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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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Confidence intervals of linear model with several factors

I am trying to interpret the coefficients and confidence intervals of a model that has several categorical variables. I cannot share this model but I managed to narrow down my situation to a simple ...
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Confidence regions on bivariate normal distributions using $\hat{\Sigma}_{MLE}$ or $\mathbf{S}$

Given a $5 \times 2$ dataset $\mathbf{X} =\left( \begin{array}{rr}-0.9&0.2\\2.4&0.7\\-1.4&1.0\\2.9&-0.5\\2.0&-1.0 \end{array} \right)$. Assume that $X\sim N_2(\mu, \Sigma)$. ...
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Sample mean outside of 95% confidence interval but not significant at alpha=0.05 [duplicate]

Sample 1: n=960, mean=815.82, s=305.42 Sample 2: n=23, mean=887.02, s=186.02 I am testing whether the mean of sample 2 is different to sample 1. I generated the 95% confidence interval for sample 1 ...
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Bernoulli / binomial trials for a process with variable probability of success

One of the conditions for a Bernoulli trial (and by extension binomial proportion confidence intervals) is that the probability of success is the same every time the experiment is conducted. In the ...
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9 views

Errorbars for the intersection point of two regression lines [duplicate]

Let's say I have two sets of data and I've fit lines $l_1$ and $l_2$ to each of them. Each line has its own coefficients that have their own confidence intervals. How can I derive the errorbars for ...
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41 views

How many sample needed for 95% confidence of a rule

I've got an electronical component measuring some voltage. The documentation of this component say the maximum error of measurement of this component is 3%. Assuming a chosen component always do the ...
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22 views

replicating SPSS confidence intervals with R [on hold]

Consider this SPSS command ...
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10 views

Confidence Interval in a linear model with restrictions

I am reading the paper by Hannes Leeb and Benedikt Potscher "Model Selection: Facts and Fictions",(available as a working paper here https://www.wiwi.uni-frankfurt.de/profs/klump/D/koll/...
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Errors using boot() and boot.ci (parametric vs. non-parametric) [on hold]

I'm pretty new to R and bootstrapping, so I'm having trouble understanding where this is going wrong. Below is my full code I am using. For this dataset I want to do both non-parametric and parametric ...
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1answer
47 views

Statistical analysis on confidence intervals

I have a data set where the data, when plotted, is not normal. Log-transforming the data makes it normal. Should confidence intervals for the population mean and hypotheses testing about the ...
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9 views

Coverage probability for Wilson Score with Continuity Correction

Asked on the maths site but no answer. From A. Agresti & B.Coull, “Approximate Is Better than ”Exact” for IntervalEstimation of Binomial Proportions”,The American Statistician, vol. 52,no2, pp. ...
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Using confidence intervals to compare regression coefficients

We are currently investigating time trends in mental health. We are questioning our interpretation of our analyses using confidence intervals and wonder if someone could advise us. We use repeated ...
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2answers
53 views

How to calculate the confidence interval of a line based on its coefficients?

I fitted a mixed model as following: $Y = \beta_0 + \beta_1 T + \beta_2 X + \beta_3 X T + \beta_iW_i$ $T$ is time, $X$ is my variable of interest and $W_i$ are various confounding variables. I also ...
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29 views

adequate subsample size [closed]

I am an engineer and running N number of computer analysis (N=50 presently). Analysis results are linearly regressed to find out relationship between independent and dependent variable (y=a+bx). ...
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2answers
117 views

Trouble relating the Central Limit Theorem to confidence intervals

I'm having trouble understanding how the Central Limit Theorem (CLT) implies that we can create confidence intervals as we do. For example, Slide 5 from these lecture notes essentially lays out the ...
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17 views

probability confidence intervals for intercept

I have a GAM model with about 10 variables and 450 observations. I ran a simple GAM regression using R and I noticed that everything looks OK, except that one of the splines has many zeros in the p ...
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41 views

how to estimate confidence interval when p is close to 0 for binomial distribution? [duplicate]

