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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Situations when we cannot use confidence intervals in hypothesis testing?

It seams like confidence intervals resemble critical regions in hypothesis testing .. are there cases when one cannot use these intervals in testing? In critical regions we use the mean and see where ...
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Conceptualizing the difference between sigma, sigma "hat", and standard error for estimated beta coefficients

I've been struggling to comprehend the difference between σ (true standard deviation), σ"hat" (estimated standard deviation), and standard error of the estimated beta (for example, slope) ...
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justification for 'population prediction intervals'?

Suppose we are living in a frequentist world and want to compute confidence intervals on some quantity that is a complicated function of the parameters $q_1 = f(\Theta)$ (i.e., there's no closed-form ...
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How to interpret below, which formular is meant to be used [closed]

A study shows that 70% of consumers believe cheaper supermarket brands are just as good as national name brands. In response to these findings, the manufacturer of a national brand asked a sample of ...
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Monte Carlo simulation to obtain confidence intervals for non linear regression of data with different standard deviations

Could you, please, help. I have pretty standard experimental data taken from scientific paper which is set of N points $x_{i},y_{i}$ on $y(x)$ graph with each $y_{i}$ having standard error $\sigma_{i}$...
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Interpretation of confidence interval with repeated experiment

I have this situation where we perform an experiment which yields 5 samples. The experiment is considered a success based on the following requirement: The standard deviation (of the 5 samples) for ...
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Calculate minimum sample size needed for statistical significance

I am implementing a market survey question and would like to know the minimum sample size needed to report the results with 95% statistical significance. Not sure if this is relevant, but here is a ...
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confidence interval for linear regression coefficient with error following a t distribution

I have this linear model $$𝑌=𝛽_0+𝛽_1𝑋+𝜖$$ where the error terms 𝜖 are iid from a student t-distribution with constant degrees of freedom k. I want to construct a 95% confidence interval for $\...
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Using the bootstrap estimates to compute the acceleration parameter for BCa bootstrap CI

I have noticed different software use different method of calculating the acceleration parameter, $a$, for computing the bias-corrected and accelerated (BCa) bootstrap confidence interval (CI). In ...
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Suppose $X\sim Normal(\mu, \sigma)$ and that $y_i = f(x_i)$ where $Y\sim Bin(p)$. Is the confidence interval of $\bar{y}$ dependent on sigma?

I have a discussion at work on this topic and want to leverage the wisdom of the stats crowd :-) Suppose $X\sim Normal(\mu, \sigma)$ is observed and that $y_i = f(x_i)$ where $Y\sim Binomial(p)$. Note ...
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How does using log transformation for a confidence interval of the survival stabilizes variance?

I only found that it eliminates the estimator of survival from the variance formula, but could anyone show some references or write a few formulas to show how exactly the Greenwood becomes more stable ...
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How to obtain a confidence interval for the cumulative incidence (1-KM) via "log" formula?

I want to show the "mirror" to the survival probability calculated with the Kaplan-Meier estimator, that is the cumulative incidence (or probability). I would like to add the pointwise ...
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What measures of difference can be used to compare two confidence intervals?

Suppose I have two confidence intervals that measure accuracy of two different classifiers on the same data. In the first, I have $0.9087 \pm 0.0073$ for one, and $0.9123 \pm 0.0075$ for the other. ...
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How can I back transform a log data to interpret t-test and get original CI?

I have data that is not normally distributed. I can log-transform it to be normally distributed, and then perform a t-test and get confidence intervals (CI). But how do I interpret the results of the ...
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Overall acurracy +/- E (with 90% C.I.)

I am assessing the accuracy of my classification model. I performed a 4-folds cross-validation and I obtained the following OA = (0.910, 0.920, 0.880, 0.910). So, the average OA is 0.905. My dataset ...
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What does the CI interval mean? [duplicate]

I created a plot with the help of ggbetweenstats: I wonder about the meaning of the CI-interval which is [-0.37, 1.49]. What does this mean? Sorry for cutting the labels on the y-axis. The numbers ...
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How to interpret/report a confidence interval for spearman rho

I am doing my thesis in behavioural psychology and could use some stats guidance. Being a behavioural study, I have a low-n but lots of frequency data. I am using bootstrap statistics confidence ...
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How to find the confidence level of a classification?

Say these's a random forest model used to classify 5 different classes. How do we get a confidence level of the prediction? Say business wants to know what class will happen with high confidence
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Finding Confidence

I am running A/B testing . Created 4 groups with 3 group as variant and one as Control. I found the confidence values for this hypotheses More Number of events(Group) per day Drive Higher Uninstalls ...
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Problem in calculating the confidence interval (Fleiss Kappa) in SPSS

I'm calculating the Fleiss Kappa for inter-rater and intra-rater reliability. I have 3 raters and they rated 10 types of forests as 'tropical', 'temperate' or 'boreal'. This is done twice with the ...
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How to calculate 2-D confidence intervals with the boot package in R? [closed]

I'm making a scatter plot of two statistics X(e) and Y(e) for various values of scalar parameter e. The sampling distribution of both X and Y is not normally distributed. Now I want to calculate a 2-D ...
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How to get standard error from the odds ratio confidence interval?

Given the point estimate, lower, and upper confidence limits, I'm trying to get the standard error of an odds ratio ($\hat{OR}$). Suppose that we have $1.19 [1.14, 1.23]$. Assuming it's 95% confidence ...
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What is considered a a wide 95% confidence interval, what is considered a small 95% confidence interval?

I am revising confidence intervals, and the books that I have found mentioned a wide confidence interval and a small confidence interval but do not define what is "wider/large" or "...
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What should the confidence interval with the whole population as sample result in?

