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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checking validity of sample using confidence interval

we know that in order to calculate the confidence interval at 95% we can do mean +/- Z95*SD/sqrt(N) using the mean of the sample data and StdDev of the data with N equals to the data size But if the ...
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How many psychics can be compared using n trials

I have a bit of a tricky question, which I honestly have no idea how to approach. The scenario is that I want to compare as many psychics as possible. I am told that I can do a total of 10000 ...
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Incororating model uncertainty into confidence interval for proportion of positive model outputs

does anyone know much about incorporating model uncertainty into a confidence interval? Analysing an experiment, I want to compare the proportion of “successes” between experiment arms. I could just ...
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Calculating Highest Posterior Density Interval in R [closed]

I have a data.frame that lists the probabilities of 2 stages. I'm wondering if someone can explain how to calculate HPD intervals. age P(Stage 1) P(Stage 2) 0 1.0000000000 0.000000e+00 1 1....
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How well does OOB estimate the generalization error?

I frequently see people evaluate the models using the OOB, but well does OOB estimates the generalisation error? Is it an unbiased estimator for the generalisation error ? How large is the margin of ...
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Confidence interval of the sum of beta coefficient

I'm currently trying to estiamates the evolution of runner speed in function of distance and sexe. I'm building a GLMM Gamma Model. For thoses using R, here is my model. ...
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8 views

Calculating variance / standard errors for a Weighted Repeat Sales model

I'm writing an implementation of the Case-Shiller Real Estate Index, which is based on a variation of the weighted least squares, except for the introduction of a dummy matrix Z. I've calculated the ...
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55 views

Why bootstrap-based confidence interval didn't include the point estimate?

I have constructed a nonparametric bootstrap confidence interval using 1000 iterations. However, I got a result of CI: 0.72 [0.63, 0.68]. As you can see, the point ...
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Confidence interval / p-value duality: don't they use different distributions?

Idea: p-value is less than the level of significance if and only if the corresponding CI does not include the null value; and vica versa, the p-value is greater than the level of significance if and ...
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Calculating a 95% confidence interval without the original dataset

I have been asked to calculate a 95% confidence interval based on the following paper: https://www.nber.org/system/files/working_papers/w26107/w26107.pdf The question reads: Suppose rainfall in the ...
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How can I confidently state the error of a specific test is within a range with a 95% confidence interval

I have a test that provides values with known amounts of error. For instance the error on the test (Value - TrueValue) = -7.62, -9.33, -8.36, -9.79,-10.45, -9.51, -10.83, -10.64, -9.96, -10.30 I want ...
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How to calculate 95% CI for cumulative incidence rate using python [closed]

How to calculate 95% CI for cumulative incidence rate using python using poison distribution
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Is it appropriate to put "error bars" on data when you have the full population?

I have data on the large number of people who were applying to receive an award. Everyone who applied must fill out a survey and specify their gender (although they can choose "prefer not to say&...
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Fixed Horizon A/B Tests - When to stop?

Suppose I'm going to run an online controlled experiment. I'm aware that we could estimate the number of samples needed for a given MDE, power, alpha, baseline conversion rate, and baseline std dev. ...
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Clopper Pearson Confidence Interval for 100%

I was using the following site: https://www.medcalc.org/calc/diagnostic_test.php to generate confidence intervals for some data I collected. One of the data-subsets had 81 true positives and 0 false ...
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Methods to calculate confidence interval for proportion with potential bounds?

I am trying to calculate the confidence interval on a time series proportion. For example, I have 1000 years of data, and I use 20 days to calculate some proportion. The thing is, I know the ...
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Determine confidence level in guesstimate: gas stations in Germany

I read in the internet about the following guesstimate during a job interview for a trading position: Give an estimate for the bid-ask on the number of gas stations in Germany (with max spread of 10 %)...
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Confidence interval over mean or over all values?