I was trying to get confidence interval for $\hat{p}$. However, the estimated p in the population is close to zero. So I am wondering how I can calculate the confidence interval when p is that small? (...
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Create a statistical test for an experiment [closed]

Basically I have a large set of observations taken by doing an experiment, my observations are similarity scores between [-1,1] interval. Expected value of similarity scores is 1. According to my ...
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plots to show whether the observed data is contained within a distribution

library(dplyr) library(ggplot2) df <- data.frame(year = 1980:2014, y = rnorm(35)) For each year, I have a model that predicts ~5000 values of ...
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1answer
19 views

How to calculate 95%CI for F1 score and Matthews correlation coefficient?

How can I calculate the 95%CI for F1 score, Matthews correlation coefficient and fraction correct ((TN+TP)/(TP+TN+FP+FN)) when I evaluating a perfomance of binominal diagnostic test?
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118 views
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Testing if two distributions have the same mean by using a sample distribution

ORIGINAL Phrasing: Let's say I have a population distribution, A. For example, this could be the distribution of the maximum height (not the current height) that someone will reach during their life. ...
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What properties should a variance estimator have, when we propose 95% CI?

I have a estimator $\hat{\mu}$ for $\mu$, and I know the estimator follows the normal distribution asymptotically, with the mean $\mu$. But the problem is, we don't know the true variance of $\hat{\mu}...
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Are these statements about Confidence Interval correct?

These are statements I got from a pile of homework my colleagues have submitted for a statistics course "...(if) mean is contained in the confidence interval, we can tell that there is a 95% ...
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Does the Neyman construction extend to probability distributions with multiple parameters?

I ran across the Neyman construction of confidence intervals for parameters in reading. In all examples I could find, the distribution of the sample estimator has a single real-valued parameter. Does ...
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Tutorial question on min number of sample size for confidence interval

I'm stuck with this question from my tutorial (and there is no worked solution), and I can't seem to get the correct answer of 411. There were 904 new Subway Restaurants franchises opened during 2002....
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Confidence intervals after one-to-many matching - number of degrees of freedom

I have propensity score matched data after 1-to-3 matching. I am trying to use the code from the answer to https://stackoverflow.com/questions/37973240/ The question is: what number of degrees of ...
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Interpretation of a hypothesis.

suppose If I hypothesize that "a" have a negative relationship with "b". The resulting path coefficient is significant with 99% confidence interval but with positive beta or a positive relationship. ...
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Confidence interval based significance estimation for pearson correlation

When I have two parameters A and B based on 100 values each, I can calculate the pearson correlation coefficient and the confidence interval (95%). If the confidence interval is crossing 0, I can say ...
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3answers
54 views

Confidence interval of inverse model parameter

Let assume that we have a model from which we estimate a parameter with physical meaning, such as a thermal resistance, $R = 0.1$. The unit of the $R$ is kelvin per watt $ \left[ \frac{K}{W}\right]$, ...
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Problem getting SD from a 95% CI of a probability

I'm working on a simulation designed to investigate fertility, birth control, etc. One of the inputs to the simulation is the probability that a given ovulatory cycle is capable of producing a ...
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1answer
35 views

Confidence Interval of the mean response for Weighted Least Squares (WLS)

I know that the confidence interval of the mean response for OLS is: $$ \hat{y}(x_0) - t_{\alpha /2, df(error)}\sqrt{\hat{\sigma}^2\cdot x_0'(X'X)^{-1}x_0} $$ $$ \leq \mu_{y|x_0} \leq \hat{y}(x_0) + ...
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Contingency table (2x4) - right test & confidence intervals

I have 2 categorical variables for each observation in my dataset: environment and behaviour. I'm trying to test association between them i.e. does the environment affect behaviour? The resulting ...
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ML estimator, Confidence interval and Central limit theorem

