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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Making a forecast: Confidence/Prediction/Tolerance Interval?

I understand the the difference between these three types of intervals but I will summarize briefly: Confidence Interval: an interval that will contain the true mean value say, 95%, of the time. ...
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Confidence interval for Bayesian expected probability in categorical data

The context of the question is survey results analysis. I am focusing on categorical data : N respondents answer some questions and each question has $k_{q}$ choices. I want to compare what subgroups ...
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Logistic regression: Is there a significant difference for probability p between groups of Bernoulli random variables?

I have exactly $n$ observations of independent Bernoulli distributed random variables $Y_1, \cdots, Y_n$. I divide the observations into $k$ disjoint groups. In my case $k=3$ and $n=1450$. I proceed ...
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Calculating standard error for a ratio of hazard ratios

I'm trying to calculate if there has been a change in risk over time, during 10 years of follow-up, for young adults to develop depression. I've successfully calculated the hazard ratio and 95% CI ...
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Why does the Arima() method in the forecast package in R not calculate standard errors for coefficients passed to 'fixed'?

In the Arima() method, in the forecast package in R, I can provide a vector of parameters to the ...
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14 views

Confidence intervals for odds ratio in GLMM with interactions

I have the following output from a GLMM The model is $$ \log\left(\dfrac{p_{i}}{1 - p_{i}}\right) = \beta_0 + \beta_1 \texttt{type}_i + \beta_2\texttt{treat}_i + \beta_3(\texttt{type}\times\texttt{...
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26 views

Most reliable method to compute 95% confidence intervals of proportions for small samples

I am planning a prospective trial for CE mark of a new cardiovascular device, and wish to use 95% confidence intervals to present, once data are collected, the inferential estimate for the occurrence ...
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29 views

On finding a confidence interval. (exercise)

I am having some problems with the second point of this exercise Let $(X_1, \dots, X_n)$ be a random sample extracted from a population $X$ that is distributed as a uniform $(0, \theta)$ and let $Y_n ...
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Is frequentist conditional inference still being used in practice?

I've recently reviewed some old papers by Nancy Reid, Barndorff-Nielsen, Richard Cox and, yes, a little Ronald Fisher on the concept of "conditional inference" in the frequentist paradigm, which ...
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How can I use RLRsim to get for the results of a fitme() model (from the spaMM package)? [migrated]

I've found that the spaMM package fits my generalized linear models where others (e.g., lme4, glmmADMB) don't. Because my data is very uncooperative. I really need some kind of confidence intervals or ...
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Confidence that a percent of population will be within bounds (parameter-less) [Tolerance Interval]]

Sometimes it's nice to be able to estimate the proportion of a population that will fall within certain bounds, given a set of sample data from that population. This is essentially a tolerance ...
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22 views

How to apply a confidence interval

I'm a little confused about the following question: In a study of the length of time that students require to earn bachelor’s degrees, 80 students are randomly selected and they are found to have a ...
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Contradictory p-value and confidence interval in permutation test

I am using the MICOM procedure to test for measurement invariance among groups in PLS SEM modelling [1]. This procedure consists of 3 steps, where in step 3 one tests for equality of composite means ...
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142 views

Does a confidence interval carry some extra error for non perfectly normal distributions?

I'm not trying to nitpick but I always want to make sure with stats that I clearly understand the delimitation between exact/theoretical measurements and "real life" measurements. Let's say for ...
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40 views

How to calculate confidence intervals for a population proportion (ordinal variable)

How can I compute confidence intervals for an ordinal variable (or Likert-type scale)? My sample size is 430, and the proportion of each category is as follows: 5 = 24%, 4 = 29%, 3 = 27%, 2 = 15%, ...
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How to validate simulation result with real data

I have made a computer simulation, which is a model of a machine process step in a real factory. This factory keeps track of certain KPIs (key performance indicators), like utilization (% of time in ...
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39 views

How to add up partial confidence intervals to create a total confidence interval?

I have a response variable that obtains different confidence intervals (CI) when calculated with different explanatory variables. I want to add up all values of the response variable and create a CI ...
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Ranking of findings

Let's say I have 100 different types of seeds - Apple, Banana, Celery, ... and I am looking at some data for germination rate. Each individual test is binomial - the seed either germinates or it does ...
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Prediction interval for a future proportion of successes under Binomial setting

Suppose I fit a Binomial regression and obtain the point estimates and variance-covariance matrix of the regression coefficients. That will allow me to get a CI for the expected proportion of ...
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24 views

Confidence interval for the p-value estimate when doing Monte Carlo testing

The second paragraph of the Monte Carlo testing section of the Wikipedia article on resampling statistics, the values of a confidence interval for a p-value from a MC sampling is given: After $N$ ...
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47 views

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: ...
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Applying delta method on Euclidean distance

In order to estimate confidence interval of a k-dimension Euclidean distance, I need to use delta method to estimate standard ...
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Statistical comparison between two stochastic algorithms

I am working on a mechanics problem with variability in material properties. For that I need to analyze the efficiency of two methods for same accuracy (confidence level I guess?), the first one being ...
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LASSO confidence interval in a randomized experiment

I want to use the LASSO for analyzing the results of a randomized experiment. I have more covariates than data, hence the motivation for using the LASSO. The treatment that was randomized in the ...
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Calculation of standard errors and confidence intervals in lme (nlme package) and jointModel (JM) package

Does anyone know how the standard errors are calculated for mixed models fit using "nlme" package and joint models fit using "JM" package? I am trying to compare the precision between mixed models fit ...
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Is this data's mean significantly different from zero?

