# 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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### 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 ...
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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### 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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### 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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### 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 ...
563 views

### 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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### 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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### 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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### 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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### 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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### 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 ...