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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Why do the bootstrap calculated p-value and the confidence intervals seem to contradict each other [R code, specific example]?

Below you'll find the data and the corresponding R code used to perform the bootstrap hypothesis test to compare the ratio of the means of two samples and additionally, to estimate the 95% confidence ...
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How to manually calculate p-values for lmers?

Hopefully this is not a duplicate. Provided the t-statistic, SE and 95% CI, how can I manually calculate p-values for lmers in R? More details in the quoted link below. I've used ...
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p-values and confidence intervals are not matching

My model is here. I'm running a bootstrapping mixed-effects model with "case" type with lmersmapler. The thing is, now I'm using bootstrap_pvals()to ...
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How do we report significant tests without p-values? Reliance on confidence intervals

I'm pretty much reporting these results. I've bootstrapped my sample using lmersampler, which does not provide p-values for bootstrapped models. I relied on confidence interval boundaries to justify ...
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Incorporating denominator uncertainty into a proportion

I am calculating an incidence risk (r): number of cases of a disease in a population over one year (c) divided by the total mid-year population (N). $$ r = \frac{c}{N} $$ Let's assume that c is a ...
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Confidence interval for logistic regression in R

After logistic regression analysis using gtsummary package in R, I got p-value, odds ratio and 95% confidence interval as below With the p-value>0.05, however, 95% CI did not include 1. When ...
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How to properly use the target of one regression model as a feature in another model?

I created a SVM model which predicts one target. I then used the percentiles of the residuals from the test set to define the distribution of the prediction error (normal with 0 mean and $\sigma$ ...
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Codes/Commands for estimation of Marginal Expected Shortfall (MES) and SRISk [closed]

I need codes/commands to estimate marginal expected shortfall (MES) and SRISk. Thanks Shakeel
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Compute the two-sided confidence interval for specific power

Suppose I have a hypothesis test for $H_0: est_{LCL} \le 0.4$ vs $H_1: est_{LCL} > 0.4$ where $est_{LCL}$ denotes the lower confidence limit for a two-sided $100(1-a)\%$ confidence interval for $...
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How to calculate confidence intervals for circular data?

I managed to convert my data i circular/polar data (angle, r). Now I would like to compare two treatments to see if they are statistically different. I thought to use the Watson's U2 test but ...
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Why does the confidence boundary contains fewer points than expected in R (`ggplot`)?

I use a LOESS regression and draw a confidence boundary with a 99% level. ...
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Calculate hazard ratio and 95% conf.int from flexsurvreg-weibull fit output

I am trying to calculate confidence interval 95% for hazard ratio from flexsurvreg-weibull distribution output. Please provide the formula of the same. I have ...
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Infering missing population's sex

I have a dataset with the following characteristics: Total number of samples: 319 813 Sample percentage of people not declaring their gender: 0.57 Sample percentage of people declared as Female: 0....
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Required sample size $n$

How can I estimate the required sample size $n$ from a population of unknown standard deviation $\sigma$, in order to estimate the mean of a variable, given the margin of error $\epsilon$ and a ...
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Can the jackknife be used for asymmetric confidence intervals?

All of the jackknife methods (JN) I have seen (for example) use the JN to estimate standard errors and then use those estimates in standard normal-assumption symmetric intervals constructions ($ \hat{\...
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Hypothesis testing using samples with different measurement errors/intervals

Are there generalizations of common hypothesis tests (e.g. t-test, mann-whitney) that can take into account different confidences in the sample measurements? For example, if I have two sets of ...
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Is it possible that a confidence interval for a sampling distribution of the sample proportion to be < 0 or > 1? [duplicate]

A proportion or percentage must be between 0 and 1, therefore, a confidence interval for a proportion should also be between 0 and 1. But is it possible that if the "10-successes-and-10-failures&...
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Central Limit Theorem and Confidence Interval

Let $\{X_n\}_n$ be a sequence of i.i.d. RV's, where each $X_n$ is a copy of RV $X: \Omega \rightarrow \mathbb R$. For $n > 0$, I can define $\bar X_n := \frac{1}{n}\sum_{i=1}^n X_i$. Then, central ...
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Meaning of 95% confidence interval [duplicate]

If I take a 95% confidence interval $I_k$, then it means that if I sample 100 confidence intervals $\{I_1, \cdots, I_{100}\}$, then it is expected that 95 of $I_k$'s contain the true parameter. Of ...
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Calculating confidence Interval for a return time curve, via non-parametric bootstrapping

I have some precipitation data (yearly extremes), which I have fit with a Gumbel distribution (CDF), from which I have calculated a return time distribution. I want to calculate the 95% confidence ...
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If a confidence interval and test error are both expressions of a margin of error, why do we need both?

