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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Comparing multivariate datasets
I have a list of products sold in different countries by 2 vendors. The table below is an example (productID is the concatenation of country code and product name, Vendor1 and Vendor2 columns ...
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Face and tails confidence interval [closed]
Suppose that when throwing a coin $400$ times we obtain 175 faces and 225 tails. Find the confidence interval with an approximation of 95% for the probability to obtain face. The question is, ¿Does ...
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Number of replications needed for coverage probability study
I am constructing confidence interval based on Wald, likelihood ratio and jackknife for the parameters of a model via simulation. To evaluate which methods is preferable for the parameters, I did a ...
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Did I get too good a confidence interval for Pearson's R using bootstrap on a very unbalanced data set?
I can't find this type of bootstrap problem described anywhere, where the data is so unbalanced: 50 y-values vs 2500 values yielding 50 means that become the x's. Another thing: the 50 strata yielding ...
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Ideas in calculating linear regression confidence interval for mean response [closed]
I am doing econometrics with the text James Stock and Mark Watson. there are equations that bug me for a while.
Below is the equation copied from the book
$$
s^2_{Y} = \dfrac{1}{n-1}\sum^n_{i = 1}(Y_i ...
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what is the difference between a two-sample t-test and a paired t-test
While I was glancing at hypothesis tests, I saw paired and two-sample t-test but couldn't understand the difference. For the explanation of these two tests, I saw the following sentence
" Two-...
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confidence interval for $\hat{\theta}_{MLE}=\frac{1}{2}\underset{i}{\max} \ x_i$ [duplicate]
Let $X_1, X_2, \dots , X_n$ be a random sample of size $n$ from the uniform distribution $U(2\theta)$ whose pdf is $f(x;\theta)=(2\theta)^{-1}$ , if $0<x<2\theta$ , zero otherwise.
i) We can see ...
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Is there a difference between these “definitions” of confidence interval [duplicate]
Today, my instructor was going over some of the misconceptions about confidence interval, e.g., how it's frequently incorrectly stated that "a 95% confidence interval that there is a 95% chance ...
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Sample size of a vote transfer poll
A vote transfer poll asks the electorate about how they voted in the last election and how they would vote if the next election was now. With the result from both questions one could build a matrix of ...
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Confidence intervals and uncertainty estimation of classified polygon map
I am not mathematician, neither statistician, but I try to use statistics in my work, so I do my best here to explain the problem I have.
I have a map of millions of hectares that consist of nine ...
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Bayesian interpretation of a confidence interval as prediction
Classical and Bayesian approaches to parameter estimation are often compared. See, for example
What's the difference between a confidence interval and a credible interval?
What I cannot find is &...
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Simulating Monte Carlo with different standard deviations and interval confidence
I have a question regarding Monte Carlo simulation (direct simulation), applied to propagation of uncertainties.
From what I understand Monte Carlo accepts random numbers of each input variable of ...
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Difference between pointwise and uniform confidence sets
According to Wasserman's All of Nonparametric Statistics p.6, let $\mathfrak{F}$ be a set of distribution functions $F$ and $\theta$ some quantity of interest. A uniform asymptotic confidence set $C_n$...
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When can a winner of the election be called: estimating population proportion without the assumption of random sampling
While following a recent election, I wanted to estimate population proportion of people who voted for a certain candidate knowing the sample proportion, sample size (and population size).
I first ...
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Stop collecting data when our confidence interval is sufficiently narrow?
I am running an experiment that is unpleasant and time-consuming, so I want to minimize the number of times I have to do it. I have done a sample size calculation to determine that I need $100$ ...
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Overconfidence-intervals of a regression coefficient of time-varying variables
I was simulating different types of data-generating processes of time series data and estimating effects of predictor variables that are also time series. Here is my equation system:
I want to ...
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How to get 90% confidence interval [closed]
Suppose a real estate broker is interested in comparing the asking prices of flats in the British cities of Exeter and Cardiff. The broker conducts a small telephone survey in the two cities, asking ...
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Calculating confidence intervals for a linear regression/probit model
I'm a software developer at a military diagnostics branch, and I've written a program to calculate the lower limit of detection for a nucleic acid test (qRT-PCR). The program takes the raw data (a set ...
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Is there a way to add sample confidence interval to regression?
I have the following situation. We want to measure if animal weight has an influence on their home range size (measured as an area).
However, there is inherent error measuring an animal home range. ...
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Dealing with independent variables where each point is an coefficient
I want to test if a behavior is influenced by population size. The former is measured as a continuous normal variable. The latter is estimated using Schnabel's method, and thus each sample has a ...
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Uncertainty of a trend
I need to estimate the confidence interval of the solar radiation change (in %) over time. For this, I'm going to use R default dataset ...
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How to determine the confidence of a neural network prediction?
To illustrate my question, suppose that I have a training set where the input has a degree of noise but the output does not, for example;
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Does $\alpha$ for Tukey change like it does for Bonferroni?
If you are trying to find confidence intervals, how does $\alpha$ for Tukey and Bonferroni differ? I understand that for Bonferroni the $\alpha$ is divided by the number of groups; however, does the $\...
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Is it safe to calculate confidence interval on normally distributed ln(x) and convert the confidence interval to x by calculating e^x?
Lets say that i have a skewed variable x, that have a non-normal distribution. I want to calculate mean and confidence interval for x but confidence interval assumes normality. So i take natural ...
