Questions tagged [confidence-interval]
A confidence interval is an interval that covers an unknown parameter with $100(1-\alpha)\%$ confidence. Confidence intervals are a frequentist concept. They are often confused with credible intervals which is the Bayesian analog.
111 questions from the last 365 days
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Confidence interval for the parameters of a non-linear model
I am trying to understand how to obtain the confidence interval for a function fitted with scipy.optimize.least_squares. If my understanding is correct, I'd need to take the "Modified Jacobian ...
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Different CIs for the same linear mixed model emmeans, ggemmeans, ggpredict
I fitted a linear mixed model in R and tried to compute marginal means using emmeans, ggemmeans (from ggeffects), and ggpredict (also from ggeffects). The predicted means are similar, but the ...
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How to design a minimal test (sample size + combinations) when two components both affect accuracy?
I’m trying to design an experiment for a system where two different components both contribute to the final accuracy, and I can only test a small subset of all possible combinations.
A concrete ...
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Why can I fit a horizontal line through the 95% confidence intervals region of my OLS model even though its overall p-value is close to 0.05?
Original question: ~~I don't know how to intrepet the result I got from my OLS analysis. The issue is that I can fit a horizontal line within the 95% CI even though the overall p-value for the model ...
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references on how to include nonsampling errors in the measure of uncertainty
On the page https://www.ons.gov.uk/methodology/methodologytopicsandstatisticalconcepts/uncertaintyandhowwemeasureit, there's a section where the UK Office for National Statitics talks about non-...
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Is this confidence interval lower bound for $| \mu |$ valid?
Many years ago, I needed a lower bound for a $(1- \alpha )100 \% $ one-sided confidence interval for $| \mu |$, assuming $X\sim N( \mu , \sigma^2I_n) $ with $ \sigma^2 $ known. Now $\bar{X}\sim N( \mu ...
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Calculating standard errors in least squares and the normality assumption
The question titled “How are the standard errors of coefficients calculated in a regression?” is asking how the standard errors of regression coefficient estimates are computed (for example, the ...
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chi-squared significant for dose-response function obtained through meta-analysis but confidence interval around plotted predicted values not
The question:
I obtained a dose-response function (predictor vs relative risk) through meta-analysis using the dosresmeta package for R. The package applies a random effects model (REML)and I fitted a ...
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Probability of a failed component from an accepted component lot - tolerance analysis
Question: Given a component lot where a sample is drawn for testing leading to the determination of the sample mean and variance, a one-sided tolerance limit,$\mu + \mathrm{KTL} \cdot \sigma,$ is ...
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How to find confidence intervals for binary outcome probability?
I'm doing stats for medical chart review research. The binary outcomes vary in probability from less than 0.05 to greater than 0.5 depending on risk factors. For relatively more common outcomes like ...
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Error bars for slopes on probability scale crosses 0 but interaction is significant
I am trying to understand this multinomial logistic regression model. The dependent variable is subjective class. There are two independent variables and an interaction term (objective class and year)....
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Control false-accepts via Confidence bounds for a quantum authentication protocol
I have problems designing a confidence interval for an quantum-based authentication protocol in my thesis. The protocol is based around measuring (Pearson) correlation $\rho$ between $2\times N$ ...
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Confidence interval for difference of probabilities, for paired data
Let $X,Y$ be random variables given by $X=X_1 + \dots + X_n$, $Y=Y_1 + \dots + Y_n$, where the $X_i$ are iid with distribution Bernoulli($p$) and the $Y_i$ are iid with distribution Bernoulli($q$). ...
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Why don't people add "coverage" intervals on the p-values they report? (E.g. from bootstrapping the sampling distribution of p-values)
Let's say i want to test for the difference of mean values of two distinct groups having each N observations. The null hypothesis would be that there is no difference - this could for example be ...
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Can the random effect estimates of a GAM model be used for developing risk maps?
I have implemented the following model using mgcv package
...
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What information do p-values and confidence intervals provide?