I need to make a statement regarding whether the mean of this data is significantly different from zero. The data can not be described by a normal distribution. The population's size is 27, mean is -...
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How to extract the confidence limits of LSMEANS? [migrated]

I am using the oranges data provided with lsmeans. ...
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Is there any prerequisite before using the student law for creating confidence interval?

I'm currently calculating some confidence interval for some mean value by group. Some of them has less then 30 individual inside. Does it still make sense to calculate the confidence interval for ...
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42 views

How to find smallest sample size such that the sample mean is within delta of the population mean with 95% confidence?

Let $\mu$ be the population mean and $\hat{\mu}$ be the sample mean. For a given $\Delta$, I would like to find the least $N$, the sample size, such that $$ P(|\mu-\hat{\mu}| < \Delta) = 0.95. $$...
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unstandardised b coefficient, 95% CI and p-value interpretation in a linear regression

How could I interpret the table when: 1. the unstandardised coefficient has a value equal to 0? 2. either the lower or the upper bound of the 95% CI is 0 but the p-value is less than .05? I just run ...
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significant chi-squared test but confidence interval for odds ratio does include 1

I have the contingency table: A B a 28 0 b 35 9 I applied the chi-squared test with Yates's correction, with p-values: ...
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28 views

standard deviation in calculating confidence intervals

I asked a question earlier and realized the question I asked wasn't a good representation of what I meant to ask. (Why use the standard deviation of sample means for a specific sample?) Now that I'...
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Wald confidence interval with delta method

Using the delta method, show that the Wald confidence interval for the logit of a binomial parameter $\pi$ is $$\log \left(\frac{\hat{\pi}}{1-\hat{\pi}} \right) \pm z_{\alpha/2} \sqrt{\frac{1}{n\hat{\...
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Confidence interval for effect size for a within-subjects t-test

does anyone have a suggestion for an expedient way to calculate confidence intervals on effect sizes (cohen's D) for dependent-samples (edit: within-subjects) t-tests? For a meta-analysis, I've ...
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Combining Fixed Effects and Random Effects Confidence Intervals, Is this Possible?

I estimated a random slope,random intercept model and have estimates of the fixed-effects $\beta_i$ and the random effects $b_i$. I also have their associated standard errors $SE_{\beta_i}$ and $SE_{...
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Odds ratio confidence interval using bootstrap

I have model with four predictors in logistic regression and sample size 39 (6 positive patients and 33 negative). When I perform logistic regression with bootstrap method it gives me b coefficient ...
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How to calculate the confidence interval of the x-intercept in a linear regression?

Since standard error of a linear regression is usually given for the response variable, I'm wondering how to obtain confidence intervals in the other direction - e.g. for an x-intercept. I'm able to ...
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Inconsistent P-Value and Wald Confidence Interval in R Survey Package

I am using the svyglm function in the survey package in R to fit logistic regression models ...
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95% confidence intervals on prediction of censored binomial model estimated using mle2 / maximum-likelihood

I am working on a problem in which I have multiple pairs of currently living males i that each have a presumed paternal ancestor ...
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Freeman & Tukey interval [duplicate]

If $Y$ is $\text{Poisson}(λ)$ distributed, how do we obtain this confidence interval for $λ$: $\:l=\frac14 [(\sqrt{Y}+\sqrt{Y+1}-z_{α/2} )^2-1]$ $u=\frac14 [(\sqrt{Y}+\sqrt{Y+1}+z_{α/2} )^2-1]$
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Application of Wilks' theorem to poisson data

My parametrized astrophysical model predicts a mean bin count $e_i(\theta_1,\ldots,\theta_p)$ for each of $N$ non-overlapping energy regions. For a set of observed counts $k_i$ the joint likelihood is ...
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Jeffreys Interval Calculations and Sample Size

I have a rough understanding of bayesian statistics and of the Jeffrey's Interval/priors. I understand that the Jeffrey's interval takes the form: $$p\mid x \sim \mathrm{Beta}(x + 0.5, n - x + 0.5)$$ ...
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Is there a non-boostrap way to estimate confidence intervals for Kernel regression predictions?

Simple problem of estimating: $$ y = f(x) + \epsilon $$ Where I use your standard Nadaraya-Watson Regression to guess $f(x)$. This is relatively fast and works well even in an online setting. Now I ...
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what is the estimated variance of predictions from mixed model?

I have fitted the following lmer model (assume it is "correct") with lme4: Y ~ X1 + X2 + X3 + (1 | year) + (1 | site) + (1 | site:year) where X1-X3 are ...
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Sample size determination for estimating a count

I want to estimate a simple variable: "**how many times my website is visited in 2015?". Suppose that I cannot count all visits to my website (it is expensive!), but I can count the connections on ...
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32 views

Uncertainty in parameter estimates when fitting distributions

I used the fitdist function from the "fitdistrplus" package in R to estimate the parameters of my data. Once I get the parameters, I must get the confidence ...
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Hypothesis testing. Why center the sampling distribution on H0?

A p-value is the probability to obtain a statistic that is at least as extreme as the one observed in the sample data when assuming that the null-hypothesis ($H_0$) is true. Graphically this ...
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Removing undefined (NaN) values during log-likelihood maximization

I am trying to maximize a Poisson likelihood function for an array of values, of the form llhij = -mij + kij*ln(mij/kij). (where I use the numerical approximation ln(k!) ~ k*ln(k)). For my ...
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Given a 1-Sided Lower Confidence Bound value, How to determine target failure rate

$R(t)$ = reliability = 1 - unreliability (probability that item is still operational for a given time t) unreliability = Cumulative Distribution Function (CDF) = (...