Given the formula for Confidence Interval = x̄ ± z * ơ / √n If I have a population of 3000 people. I take a sample of 3000 (I assume I can do this without replacement, so this is the whole population) ...
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Confidence Intervals for Odd's Ratio? [duplicate]

I am an MBA Student and I am trying to understand how to calculate the Confidence Interval for an Odd's Ratio. Our professor gave us this link (https://www.ncbi.nlm.nih.gov/books/NBK431098/) which ...
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Estimating the confidence that annotations (labels) are correct by a human annotator

I have a task with the following setup. Annotators are given $n$ binary tasks to annotate. For $k$ tasks, the true label is 1. For $n-k$ tasks, the true label is known to be unknown and random ...
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Variance in a confidence interval for a percentage in a survey sample

I'm teaching an undergrad class on survey sampling (not in the stats department) for the first time. This seems like a very basic question that I should know the answer to, but I can't find it ...
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How to obtain the confidence interval for the median and for the difference in median between two groups without having the individual data

With two samples A and B having nA and nB as size, ...
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is there a way to obtain difference between two estimates with confidence intervals?

I am using time-based regression to estimate an effect of an intervention. I have two separate hypothesis: H1A: the intervention will have a positive effect on one time series a1. H1B: the ...
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Calculate the confidence level

I have to calculate the CI for the following problem: The mean grade at the class is 65. Assuming a constant standard deviation of 10 in exams grades for any year's grades for this exam, and the mean ...
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Compare single observed value to simulated distribution

I have a distribution of values that I have simulated for a null hypothesis data generating process. I have a single real-world observation that is wayyyy outside the percentiles of this distribution. ...
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Monte Carlo method for confidence intervals

I would like to attempt a Monte Carlo procedure to filter composite anomalies at 90% confidence level from the rest of the composite anomalies. My data is a NetCDF of hourly surface temperature that I'...
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Confidence Interval Estimation question [closed]

Is the confidence level of an interval only valid if the samples drawn are equal to the original sample size used when calculating the confidence level and interval? Why must it be equal? Why not less ...
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Estimation of Bernouilli parameter: what confidence interval?

Two years ago I answered the question: What are the odds in Scrabble of not being able to make a legal move on opening? This question is asking for the value of the parameter in a Bernouilli ...
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Why are confidence intervals generated by metafor (rma.mv function) wider than in Comprehensive Meta Analysis (CMA) software?

I have been asked to compare my meta-analytic results obtained from the CMA software to the results from metafor. I find that the width of my confidence intervals are larger with metafor than with CMA,...
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Are these two definitions of a 95% confidence interval equivalent?

A definition that I am aware of is interpreted as follows. Given a fixed probability parameter $\theta$, if I construct $100$ confidence intervals $\{I_1, \cdots, I_{100}\}$, then it is expected that $...
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How to calculate the confidence interval around a ratio, when the margin of error is known for the two numbers

I've got this table from the U.S. Census Bureau's American Community Survey. The moe column contains the 90% C.I. ...
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Can I compare the confidence interval when having small sample sizes?

I ran an experiment in which I calculated the biomass of 2 treatments - say A and B. Each treatment had 4 replicates. I now would like to calculate the 95% confidence intervals of the mean biomass of ...
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Comparing two sample proportions with dependent (?) data

Case: I want to know whether the proportion of people getting fired is less now than it was in 2019. I know $\hat{p}$ for both this year and previous years, also I have the sample sizes $n$. I want to ...
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Logistic regression - Confidence interval for x axis

My question is very similar to the post Confidence interval for x-values given a probability in a logistic regression where ultimately no answer was given. I have also posted a similar version on the ...
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1 answer
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Confidence level and alpha with two one-sided t-tests (TOST)

I'm making a non-inferiority study: two groups complete a test (where it is possible to score 0-30 points). I already have the test results for groupB. I want to investigate if groupA performs non-...
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How to calculate confidence intervall and z-score for a weibull distribution? (2 and 3 parameter)

How can i calculate the confidence interval (CI) of a weibull distribution? I have raw data e.g.: 3,5,7,2,11,97, 223, ... I can calculate the mean (µ), standard deviation (SD). But how can i ...
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Confidence bounds for coefficients of a fit of data set obtained with another fit

I fitted an equation to a set of data points. Then I substracted the fit previously obtained to another set of data points. After that, I fitted another equation to this new data (result of the ...
2 votes
1 answer
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Interpretation glmer output and CI with interaction for non-reference level

I could use some help interpreting a glmer output? I am unsure how to get the odds of a non-reference level since there is an interaction. I have observations of ...
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Confidence interval for the difference of two negative binomial rates

I have a model with a negative binomial distribution using the glm.nb function from R: ...
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On the derivation of confidence intervals for hypothesis testing

I understand that a 95% confidence interval should contain the value of the population parameter under the null hypothesis 95% of the time. That is, for $H_0: \theta = \theta_0$: $$ \begin{align*} &...
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Confidence intervals for probability such one event is more likely than the other [duplicate]

Let's base my question on an example. Let's say we toss a weighted coin with probability of tails = 0,05. We do it 100 times and we observed exactly 0 tails. What I am trying to estimate is the ...
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Inverse response variable and CI in Superiority Trials

The hypothesis of superiority is tested for two treatment arms. Let the variable of interest represent changes in a quantitative parameter from baseline. The lower the value of the parameter - the ...
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Block Bootsrap with Weekly Data

I have 20 years' worth of temperature observations where observations are taken every Monday. I am calculating some statistic on this data and would like to use block bootstrap to find confidence ...
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Confidence interval and/or sampling distribution in double / two-phase sampling for stratification

Question: How to calculate a 95% confidence interval for estimated population mean in double / two-phase sampling for stratification where a simple random sample is taken at each phase? Consider the ...
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