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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26 views

Confidence interval for combined populations

I'd like to compare two approaches for calculating the confidence interval ($CI$) when estimating the mean for a sample of weighted values: The first approach is based upon the standard error of the ...
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How to combine the estimate and confidence intervals of the fitted parameters that you obtain in every run of cross validation?

I am fitting quite a complex model to experimental data points (lots of equations, but just two parameters). The nonlinear least square regression tool (I use fitnlm in Matlab) outputs the estimates ...
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Percentile interval Lemma - proof

Let $\theta$ be a parameter and $\hat{\theta}$ the plug-in estimate, I need a proof of the following lemma, as given in [1], p. 173, in the form of a reference or of a direct argument: Percentile ...
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R Confidence Intervals for quantiles from Generalized Lambda Distribution

I'd like to compute confidence intervals in R for quantiles from generalized lambda distribution. Steve Su (2009) introduces below 2 ways to calculate confidence intervals. I think I could understand ...
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confidence intervals for mixed model with pronounced random effect unexpectedly large

Assume I generate some data with a very tiny random effect and calculate a lmer (y ~ group + (1 | surgeons)) and glm (y ~ group) ...
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Confidence interval calculations Tukeys vs Bonferroni vs Fishers LSD?

I am trying to work out how the Confidence interval calculations for the Tukey, Bonferroni and Fishers LSD differ and/or are similar from each other? From my understanding they all consider the ...
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Finding changepoints in a GAM?

I'm using generalized additive modeling to investigate the relationship between two variables, X and Y. I want to find changepoints--i.e., X values at which the slope changes direction. I can get ...
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How to interpret discrepancy between confidence interval and p-value

My main statistical model returns a significant treatment effect with a p-value below 0.05. Usually, this means that we can reject the null hypothesis that the treatment effect is zero. However, the ...
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How to report odds ratio with confidence interval when it looks like this [closed]

OR 2.5 % 97.5 % p (Intercept) 0.036616 0.030116 0.0509 <2e-16 *** weight 1.000231 NA 1.0043 0.9458 Above is the ...
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Reporting on reliability of relatedness estimates

I have conducted pairwise relatedness estimations between over 100 samples from one termite population, which is divided into five colonies. The estimator basically looks at the genotypical ...
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Question about confidence intervals and prediction intervals

Considering following linear multiple regression model: \begin{equation} y=X\beta + e, \end{equation} where observations $y\in\Re^n$, coefficents $\beta\in\Re^p$ and $e\sim N(0,\sigma I)$ is a white ...
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Additional steps when fail to reject null hypothesis

My understanding of the hypothesis test below is: $H_0: \theta_0$ = 0 ; $H_A: \theta_0 \neq$ 0 given $\alpha$ = .05 if my p-value is < .05 I reject the null in favor of the alternative then: ...
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Why is the cohen's d effect-size from this study so different from the value I've computed manually?

In this study [1], they estimate an overall cohen's d effect-size of .70; however, when I try to compute the cohen's d using their means/stds, I get a much smaller effect-size of .47. Am I doing ...
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What does asymptotic significance value less than 0.95 tells when results are already significant with 0.05 value? [duplicate]

I am relatively new in statistics and it is also not my major. I am just using it due to the need. I have used the SPSS tool to establish the statistical significance of two or more scales between ...
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44 views

Finding a confidence interval with two samples

Let $X_1, X_2, \ldots, X_{n_1}$ and $Y_1, Y_2, \ldots, Y_{n_2}$ be two different independent i.i.d. samples from $N(\mu_1, \sigma^2)$ and $N(\mu_2, \sigma^2)$, respectively. Note the variances are ...
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Nonparametric confidence interval for the mean: Failure to reproduce formula from Zhou & Dinh (2005)

Zhou & Dinh (2005) propose the following formula for a $(1 - \alpha)100\%$ confidence interval for the mean of one sample. The confidence interval is based on a transformation of the $t$-statistic:...
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Confidence interval vs. cross validation to estimate performance of a machine learning model

When training and testing a machine learning model, if I split the dataset just once, I may end up with the "good" portion so I can have a good performance. I may also end up with the "...
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How to construct a confidence interval of the mean, when the distribution is unknown and the sample is small?

