidence interval for the calculated parameter. I first obtained the parameter CNIV: ...
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62 views

What is the *finite-population correction* for the Wilson score interval (for a binary proportion)?

The Wilson score interval is an approximate confidence interval for an unknown binary proportion for IID binary data. The interval is based on the central limit theorem like the Wald interval, but it ...
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Using pivotal quantities for transformed parameters

Setup Suppose we have some iid data $X_1, \ldots, X_n$ that arises from a distribution with parameters $\theta$ and $\rho$. $\theta$ is the parameter of interest, and $\rho$ is a nuisance parameter. ...
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Confidence interval for the norm of linear model coefficient vector

Given observed data from a normal model, $Y\sim N(X\beta, \sigma^2 I)$, where $X$ is a $n\times p$ matrix of known predictors, I want to compute a confidence interval for $||\beta||_2$, the L2 norm. I ...
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How to determine confidence %?

Scenario: A pastor has a congregation of 2,000 people. He asks a sample of 10 random members whether they had a favourable or unfavourable experience relating to an event that was held. 8 out of 10 ...
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How to construct the confidence band for a timebased sample of n individuals

Let $X^{(i)}(t)$ be some measurement at time $t$ for individual $i$. Let $\bar{X}(t) = \frac{1}{n} \sum_{i=1}^n X^{(i)}(t)$ be the mean of the individuals at time $t$. Let $\bar{X}_{t_0} = \frac{1}{T}\...
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Why effect size magnitude is correlated with p value and confidence interval width in resampling statistics?

I use effect size (e.g. mean difference) to compare two groups. I do randomization test to calculate the P-value and bootstrapping to find the percentile confidence interval. I notice that at a fixed ...
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Why are my confidence intervals wider for predicted marginal effects with additional covariables? Using ggpredict/sjplot after lme4

I have been struggling to find out whether what I am observing is normal/expected or a problem with my model. I fit a linear mixed model with random intercepts at two levels with the lme4 package. I ...
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1answer
22 views

Matched pairs design: individual confidence intervals for pre and post

I have a matched pairs design. I have a 2x2 table showing success/failure in pre and post: Post (yes) Post (no) Pre (yes) 0 10 Pre (no) 20 30 My colleague would like a confidence interval on the ...
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58 views

Interpretation of emmeans table

I have a question about emmeans Variables are A = {a1, a2, a3}, B= {b1, b2}, C = {c1, c2} Model ~ A+B+C+A * B+A * C+C * B One of research questions: Is there an effect of C on a1, a2 und a3 (A)? And ...
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Practical use for heritability value at sub-population level?

For me as a layperson, heritability is something that much smarter people than me calculate, and there are several questions already on the forum about how to do that (eg, this and this). I ...
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How can I obtain a confidence interval for the difference between two probabilities from a binary logistic regression model?

I saw this question here, but it doesn't have a clear answer. Suppose I have a simple logistic regression model with binary $x:$ $$\log(p/(1-p)) = \beta_0 + \beta_1x$$ Then I know: $$p/(1-p) = e^{\...
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Confidence Interval - Revisit [duplicate]

I've read in many articles about Confidence Interval as below One such article link: https://www.statisticssolutions.com/misconceptions-about-confidence-intervals/ [FALSE] - There is a 95% chance ...
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60 views

Logistic regression: how to compute a prediction interval

Suppose I have a simple logistic regression model: $log(p/(1-p)) = \beta_0 + \beta_1x$ Then I know: $p/(1-p) = e^{\beta_0 + \beta_1x}$ and $p = e^{\beta_0 + \beta_1x}/(1 + e^{\beta_0 + \beta_1x})$ How ...
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What is the point of using a Bayesian prior?

I do struggle with the most basic starting point of Bayesian statistics: why is using a prior useful? It seems to me that if anything they hurt much more than help. Moreover, Bayesians always say ...

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