Say I have a dataset generated by running my AI on a boardgame. The data set consists of two "main" values: Actual gained reward from running the AIs optimal policy and the reward my AI ...
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Estimating confidence interval of a parameter from the MLE of another parameter

Let's say I have a maximum likelihood estimate (MLE) for my parameter $\theta$ as in $$\hat{\theta}\sim N\left(\theta, \frac{\theta^2}{n}\right) $$ and we have $$\mu = \sqrt{\frac{\theta}{2}}$$ If I ...
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Aggregate two proportions from subpopulations to estimate population proportion

Assume there is a population of 2000 individuals, of which 1200 are male and 800 are female. Assume samples have been drawn from the male and female subpopulations separately to compute a proportion ...
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Confidence Interval for Expectation using covariance matrix [duplicate]

Say I have a regression model as follows: $\ \hat{y}_i = \hat\beta_0 + \hat\beta_1x_1 + \hat\beta_2x_2, n = 79$ and I have the following covariance matrix $\ \begin{bmatrix} intercept & 6.5949972 &...
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Large confidence bands for inhomogeneous Poisson process model

Forgive me if this question falls under StackOverflow's domain, but I cannot tell if the issue is programming (R) or statistics based (happy to relocate post if need be). I am graphing an interaction ...
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Bootstrap confidence interval for mean

Take an iid sample $X_1,\dots,X_n$ from a distribution with (unknown) mean $\mu$ and variance $\sigma^2$. Let $\bar{X}_n^b$ be the bootstrap sample mean, and choose $R_n=R_n(X_1,\dots,X_n)$ s.t. $$C_n=...
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What is the meaning of " Confidence interval of less than 1% of the average value"?

I want to find confidence intervals for my scenario and I see this sentence in many research papers related to my work. " Confidence interval of less than 1% of the average value"? What does ...
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Calculating the accuracy of an estimate when the true value is unkown

This is the context for the problem I've run into: A program starts counting down in seconds, choosing a random value with a min of 300 and a max of 600. At the end of the countdown event A occurs, a ...
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Find a pivotal quantity

I have a random sample from $X$, $X_1,...,X_n$, with X having probability density function $f_X(x;\sigma^2)=\frac{x}{\sigma^2}e^{-\frac{x^2}{2\sigma^2}},\;\; x>0, \sigma^2>0.$ We are also given ...
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Are Large Confidence Intervals "Necessarily" Bad? [duplicate]

When it comes to confidence intervals on parameter estimates and prediction intervals on the predictions of a statistical model - do larger "widths" of these intervals "necessarily"...
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Performance comparison of one model on two datasets

I have a learning algorithm $A$, which is a neural network, and two different datasets, $D_1$ and $D_2$, that consist of data with the same set of features. I don't know if it's relevant, but the ...
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Wilson confidence interval for partially-paired data

I have a data set with paired observations (before and after a specific intervention). There are a lot of metrics in this data set, some of them numeric (of unknown distribution) and some of them ...
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1answer
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Describing normal volume change with age: use a linear model and the standard deviation?

I would like to use a large dataset with tissue volume measures of 500 volunteers over a given ageframe to compare it to a small dataset with volunteers and patients (20-30 datapoints). The tissue ...
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How much confidence to have data is correct based on checking N samples

If I have a dataset of size $N$, and choose $n$ samples, where $k$ of the samples are OK, how confident can I be that the dataset is OK? To make it more concrete, suppose I have a dataset D1 with 5,...
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How to caluclate conditional probability over 2 confidence intervals after a softmax on a classifier prediction?

Given 2 confidence intervals from 2 different models with 3 classes each: ci1 = [0.2, 0.4, 0.4] ci2 = [0.1, 0.5, 0.3] Where each score corresponds to a class. How to find the conditional probablity of ...
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Prediction and confidence intervals - large number of predictions

I'm using a regression model to predict one quantity, $y$, given another, $x$. I'm trying to estimate the error in future predictions of $y$, but I'm wondering in which scenarios I can fairly use the ...
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38 views

Using the terminology "Bayesian confidence interval" in place of "Bayesian credible interval."