I'm looking for the preferred approach to construct a finite sized confidence interval for the population mean, assuming: The distribution of the population is unknown The sample size is low The ...
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How to predict the probability of a periodically happening event occurring at a given time

I have encountered this problem on how to predict the probability of a periodically happening event occurring at a given time. For example, we have an event called being_an_undergrad. There are many ...
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Uncertainty reduction with additional samples

I'm trying to estimate the uncertainty of a premium when we have $n$ observations of losses. My goal is to estimate the benefit (e.g., uncertainty reduction) when we add an additional sample to our ...
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Confidence ellipse in PCA

Is there any good explanation about the confidence ellipse used in PCA analysis which briefly describes how to interpret the result? For example, I am looking for the following cases: Some points are ...
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why are confidence intervals so wide with nested random effects design for factorial linear model?

I am analyzing historical data conducted from a factorial experimental field study with nested random effects. The investigator counted indicated breeding pairs of ducks per hectare (ip.ha) in ...
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Estimating intercept from interval for slope and prediction interval

Suppose we have collected some data and formed a simple linear regression model for $Y$ versus $X$ . Suppose further that $[a,b]$ is an $\alpha$ % confidence interval for the true slope $\beta_{1}$, ...
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Can you use a given prediction interval to find the predicted value of Y on the estimated regression line?

Suppose you don't know the estimates of a linear regression model (b0, b1 are unknown) and you are given a 95% prediction interval at x = 6 to be [5,15]. Then, since prediction intervals are ...
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Is the train/test split necessary for parametric models like logistic regression?

In order to have an estimate of the prediction error in a machine learning model, I am used to split my dataset into a training set and a test set. I will train my model on the training set and ...
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Average length of confidence interval

For a particular sample, the small value of this length indicate greater confidence but in many research articles, authors report average length of Confidence interval based on simulation study. Why ...
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1answer
28 views

Bootstrapping mean difference: standard error versus quantiles

I am implementing a bootstrap procedure (in R) to calculate the confidence interval of a difference of two means. I have little experience with bootstrap but I am ...
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What would you recommend to someone interested in paying people to wake up earlier based on the research abstract below?

Experiment design: Researchers ran an experiment to test whether paying people to get up on time made them less likely to sleep in late. Fifty participants were randomized to 2 groups: a control group ...
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confidence interval of $\beta$, where $X$'s are from exponential distribution

Suppose $X_i\overset{ind}{\sim}\mathcal{E}(\lambda_i)$, where $\lambda_i=(t_i\beta)^{-1}$, where $t_i$'s are positive known values and $\beta$ is positive unknown parameter. Here $i=1,\dots,n$. It can ...
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Hypothesis Testing/CI on Variable Importance in random forests

My question refers to features of the packages randomForest, rfPermute and randomForestSRC, in particular to topics on VIMP (and CI). My questions are based on the reading of ch 15 of The Elements of ...
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I want to compare two least-squares algorithms. One provides lower CI than the other, but not always. How do you compare?

I am trying to compare two weighing schemes of a least-squares fit for several datasets (about 100). I can calculate the confidence intervals and the sigma values of the parameters (a,b,c). I compare ...
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35 views

Confidence interval for the change of a GAM over a period

Similar to Confidence interval for the slope of a GAM, I am fitting a number of gam models to time series data and want to estimate the change (and its uncertainty) over an interval of time (e.g. from ...
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How should I compute confidence intervals for a proportional estimates of a Poisson count?

I'm developing an microbiological assay for enumerating defined mixtures of different bacterial strains that all have similar growth requirements and can't be distinguished by visual characteristics. ...
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One-sample: difference between two proportions that are parts of the same whole

What is the sampling distribution of the difference between two proportions when they are parts of the same whole. It's relatively easy when one proportion is binomial, the one of the common ways to ...
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Is it possible (and even correct) to calculate a confidence interval from an interpolated value?