I have some questions concerning the following problem especially about b). My problem is the following: Let $X$ be an observation from a $\operatorname{Bin}\left(n,\frac{1}{2}\right)$: a) ...
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Confidence intervals for emmeans estimates after multilevel binary logistic regression

I ran a multilevel binary logistic regression / generalized linear mixed-effects model in R, and then ran the following code to get post-hoc tests for a significant A x B interaction where A is a ...
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The basic logic of constructing a confidence interval

Consider a model with a parameter of interest, $\theta$, and its point estimator, $\hat\theta$. For simplicity, assume $\hat\theta\sim N(\theta,\sigma^2/n)$ (in numerous instances this could be ...
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Multiple Comparison Correct Group of Confidence Intervals

I have a number of data points (~10,000) compared against different confidence intervals to determine whether or not they are significantly elevated or not. Now I would like to correct for multiple ...
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What formula for a Confidence Interval of the difference in proportions when sample sizes are small

Suppose that we are interested in comparing two approximately normal sampling distributions described by random variables $ \displaystyle \frac{Y_1}{n_1} = N(p_1,p_1q_1) $ and $ \displaystyle \frac{...
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1answer
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Distribution of estimator of multiple (spatially related) proportions

Consider a spatial random process $Z(s)$, where $s$ denotes the spatial location. Our objective is to delineate the zone $\mathcal{Z}$ where the probability that $Z$ exceed a given threshold $\zeta$ ...
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43 views

Confidence interval for raw number of correct binary predictions

Let's say there are 600 games in an NBA season, and a competition among individuals to correctly forecast the winners of the games. The forecasts are not expressed probabilistically but simply in ...
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Confidence Interval for Exponential

I am simulating exponentially distributed data with rate $5$ and I want to construct the confidence interval for usual convention $\alpha = 0.05$. ...
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26 views

Prediction interval for sampled count data

I am trying to get prediction intervals around a sampled count variable. For example, say I want to know the number of letters an apartment building receives every day. Each day I record the count ...
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Discrepancy between MATLAB's paramci confidence interval and Reliawiki's Likelihood ratio confidence bounds

I've been learning how to calculate and fit probability distributions to life data and have been following the documentation on reliawiki.org; specifically, I've been reading the chapter on confidence ...
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upper confidence bound of a non-linear model seems wrong (predictNLS)

I have the following data and R-script: ...
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38 views

Interpreting a Monte Carlo Simulation’s Results

I generally run 1000 iterations whenever I simulate things like stock prices. When interpreting the results, how do I find which simulation is the median, or highest probability of occurring in ...
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1answer
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Does the Confidence Interval Contain a Mean If It Equals One of the Limits?

Does a confidence interval contain a mean if the proposed mean equals one of its limits? For example, say I have a 95% confidence interval ranging from 3.19 to 3.49. Does this interval contain the ...
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24 views

Calculating one-and two-tailed t-tests manually in R

I have two samples d1 and d2: ...
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1answer
38 views

Confidence interval on binomial distribution on one sample predicted from another sample

I have a work problem that seems to match pretty much exactly the "drawing balls from urns" type of problem, and it must be a pretty common type of problem, but my googling didn't find a solution. I ...
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2answers
49 views

Is it possible to calculate a confidence interval related to a significant p value from the kruskal wallis test?

I have run the nonparametric Kruskal Wallis test with pairwise comparisons in SPSS to understand if my 3 groups of survey participants were different in their responses to a range of 5 point ordinal ...
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42 views

Does confidence interval of the mean fully correct for size?

Say I have heartrate data at every minute during the day. I suspect the person was exercising at different points during the day (based on some other data), and now I want to examine my hypothesis. I ...
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Confidence bounds for Weibull MTTF

I have three times-to-failure (TTFs) as 28, 40, 43. I fit a Weibull distribution on the data, and want to calculate a 95% confidence interval for the mean-time-to-failure (MTTF). Using ...