I am in the field of medical research and had a few questions regarding statistics. Is it preferred for a study to state both p-values and confidence intervals together? What extra information do ...
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Which model to use for power analysis and sample size calculation for interval-censored and right-censored data?
There is a population of devices that undergo a repeating cycle of stimuli when in standby. The time in standby mode is a random variable. When called upon to operate they may either fail to operate ...
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Sign test: p and CI contradiction (significant but CI includes 0 AND not significant but CI doesn't include 0)
I run a sign test in R and get repeatedly contradicting p-values and confidence interval (CI). See for example these results of BSDA::SIGN.test() with two dummy ...
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Exact Wilcoxon signed rank test: p >.05 but CI (95%) does not include 0
I run an Exact Wilcoxon signed rank test using exactRankTests::wilcox.exact() in R. The test is not significant (p>.05) but the 95% CI does not include zero. How ...
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Coverage for all parameters in confidence intervals
Consider a random sample of size n $X$, and a statistical model for the data generation process $\{{\mathbb{P}_\theta}\}_{\theta \in \Theta}$ with the true parameter being $\theta_0$. In many ...
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Reference request: Where is it shown that adjustment of confidence regions for selection of predictors is NP-hard?
In ordinary least squares regression with multiple predictors, statisticians sometimes choose a model using only some of the predictors, after concluding that the others are not significant. I have ...
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Estimate the changepoint where two marginal predictions converge
I have a dataset of participants performing a maximum work task at various loads, under two conditions c("A", "B"). I would like to estimate at what load work becomes the same in ...
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Connectedness of LRT Poisson Confidence Sets, i.e., Monotonicity of the LRT Poisson Acceptance Regions
Background: Working on Exercise 9.23 (a) in "Statistical Inference, 2nd Edition" by Casella and Berger. Simply speaking, the problem asks for a $1 - \alpha$ confidence interval for a Poisson ...
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How to be confident of some program failing less often than a threshold?
When writing complex software, it is common for some of the tests to be "flaky", failing in a seemingly random fashion some fraction of the time. Such failures can often be eliminated by ...
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How to compute confidence intervals and effects sizes for all effects, mixed modeling
I’m plodding along as I try to figure out my mixed modeling output. I have some confusion understanding the output that I hope someone can clarify.
I have a 2 x 2 repeated measures design (Consistency:...
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How to optimise the selection of sample points to minimise total model uncertainty?
I am building a model to predict an output parameter based on three inputs, and collecting sample data is relatively expensive. I'd like to optimise the selection of the next sample points I take to ...
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343
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bootstrapping for variance estimation takes too long
I am not sure if my question is more for crossvalidated or stackoverflow, because I am not sure if the problem is in the code or my understanding of the problem. I am trying to run Inverse Probability ...
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Getting the confidence interval of the mean of values, each with its own SE
Assume I have several estimates each with its own SE. If I compute the mean of those estimates, how can I compute the final CI of the mean?
This is how I would do it if those values were random ...
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Is there a way to estimate power from the confidence intervals in a similar study?
A colleague of mine is running fresh analyses on an old dataset, using multiple logistic regression.
We have the output from an old analysis, giving 95% CIs for odds ratios for different predictors, ...
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Bounding the Tail of a Sum of Dependent Bernoulli Variables via Conditional Expectations
I'm working on a problem that arises in a physics context and involves probabilistic modeling using binary outcomes. I'm not a mathematician by training, so apologies in advance if I miss standard ...
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How to calculate confidence intervals for single side bounded proportion
I have aggregated data on disease occurence for two time intervals, time A and time B say, in different countries.
I am interested in the relative change from time A to time B relative to time A. (...
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Confidence interval for the variance of a sample mean from a mixed model
Imagine we have a random variable: $$X = \mu + I + J + K + \varepsilon$$ where $\mu$ is a fixed unknown parameter, $I \sim \mathcal{N}(0, \sigma_i^2)$, $J \sim \mathcal{N}(0, \sigma_j^2)$, $K \sim \...
