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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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Why does my model predict symmetrical CI for Poisson-distributed data?

Given a set of Poisson-distributed data, I would expect the confidence interval for a glm(..., family="poisson") to be asymmetrical, because of Poisson ...
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CI using Bootstrapping on GLM (log link, gamma dist)?

I am running this exercise on SAS but don't think the choice of software is relevant: the question still legit when I am using R or others. I was working on medical claims data (typically having ...
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Is it possible to determine significance with a defined alpha (.05) from an effect size estimate with a 95% CI?

Say for example, there is an observed estimated standardized mean difference of $d = 0.44$ with $CI_{95} = [-.10, .89]$. This is the only information we have available (i.e. we do not know the sample ...
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Construct a confidence interval given sample and population size for binary responses… I think

If 1,000,000 t-shirts exist in total, and you can track 25% of them (see if they have been purchased or not), and you find that of that 25% half have been purchased, you might believe that half of the ...
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Binomial confidence limits with zero observed [duplicate]

I know that the standard approach to finding the upper confidence limit of a binomial distribution f(n; N,theta) with an observed n=0 and N=10 is not valid as n is too small. However, I am trying to ...
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I have this as an assignment question and can not figure it out, need some help please [on hold]

a)The mean weight of King Penguins found in an Antarctic colony last year was 15.4 kg. In a sample of 35 penguins same time this year in the same colony, the mean penguin weight is 14.6 kg. Assume the ...
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How to find exact confidence intervals for a quantile (assuming iid)?

Assume $X_1, ..., X_n$ are iid (distribution unknown). I want to find exact confidence intervals for the common quantile $q_\alpha$. Can this be done exactly given some confidence level $p$? I know ...
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Sufficient sample size for skewed populations

I have measured 50000 individuals from a certain population, and 800 (~1.6%) of them have a certain characteristic (say green eyes). I can be pretty sure that this is an effect that is present in a ...
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Need help figuring out the R script for this question [on hold]

a) The 95% Confidence Interval for the unknown population mean is calculated using 64 samples and presented as (2.73, 6.63). Precisely interpret this statement. b) Determine the sample mean. c) ...
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Asymptotic distribution of $\sqrt{n}\left(\hat{\sigma_{1}^{2}}-\sigma^2\right)$

I'm trying to find a confidence interval for variance $\sigma^{2}$ when some sample $X_{1},...,X_{n}$, with mean $\mu$ known, may have violated normality assumption. To do this I'm investigating the ...
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Likelihood-Based Confidence Intervals for ratio of risk ratios

Ratio of Risk Ratio (RRR), along with Relative Excess Risk Due to Interaction (RERI), has been used to quantify the joint effects of 2 exposures in epidemiology. Quoting Joshua N. Pritikin CIs ...
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Resampling-based Confidence Intervals for Relative Excess Risk Due to Interaction

Relative Excess Risk Due to Interaction (RERI) has been used to quantify the joint effects of 2 exposures in epidemiology. RERI is the proportion of disease among those with both exposures that is ...
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Is bootstrapping suitable for deriving prediction intervals in models which randomly sample from distributions?

I'm working with a fairly complex predictive model which essentially produces total populations for different groups in future years. Joiners, leavers, and transitions between the groups are modeled ...
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t-distribution in confidence intervals and corresponding ti84 commands

In computing confidence intervals for population means and variances, I have come across the use of the t-test for the computations of certain intervals. For example, the formula given for the ...
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Confidence interval for $\sigma^2$

I started with any distribution and underwent the CLT on $\sqrt{n}(\widehat{\sigma}^2 - \sigma^2)$ where $$ \widehat{\sigma}^2 = \frac{1}{n}\sum_{i=1}^n (X_i - \mu)^2 $$ is a sample mean of $\sigma^2$...
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Confidence interval with an unknown constant bias

