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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.

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How to determine statistical significance for an x vs y plot of three data series?

As part of a project, I have measured several values over time. At each time point, five values are acquired: the same quantity at four different positions to give four separate values (y) and the ...
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Computing the confidence interval for difference between means with $c=0.95$

I have the following information about data: $$\sum_{i=1}^{12}x_i=2114; \;\sum_{i=1}^{12}y_i=2144;\;\sum_{i=1}^{12}x_i^2=373160;\;\sum_{i=1}^{12}y_i^2=383666$$ And I want to calculate the confidence ...
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Comparing coefficients and confidence intervals when some categories have very few observations (logistic regression)

I'm fitting a logistic regression model (with multiple predictors) to data where the outcome is a success or failure. My data points are in the range of 100,000. Most of my variables are categorical, ...
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Can/should a scientific paper simultaneously perform one-sided hypothesis testing and a two-sided confidence interval?

Let's say you wish to perform a one-sided hypothesis test in which you want to reject $H_0: \Delta \leq 0$ in favor of $H_1: \Delta >0$. You select this hypothesis test specifically because you are ...
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Confidence interval for GLMM

I am conducting a GLMM for my bachelors thesis and I am wondering, how I can calculate and whether it is common to report confidence intervals for the models' estimates. This is the model I fitted on ...
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Clopper-Pearson CI for an incidence rate in Python [closed]

I do have my own Python code to calculate the Clopper-Pearson confidence interval for an incidence rate. Beside a review of this code I would prefer to have a standard package function for this. But ...
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Highest-density vs equal-tailed confidence interval

When a sampling distribution is symmetric (and I'm okay assuming unimodal too, if necessary), it's natural to center confidence intervals around the point estimate. But for a skewed distribution (e.g. ...
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How do I find confidence interval and what do I do with confirmation points?

I'm running a face-centered composite design with confirmation points. Am I correct in my assumption that the "S" I get from Minitab can be used to calculate CI? If not, how do I get the CI? ...
Ladislav Révay's user avatar
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Standard error and confidence intervals [duplicate]

About theoretical concepts... We use confidence intervals to do an inference to extrapolate results from study to similar sample. Is this true? Which is the difference between a confidence interval, ...
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Is it incorrect terminology to say "confidence interval of a random variable"?

I have seen claims that "population paramter is not a random variable" when discussing confidence intervals. eg here Be sure to note that the population parameter is not a random variable. ...
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Gaussian Process: confidence interval vs prediction interval vs credible interval

Let a distribution over functions be described by a Gaussian Process (GP) prior, following the notation of Rasmussen and Williams: $$ f(\mathbf{x})\sim\mathcal{GP}(m(\mathbf{x}), k(\mathbf{x},\mathbf{...
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Why confidence interval for proportion uses z instead of t score? [duplicate]

The confidence interval (Wald interval) for the parameter $p$ of a binomial distribution is computed from the approximation by a Normal distribution: $$ \ p ~~ \approx ~~ \hat p \pm \frac{\; z_\alpha\ ...
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P-value vs confidence interval interpretation

Refreshing on hypothesis testing. A p-value is defined as "the probability that an observation would be as or more extreme than observed given that the null hypothesis is true." The null ...
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Help with sequencing topics in undergrad stats course

For several years I sequenced my stats course so that estimation theory came before sampling theory. Seemed to make sense—you need a couple of estimators in hand to talk about their distributions. But ...
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What is the meaning of confidence intervals when NOT using sample data and instead have data on the whole population? [duplicate]

I'm trying to understand why you would need confidence intervals or compute statistical tests (for comparing proportions) when your data is NOT from a sample and you have data on the whole population. ...
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Start of instantaneous hazard rate

I'm looking at survival of organizations, with survival in years. I want to produce an instantaneous hazard plot with a confidence interval. I first used pehaz from ...
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Bootstrapped confidence interval overestimates variance in difference of means

I'm trying to translate a Welch T-test into a bootstrap sampling scheme. However, I'm finding that the bootstrapped 95% confidence interval is much larger than the Welch T-test. Perhaps this is just a ...
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Multinomial one-sided confidence intervals