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Confidence interval for categorical data
I have the following data about companies who respond timely or untimely and another category of the answer:
...
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calculating odds ratio confidence intervals
I have a question about the formulas for confidence intervals for odds & odds ratios. In a nutshell I understand the logic behind the formula for the odds confidence interval, but the same logic ...
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Calculating confidence intervals for the variance of the residuals in r
I have three variables:
Number of house sales
Month (in couples)
Region of a city (N-W-E-S)
and I want to calculate confidence intervals for the residual of the errors. So, given the data:
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Computing confidence intervals empirically with final model on the test set
I have a binary classification task where the goal is to build a classifier that outputs the probability of a patient to develop symptoms based on several predictors.
My dataset is comprised of 790 ...
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Why don't confidence interval calculations take true population size into account?
Let's say I have a sample of one million observations that each get a score of 0-1. I would like to use the average score in the sample as an estimate for its true value in the population.
To get the ...
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Plotting Error in Log Odds Space
I'm having trouble understanding what one should do for plotting error with binomial data. I have a yes/no answer from 183 participants over a range of x values (say -1 : 1 at .1 intervals). In ...
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Standard Errors of ECDF with Potential Model Fit Error
I have data and a proposed likelihood. I used MLE to fit the likelihood, but it is a very complicated likelihood and there is some estimation error of the model. The likelihood may be correct, but ...
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Finite population: CI of Normal Distribution same regardless of sample percent?
I am trying to wrap my head around the following. It seems that the confidence interval for a normal distribution does not rely on the sample percent.
For instance, say I am trying to find the ...
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How comparing two confidence intervals
Let's assume I have to point estimates with 95%-CI. The source can be from a simple computation of two samples or from a complex regression analysis. For example: odds ratio
(1) 2.0 (95%-CI: 1.4-2.9)
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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 ...
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Estimating sample size for relative error
Suppose I have a random variable $X$ with unknown mean $\mu$ and I can draw $n$ random samples (possibly from a Monte Carlo method, but I believe that's beside the point) from its distribution. I wish ...
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How to prove drawing the same conclusion of not rejecting H0 about Hypothesis Testing?
I'm taking a statistics course, and the problem goes like this:
Assume that 𝑋 follows 𝑁(𝜇𝑋,𝜎𝑋2). Consider a two-sided test with H0: 𝜇𝑋=𝜇0. If we do not reject H0 at a significance level 𝛼, ...
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Why does a confidence interval including 0 mean the difference is not significant?
Could someone please explain why zero being inside or outside the confidence interval tells you whether or not the difference is significant?
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Confidence interval for the product of two proportions
I grouped individuals based on their age to calculated their reproductive value. The reproductive value is equal to the product of two proportions.
Note that the data was collected over multiple years ...
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What's the right way to do Bootstrapping Analysis on UserId Randomized A/A?
My motivation is to do A/A analysis using the "Bootstrap" method to calculate the confidence interval of the "sample mean" (of treatment and control) of all metrics.
In my A/B ...
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Understanding Seaborn Barplot - Error Bars meaning & calculation
I am using Seaborn to create a barplot.
sns.barplot(df['City Group'], df['revenue']) #uses default mean estimator
I am a bit confused about the error bars. What ...
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Why don't Beta-Binomial Confidence Intervals Asymptotically Converge?
I've been using the beta-binomial for modelling overdispersed proportions, and I've become a bit confused by the behaviour of the quantiles.
I would expect that as $N$ increases, the result of $\text{...
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Interpreting phrasing of notion of confidence interval w.r.t simple linear regression from Kutner, et al
I have a question with how the idea of confidence intervals was used and phrased. This comes from Applied Linear Statistical Models 5th Edition - Kutner, Nachtsheim, Neter, Li:
So it is usually ...
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Comparing coefficients in multilevel models
Is it meaningful to compare the coefficients of two different predictors in multilevel model when the two are at different levels?
Specifically I have two variables which measure the same construct ...
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Is predict_proba() reliable for SVC?
I want to implement some kind of confidence measure for my stock prediction model, which predicts the next day's trend (whether the price would rise or fall). As in, a trade order should be placed ...
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Confidence interval x-intercept
The x-intercept of a linear regression is -y.intercept/slope. If I wanted to obtain a confidence interval (CI) for a x-intercept of a linear regression, coud it be wrong to find the CI of y-intercept ...
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What is a rigorous, mathematical way to obtain the shortest confidence interval given a confidence level?
After reading the great answer for this question by @Ben, I am a bit confused by the part " set the relative tail sizes as a control variable, and then you find the formula for the length of the ...
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Why does not the mean bootstrapped metric of an ecological bipartite network get closer to the observed metric with increased number of samples?
I wanted to construct a 95% quantile-based confidence interval using bootstrapping for the network metric of an ecological web (plant-pollinators). I realized that for some webs, despite increasing ...
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Confidence intervals for aggregated statistics
Given min, mean, max and var of scores of several subjects
...
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How do I get an asymmetrical confidence interval for population rate? [duplicate]
In Epidemiology An Introduction Chapter 9，p165：CI for Risk data and Prevalence data:
95% CI= R±1.96×SE(R)SE(R)=[a(N-a)／N³]½
In Epuation，R=a/N，a to represent cases and N to represent people at risk. ...
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In Stata, how to avoid negative values of lower confidence interval of proportion?
I'm trying to get the CI of a proportion in Stata. Starting with some reproducible example:
...