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Compute confidence intervals for observed probabilities [duplicate]
If I compute the observed probability of an event like so:
observed probability = positive outcome/total number of outcomes
How can I compute confidence intervals ...
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Should I use one-way ANOVA or pairwise confidence intervals for this data?
I’m running a study with 4 conditions, each representing a different visual design of a network visualization. I want to compare how effective each design is across different task types. Effective ...
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Bootstrapping - Interpretation and transformation
I am currently trying bootstrapping. My dependent variable is continuous (Change in ROA). My independent variables are GDP growth and inflation rate (both continuous). I also include three control ...
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Calculating confidence intervals via bootstrapping for statistics derived from dependent observations in a distance matrix
I am analyzing data consisting of observations of i.i.d. users. For these users I compute all pairwise distances, forming a distance matrix $D$. From this, I calculate for each user i the average ...
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Visualizing glmm predictions: confidence intervals from ggpredict
I'd like to create a graph for my paper that visualizes my binomial glmm, ideally with confidence intervals. However, my CIs using ggpredict came out a bit funky.
Here is some example code using the ...
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Confidence in mean of very small sample
I'm trying to calculate the 50% confidence interval of the true mean based on a sample of a gaussian distribution.
I've written some code in python which tests if the 50% confidence interval of 3 ...
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Frequentist SVAR sign restrictions IRF error bands construction
I am currently writing a small library for sign restricted SVAR, and I ran into a problem of constructing error bands for impulse responses. At this moment, I use Lutkepohl delta-method to construct ...
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How much of my timeseries data do I need to label
I've created a custom anomaly detection algorithm.
I have time series data sampled at 100Hz which contains artifacts which repeat in a semi regular pattern, at a rate of about 10/min.
The artifact ...
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Confidence Interval estimate for mean of interval constrained data
Second attempt at asking this question: Consider $N$ IID realizations of random variables $X_i, i\in\{0,1,\cdots,N-1\}$ where the random variables are interval constrained i.e., $X_i\in[0,1]$. I ...
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What is the statistical valid range and sample size of a measurement?
I have a generic but very practical question which I am not able to find answers in textbooks so far: Suppose I have taken $N$ measurements of a value with unlimited bounding range. The mean and ...
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Hypothesis testing via overlapping CIs when one sample is very small (8) and one is large (178)
I'm taking a statistics class. The question has been graded, but I question the validity of the official answer. We are asked whether, based solely on the confidence intervals, the mean BMI differs ...
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Confidence Interval for Population with Disproportionate Stratified Random Sample
I am reviewing data from a stratified random sample to describe the proportion of the total population exhibiting Trait A ($p_A$). Due to time/resource constraints, I conducted a disproportionate SRS ...
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interpretation of confidence intervals computed on different things
Below is a question that has nagged me for a long time. I've had a look at some other threads about confidence intervals (in particular this one What, precisely, is a confidence interval?) but I ...
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Correct interpretation of an estimate which is outside its confidence limits
I have computed a geometric mean ratio (variable=area under plasma concentration curve) of two groups (males/females) as 0.9338682 and its 90% confidence interval as 0.9684333 to 1.184019. Clearly, ...
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Confidence interval of the ratio of two geometric means of lognormal data
How can I compute the 90% confidence interval of the geometric mean ratio of two unequal groups given the group sizes, geometric means and geometric standard deviations of the two groups?
I have tried ...
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Statistical Approach to Counting by Weighing
I am trying to approach a problem that I have that involves portioning sufficiently-identical/interchangeable objects (think small medical devices, toys, etc.) with close, but not identical masses ...
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Estimating parameters like Correlation [closed]
Typically when estimate different statistical parameters like Correlation between 2 variables like Height and ...
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QAP regression and confidence intervals
I've run a Poisson QAP (quadratic assignment procedure) regression in R on my network data. As expected, the output provides permutation-based p-values, but not standard errors or confidence intervals....