Building on this question: Confidence interval and sample size multinomial probabilities In a binomial confidence interval, a 90% two-sided CI corresponds to a 95% one-sided CI. The question above ...
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How to combine confidence interval (or standard error, or standard deviation) for the sum of 2 fitted parameters

I am fitting a linear mixed model with the equation: $$ y = \beta_0 + X_1 * \beta_1 + \text{random effects} + \epsilon $$ I use the model to compare difference of means between two groups, $X_1$ is a ...
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Bootstrapping Methods for Logistic Regression Models

I have a continuous numeric predictor variable and a continuous numeric response variable (the response variable is bounded by 0 and 1, and there are 0s and 1s in the response column, but the ...
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Should I use parameter standard deviations or standard errors when bootstrapping to generate confidence intervals about logistic regression models?

I have binary response data that I've modeled using simple logistic regression. I have data from a few species and from several individuals of each species. I've modeled each individual separately, so ...
David Moore's user avatar
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Analyzing Cumulative Distribution Functions in Sampling Without Replacement vs. With Replacement

Originally asked on MATHEMATICS. I am studying a population of $N$ bits, comprising $K$ ones and $N-K$ zeros. For sampling $n$ bits without replacement, the situation conforms to a hypergeometric ...
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Appropriate Trend Analysis Test for Small Sample Size

Note: I have read Finding an appropriate trend test but unfortunately this post does not apply for me Suppose I have a small sample of data for 2 numeric variables $T$ and $Y$ where $T$ represents ...
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How do you calculate a confidence interval if you only have an error for each input?

I have made a model (a python script), which takes as its input a scalar value $C_d$, and outputs a vector $\vec{u}$. I also know the 'real' output $\vec{u}^{\text{actual}}$ , which is calculated from ...
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Which is the reason for 1,96 x √2 [duplicate]

Which is the reason to use 1,96 x √2? MDC = 1.96 x √2 x Standard Error of Measurement CR = 1.96 x √2 x within-subject standard deviation Sure will be some reason to use it in the same concepts. Both ...
mdscience's user avatar
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Confidence interval when extrapolating/estimating national result from state data

I have cancer incidence data for about 40% of the US, and want to use this to derive a national incidence estimate. I have age-sex specific incidence data and can use these to extrapolate. What would ...
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Thought and doubt about Student's t-distribution and confidence interval

Let's say I have $N$ observations $X_1,X_2,\ldots,X_N$, where $X_i\sim\mathcal\mu,\sigma^2$, $\forall\,i\in\mathbb{N}$, where $\mu$ and $\sigma^2$ are unknown. I want to predict $X_{N+1}$ and ...
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Moving block bootstrap to get CI around first derivative of trend

I have a time series and I want to know the rate of change of the nonlinear trend component. To do this I want to take the first derivative of the trend but I need a confidence interval around it. I ...
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Confidence interval for superiority/inferiority tests

I am looking into superiority/non-inferiority tests and my understanding is that the null hypothesis for a superiority test is $$ H_{0}: \epsilon \leq \delta $$ where $\delta \geq 0$ and $\epsilon$ ...
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Confidence interval over point estimate given regression parameters

In Bayesian analysis, the posterior distribution is often sampled when the PDF is not intractable (often). If the samples are of length $n$, then every index in $range(1,n)$ corresponds to a valid ...
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Confidence interval for a normal RV that its std is the mean of a different normal RV

Question: Suppose $X\sim\mathcal{N}(\mu_X,a),Y\sim\mathcal{N}(\mu_Y,b\cdot\mu_X)$ where $a$ and $b$ are known, but $\mu_X$ and $\mu_Y$ are not. What confidence bounds can we give for $\mu_Y$ from one ...
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Difference between a comparison of independent variables t.test and linear regression model of one category?

The thing is I am trying to obtain confidence intervals of several variables (food, blood chemical analysis...) of patients who are divided in two groups according the intervention. Until now I was ...
Javier Hernando's user avatar
2 votes
1 answer
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Confidence intervals around treatment effect in stratified experiment

Suppose you conduct an experiment, where a population is randomized and treatment is given to the treatment group and you are interested in covariates (stratification has been employed) and their ...
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Estimating Confidence in Feature Rankings from Multiple Experiments with Non-Normal Data

Hello dear Cross Validated Community, I am a new doctoral student in bioinformatics, and I am working on a project involving multiple experiments, each generating a single numerical result for each of ...
Thomas Rauter's user avatar
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Confidence interval for the sum of 2 binomially distributed variables

$P_1$ and $P_2$ are uncorrelated, binomially distributed variables with success probabilities $p_1 \neq p_2$. Say I measure: $k_1 = 9$ successes out of $n_1 = 10$ trials for $P_1$ and $k_2 = 1000$ ...
dimitsev's user avatar
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11 answers
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When is it important for a practitioner to understand CIs?