Assume that we have an estimator $T_n$ of the parameter $\theta$ where $n$ is the sample size and there exists an unknown constant $C$ such that $\sqrt{n}(T_n-\theta) - C \overset{d}{\longrightarrow} ...
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Toss coin simulation in R [closed]

I need help doing this in R. If we have an unfair coin is tossed 100 times for a total of 40 heads. Using R, I need to simulate a 95% confidence interval for p, the probability of obtaining a head for ...
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Variance reduction [closed]

I need to calculate the value of double integration using R: - Using the raw estimator - Using antithetic variables - Using control variates - Compare the estimates. Which is best?
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Statistical analysis of simulated data [closed]

I need help doing this in R, to perform Monte-Carlo estimation of θ = E (e^U ) where U is a continuous uniform random variable between 0 and 1: (a) using R, how can I estimate θ using 1000 data points ...
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Effect size of an outcome based on CI limits [closed]

Explain how to determine the effect size of an outcome based on the limits stated for a confidence interval.
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Zero-inflated Poisson distribution parameter estimates

Let's say we have a population distributed by Zero-inflated Poisson distribution: $$ f(x | \psi, \lambda) = \left\{ \begin{array}{ll} 1-\psi + \psi e^{-\lambda} & \mbox{if } x = 0 \\ \psi \...
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Which effect size when sample size and variance are not equal

I don't have extensive knowledge in statistics, therefore I have some trouble to understand which metrics I should use for my analysis. I have measure a feature (concentration) of multiple substances ...
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Bootstrapping confidence interval for regression prediction

I want to use the regularized regression technique such as partial least squares (PLS), Lasso, and the elastic-net. However, as far as I know, there is no "standard" way of calculating the prediction ...
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1answer
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Confidence interval for the square of binomial probability

I have a binomial distribution where the estimate for p is 0.03 out of 1000 sample trials. Using the normal approximation and Chi-square distribution for the square of normal distribution, how can I ...
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Bonferroni interval - quick example calculation

Problem statement: Calculate the Bonferroni interval for any pair of means $\bar{y}_{.j},\bar{y}_{.k}$ with $I$=10 groups with equal sample size 30 in each group. Write this as a multiple of $s$. ...
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Deriving an expression for a confidence interval for σ^2 using the asymptotic distribution of √n(σ̂^2−σ^2)

We have We have $X1,…,Xn i.i.d N(μ,σ^2) $where $μ$ is known and $σ^2$ isn't known. $σ̂^2=(\frac{1}{n})∑(X_i−μ)^2$. First of all what I did, I derived an equitailed 95% confidence interval for $σ^2$....
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Bland Altman limits of agreement vs. confidence intervals of regression parameters?

I would like to assess agreement between measurements made by two different methods. I am unsure whether to use Bland Altman analysis to establish limits of agreement, or use the confidence intervals ...
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Is there a relationship between the “significance level” of a KS test and the size of the error bars in a given data set?

Suppose I have a data set with error, $\mathbf{d}+\mathbf{\Delta d}$ where the error is some percentage of the data (e.g. $\mathbf{\Delta d} = \epsilon \mathbf{d}$, $0 < \epsilon < 1$). I also ...
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Is it valid to use bootstrapping to generate a confidence interval of an accuracy measured by rolling window analysis?

I would like to generate confidence intervals for the accuracy of a model that I use to forecast time series data. In order to get an average accuracy for my model I use rolling window analysis (See ...
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Confidence Intervalls for Classifier Metrics for subpopulation

I have a classification dataset of roughly 1000 records. I need to evaluate the performance of this model on a small subpopulation of records (about 20). General Question is how can I do that and ...
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vector of weights

I am using the MuMIn package for model averaging. However, I am not clear of the function par.avg(). In this function, we need to specify the following, ...
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How to practically calculate confidence interval from the following confidence equation?

How to use the following equation to calculate the confidence interval: $$CI_{j,\alpha}(y) = \left\{p | -2PL_j(p) \leq \min_\theta - 2LL(y|\theta) + \Delta(\alpha) \right\}.$$ Here, CI is confidence ...
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Multiple imputation in SPSS. Where are my confidence intervals in regression analysis?