In Peter Hoff's "A first course in Bayesian statistical methods," he states: "Most authors refer to intervals of high probability as 'credible intervals' as opposed to confidence ...
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Testing difference of medians and stochastic ordering using paired samples

I have paired samples from skewed distributions with unequal variance (before and after treatment), and would like to test for difference of means difference of medians stochastic ordering of treated ...
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Model uncertainty in a logistic regression model - binomial proportion confidence interval

In my line of work I have seen people quantify general model uncertainty, when using a logistic regression model, with an Agresti-Coull confidence interval. I am not convinced that this is correct, ...
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Can we combine CIs from dependent events?

Suppose we have calculated the following two confidence intervals: We are 95% confident that the increase in the proportion of event x is between 0.50% and 1.50% of all events. We are 95% confident ...
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49 views

Confidence interval for exponentially distributed estimator

We have an estimator $\hat{\theta}\geq 0$ for $\theta$, with distribution function $P\{\hat{\theta}\leq t \}=1-e^{-t/\theta}$, which we can recognize as the cdf of the exponential distribution. Our ...
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Finding the standard error of mean for samples of different size

I have a set of data which is the result of a set of questionnaires for different classes. The questionnaires are identical (but they refer to different subjects) Each class has different number of ...
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Does size of p-value matter beyond knowing if it is greater/less than a predetermined significance level?

In my understanding, hypothesis tests are equivalent to confidence intervals. Because of this, I initially believed $p$-values should only be reported in a binary sense i.e. is $p<\alpha$ or $p>\...
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How can I calculate a confidence metric for selecting the most frequent value in a distribution?

Let's say that I have a dataset of 100 whole numbers, and they all range from -10 to 10. I want to determine the most frequently occurring value, and calculate an associated confidence metric to ...
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1answer
25 views

How to construct a confidence interval from a delta method approximation for the variance?

If I have a complicated function of multivariables $f(x_1,x_2,x_3,\ldots,x_n)$, and I were to find the variance approximation through the delta method, say $\sigma^2_{approx}$, would the 95% ...
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Using the Delta Method to get confidence intervals for a function of a parameter

I'm trying to use the Delta Method to get a confidence interval on some function of a population parameter $\theta$. Suppose we want a 95% confidence interval on $\frac{1}{\theta}$, where we're given ...
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32 views

Conflict between p-value and confidence interval from Gamma model

I am trying to fit the Gamma model with link = log in R using the glm function. Below is the summary of the model: The p-value for level 2 of modact_3 < 0.05, but the confidence interval for this ...
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What's wrong with this interpretation of a 95% confidence interval?

Note: I asked a version of this as part of another question, but I'm re-asking it as a stand-alone question with more detail. I've been trying to come up with more intuitive/less confusing ways to ...
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Equivalence of confidence intervals and hypothesis tests

While reading John Rice's Mathematical Statistics and Data Analysis (3rd edition) and I came across this theorem in Chapter 9 (page 338): Suppose that for every $\theta_0$ in $\Theta$ there is test ...
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How to obtain confidence interval (95%) of original data in Applied Bayesian Econometrics

I used Bayes method to calculate the predicted value and the confidence interval of the predicted value and original data. Because the confidence interval of the predicted data was solved according to ...
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Asymmetric confidence intervals

Suppose we have iid data $X_i$ with known variance $\sigma^2$, and wish to write an asymptotic $1-\alpha $ coverage CI for the population mean $\mu$. CLT implies that if $z_q$ represents the $q$ ...
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113 views

Non-self-referential interpretation of confidence intervals?

Interpreting what a (say) 95% confidence interval actually means is obviously tricky, especially when you are trying to teach it to students just beginning to learn stats. One of the biggest ...
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Averaging time-dependent, heteroscedastic estimates of vaccine efficacy over time periods

Vaccine efficacy against Omicron has to be estimated for three months since the second dose. Efficacy data are given for shorter periods comprising three months. For example, the table, based on Fig ...

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