I have a physician friend who asks me questions about stats. He gets confused about stuff, e.g., the definition of a confidence interval (CI) and its intricacies. For example, he finds the following ...
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Forecasting positive time series with missing values and few observations

I am working on forecasting a positive time series dataset of prices with missing values and only a limited number of observations. Specifically, I have 150 observations, one per week, and I need to ...
anasse's user avatar
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How to calculate and plot a confidence interval for a bivariate normal distribution?

I have a two-dimensional normal distribution (with correlations). I do not have data points, but only the 2D mean and the covariance matrix. I want to draw the 68, 95 and 99% confidence intervals ...
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Calculation of confidence intervals in linear regression model - normal or student?

I am working with a pretty simple linear regression model, in which I was asked to work with confidence intervals instead of p-values (classic) The thing is I was trying two approaches to get ...
Javier Hernando's user avatar
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Standard error for optimal solution of a convex optimization problem

Suppose I'm given a sample of IID pairs $\{(x_i, y_i)\}_{i=1}^n$ of non-negative numbers from some distribution $\mathcal{D}$ having a finite mean and covariance matrix. Moreover, I'm given a strictly ...
Alex Shtoff's user avatar
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Finding a Pivotal quantity

0 I am working on this problem for class, where the setup is the following: Let X be a single observation from the beta(θ,1) pdf. (b) Find a pivotal quantity and use it to set up a CI having the same ...
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Abnormally large confidence interval with binomial gam when p->1 at max of predictor range

I am running a gam (mgcv in R) to model a non-linear effect of time on a binomial reponse (positive or negative sample). This is a minimal example of such a model: ...
Lars M. Korslund's user avatar
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1 answer
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Transformation of a Random Variable

I am working on this problem for class, where the setup is the following: Let X be a single observation from the $beta(\theta,1)$ pdf. (a) Let $Y=-(logX)^{-1}$. Evaluate the confidence coefficient of ...
Harry Lofi's user avatar
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Compare bootstrap auc confidence interval using t-test

In order to choose between a machine learning model when the number of features is 5 and a machine learning model when the number of features is 6, I want to bootstrap the auc of the model to obtain a ...
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Proof of Azuma-Hoeffding inequality for Martingales in MAB

Suppose in an MAB problem, $X_t=\mu+\epsilon_t$ represents the reward values at each period (for a given arm). If $\mathcal{M}(t)$ shows the set of periods until $t$ where a specific arm has been ...
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Heteroscedasticity-consistent (robust) standard errors complemented by i) confidence intervals for beta, ii) Tolerance and iii) VIF values in R?

In order to solve heteroscedasticity in my data, I ran a regression with heteroscedasticity-consistent ("robust") standard errors. I would also like to report i) standardized betas together ...
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Finding a specific reference on the construction of a confidence interval where by inspection we can see it does contain the parameter

I realise this is a long shot but I am trying to find a reference to a specific example of a construction of a confidence interval which I came across in the past. My memory on this is hazy and I may ...
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when doing an STL decomposition, is is possible to take the first derivative and get a confidence interval around it to test if different from zero?

when doing an STL decomposition, is is possible to take the first derivative and get a confidence interval around it to test if different from zero? I know this can be done with GAMS as shown in this ...
Justin Murphy's user avatar
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Select classification model using nested cv and bootstrap auc confidence interval

My goal is to find the best 1 model out of 55 classification models. I first ran nested cv on 55 models to see which model had better generalization. The AUC score was used as an evaluation indicator. ...
JAE's user avatar
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Statistical significance of non-overlapping 1-sigma confidence intervals

Is this logic correct or not? Given two random variables, each with its own estimate of the mean and a 1-sigma (z=1, 68%) confidence interval that do not overlap with each other: The probability of a ...
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