I am using a probit model to calculate the limit of detection of a diagnostic test. For this, in R, I used glm(): ...
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Using confidence intervals from LME to determine time point after which groups differ

I have a longitudinal dataset: cognitive scores of several subjects in two different groups (treatment vs control) over several weeks. I would like to find the point at which these two groups differ. ...
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Replicating STATA output for RR and confidence intervals based on marginal effects in [R]

I am working on replicating an output from STATA, with the following data where we want to obtain Relative risk and confidence intervals based on the marginal effects. I have been able to calculate ...
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17 views

How to think about confidence intervals in the context of linear regression?

I think I understand confidence intervals for sampling distributions, but am trying to connect this understanding to the confidence bands I see around linear regression lines. According to the ...
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Understanding the 95% confidence interval [duplicate]

I am new to statistics, and recently came over interval confidence, but did not understand very well. Will you please explain this to me. to better understand, i will put an example as well: Lets say ...
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One-way ANOVA followed by Tukey test - confidence intervals

I want to test 3 types of treatments (T1, T2, T3) along with a control/placebo treatment (T4). In order to do so, I'm performing One-Way ANOVA to my data and then proceeding to the Tukey test. ...
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Confused about the concept of confidence interval [duplicate]

I understand that under central limit theorem, when certain conditions are met, the distribution of sample mean follows: Normal distribution Mean: population mean SE: population std / square root of ...
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Associate uncertainities to variance's estimate of a distribution with heavy tails

I have a set of $M$ variables $\{ \lambda_N^{(i)} \}_{i=0}^{M(N)}$. The distribution of $\lambda$ depends on the $N$ parameter; for $N \rightarrow \infty$ the distribution shrinks around the mean ...
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How to create a 95% confidence interval? [closed]

From December 12 – 14th of 2008, Gallup in conjunction with USA Today, surveyed 1,008 U.S. adults using random digit – dialing about their Christmas practices. 937 of them stated that they celebrate ...
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Why do two confidence intervals only overlap when their difference $(\theta_1 − \theta_2) \pm z(SE_1 + SE_2)$ includes 0?

I am able to check if the interval contains 0 which I can find out by just plugging numbers into the above formula but I am curious as to why this interval containing zero means that the two CI's of $\...
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95% confidence intervals crossing 0 but p < 0.05 in glm gamma family

As title suggest: Is it possible to have confidence intervals crossing 0 but p = 0.042? This happened to me in glm model with gamma family and link identity. The conf. intervals were generated by tidy ...
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Prediction and Confidence intervals and overall error probability estimation

I wanted to understand difference between Prediction and Confidence intervals and found an ...
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1answer
44 views

Confidence interval for the mean of the uniform distribution

I can take samples of a random variable $X \sim U(a, b)$, where the length of $(a, b)$ is known. I am interested in its mean $E[X]$, estimated with $\hat{X_n} = \frac{1}{n} \sum_{i=1}X_n$, but I need ...
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How many samples to state $P(A < B) \ge 95\%, A, B \sim \text{Bernoulli}$? [closed]

Suppose I have two series of samples: $$A \sim Be(p)$$ $$B \sim Be(q)$$ How may samples samples do I need to state that: $$P(A<B) \ge 95\%$$
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Confidence interval for $\mu_i$ (multivariate normal): some $\mu_j$ are known, unknown $\sigma^2$ and an estimation of the correlation structure?

Say we have a multivariate normal with m dimensions (let's say that m=1,000), the mean vector $\mu$ is known only for the first 100 elements, but unknown for the remaining 900. We have a single ...
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Calculating confidence interval from a simulation

I run a simulation 10,000 times, and in each iteration I produce an estimate of the mean of some parameter X. At the end of the simulation I have 10,000 estimated means recorded. $$ \textbf{m} = (x_1, ...

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