I have used multiple imputation on a dataset (10x) in SPSS. Now when I analyze the dataset using linear regression analyses I can get a pooled b and p-value but it does not give a 95% confidence ...
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How to calculate sample confidence interval for 33 months consumption?

Something is wrong with my calculations This is 33 consecutive month energy consumption ...
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Calculate 95% confidence interval for profile likelihood

I'm not at all a statistician, so please bear with me. I have a mathematical system $x' = f(x,P)$, where $P$ is the set of parameters that I try to estimate and $x = (x_1,x_2,x_3,x_4,x_5) \in \mathbf{...
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Can I use bootstrapping technique to get a 95% conf. interval of conversion rate

I have a sample data about user conversion at an ecommerce site. The data contains the following variables: User Id Site visits - count of the number of times the user visited the site during the ...
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which control chart can use for error variance/

I have a series of error variances from the model With what type of univariate shewhart control chartI can control monitor error $variance(\sigma^2)$?
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Calculating Confidence Interval with log-transformation

I fitted a linear regression with a 3rd order interaction and adjustment for confounding variable which looks like this: $$ log(Y) = β_1S + β_2T + β_3M + β_4ST + β_5SM + β_6TM + β_7STM + β_XX $$ ...
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Confidence intervals and variance for ordinal scale set [0-5]

We have a known sample of data coming from a multiple choice ordinal scale survey question with scores from the set [0,1,2,3,4,5]. In one sample, the mean of this ...
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1answer
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Choose between several confidence interval procedures for randomization test

I am trying to produce confidence intervals for a randomization test of no effect and I've found two different methods in the literature. I have a hard time comparing the two and selecting the best ...
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63 views

Build confidence intervals for random effects in intercept only models

I'm building a Poisson model for a rate between an outcome and an offset (to be precise between the observed and predicted values of a phenomenon). I want to get this rate + confidence intervals (CI) ...
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How to correctly compare the accuracy of different forecasting methods using bootstrapping with time series forecasting

I am currently working on a forecasting project and I have tried several different models to forecast with. Having trained and tuned my models I want to pick which model works best for each time ...
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Computing confidence intervals for cumulative link mixed models

I would like to calculate confidence intervals for my clmm (cumulative link mixed model) - multivariate regression model specified for ordinal data. To my knowledge, there is no function for this in ...
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Margin of Error for poll that allows selecting multiple options?

I have a poll with a known sample size (let's say n=1000) which has results that look like this: ...
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1answer
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A question on Bayesian credible interval vs frequentist confidence interval

The difference of Bayesian credible interval (BCI) and the frequentist confidence interval (FCI) is well explained with a nice example in this answer. Here is my own summary of the situation in the ...
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Can MAPE be used as a proxy for confidence interval?

We are using Neural Networks to predict time series based sales data. We are predicting at category-week level. Instead of giving a point forecast, we want to give a range of forecast. If we have a ...
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Conceptual question: A confidence interval around the mean for t-values

I have a weighted graph of an airport network, where each node is an airport (associated with an N, or the number of flights landing at or leaving the airport). The ...
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Bootstrap confidence interval for slope of regression line, in the presence of heteroskedasticity

Suppose I have a simple linear regression problem, and I use the bootstrap to obtain a 95% confidence interval for the slope of the regression line. (Maybe I will use this confidence interval to test ...
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Partially-Linear Least Squares

Model I'm working with univariate time series data $(y_1, \dots, y_n)$ where time $t \in [1, n]$. Suppose the mean function has a known form, in my case $$\mathrm{E}(Y_t) = 1 - \alpha e^{-t/\tau_1} - ...
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What is the standard error of the difference in means scaled as percent difference?

Biologists frequently report the effect B-A as a percent difference (or relative effect), for example "Y was 25% bigger in treatment B than treatment A", where 25% = 100*(B-A)/A and A and B are the ...