Let's say: We have a population consisting of $N$ units, of which we take a sample of $n$ observations. For simplicity, this will be a bivariate dataset $(X, Y)$, whose true population is best ...
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Amplification effect of retweets on uncertainty

Consider you are scoring tweets for tone based on some sentiment analysis implementation. Each tweet has hypothetically a 90% chance of being correctly scored, while 10% get it wrong for whatever ...
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Updating a team's REAL ability

I am trying to think of a math appropriate way to describe the “real” talent of a team. This stems from looking at the probabilities of each team winning the Super Bowl. Let me illustrate with a ...
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Sample size calculation to bound CI around a true value

I'm working on a cold start system for a recommender system - Whenever I have a new item, I need to show it to users enough times to get a somewhat accurate estimate of CTR, and then I will let the ML ...
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How can I calculate the prediction intervals using bootstrap? [duplicate]

I have trained a linear regression model based on some data. Now I have new data, and I need to find a way to calculate the CIs for each $Y_{new}$ sample. Meaning now I have ...
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Use bootstrap to find the confidence intervals of the expected value for Y new, given X new

The following question is an assignemt I have and I'm stuck. I've trained a linear regression model based on 200 observations that I randomely picked from the data. So now I have $X_{train}$ and $Y_{...
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Propagate Poisson Confidence Intervals

I have a set of measurement of particles with 95% confidence intervals calculated with Poisson confidence intervals assumption and would like to propagate it. For example, I measured 1000 particles of ...
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Is there a formula translating between sample size formula for single mean between precision and effect size?

Let's assume I want to test a paired differences between two samples. Or, equivalently, to check, if the paired mean of differences is statistically non zero. Now I want to calculate the sample size. ...
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Does a distribution of difference-in-means, be considered as distribution of means?

I have mean sales data of a product, pre & post an event, for a list of countries. i.e I have 2 sales value for a product per country. My aim is to see if there ...
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Confidence interval for samples with frequencies

I have a total population size of $N$ (known). From the unique elements of the pool I draw samples $s_i, i=1 \ldots m$ without replacement. I also know that each sample $s_i$ appears $k_i$ times in ...
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Confidence interval and the ratio of truth values in that interval, should they match?

Say I have the following distribution of mean. ll = list(np.ravel(np.random.rand(1,1,30)))+list(np.ravel(np.random.randint(1,15,38))) As we can see almost 50% of ...
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Bootstrapping 95% CI for probability estimate returning narrow range

I have a probability estimate for an intractable underlying distribution. For a contemporary example, let's say it is the probability of a team $T$ making it to the postseason in American football. ...
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Constructing 95% confidence intervals on the average SD value

If I have one sample with repeated measurements I can construct a 95% confidence interval on the standard deviation using the Chi-Square distribution. What if I have multiple samples, each with their ...
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Confidence intervals for precision and recall of a small sample

I have a very small sample (N=12) of results from a classification problem, and would like to compute the confidence interval around the precision and recall. The results of the classification are (...
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Understanding odds ratio in logistic regression for target variable

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How to interpret the overlap of AUC-CI(95%) of two logistic regression models

Here is my question. I am comparing two logistic regression models which use the same data and endpoint but different variables. My goal is to see if the model improves based on the performance using ...
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How to interpret the calculation of the confidence interval for a Cox-Ingersoll-Ross process?

I need to interpret the calculation of the confidence interval (CI) for the Cox-Ingersoll-Ross (CIR) proсess. From the paper (Nafidi et. al., 2021) we know that transition probability is $p(t, y|s, x) ...
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Statistical parameter differences when one model is specified but confidence intervals overlap?

I have two (classically) estimated coefficients from 2 different models, $\alpha_{m1}$ and $\alpha_{m2}$, say, with 95% confidence intervals. I maintain that model m2 is mis-specified and that the ...
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How to find the confidence interval for a new Y point? [duplicate]

In a linear regression model, as Y is the target and X are predictive features,the CI for $E[Y_{new}|X_{new}]$ is as follows: Assuming $X_{new}$ is given, $X_{new}$ is the new data given for a target ...
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Creating an Example to Teach "Confidence Intervals" [duplicate]

Usually, people tend to confuse the interpretation of confidence intervals. The following two statements are said to be quite confusing (even to myself): A 95% Confidence Interval means that the ...
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Why Aren't "Non-Informative Priors" More Popular?

Recently, I have been reading about how Confidence Intervals in the Frequentist setting are often misinterpreted (e.g. The importance of a correct interpretation of a confidence interval). Supposedly, ...
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When calculating the variance of the sampling mean, if we know there is a mean-variance relationship, can we exploit that information?

My statistic is the sampling mean of a ratio statistic (call it $Q$). In my case, I know that the variance of the sampling mean is correlated with $Q$. So, for example, if the standard error is > 4,...
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Which definition of confidence interval is correct, or are they the same thing?

Wondering 1) which of the two ways of calculating confidence intervals is correct, and 2) if they both are correct, are they the same or different? How do they reconcile? CI = [Coef x1 ± 2*SE(coef x1)...
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A/B test : Confidence interval for Revenue per Visitor using Conversion Rate and Average Price per Order

I have an A/B test to improve number of orders. The result came back showing a positive impact on the number of orders per visitors (aka, Conversion Rate) but not significant on the average revenue ...
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How to interpret a "% win probability"?

I came across this explanation about a 61% win probability: 61 percent should be interpreted as: “if these teams played 100 times, we would expect Marquette to win 61 of those games.” It definitely ...
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Intuition for inverting one sided hypothesis tests

Is there an intuitive way to remember if we get an upper bound or lower bound for a parameter when inverting a one-sided hypothesis test? In Casella & Berger, it is written: If we have $H_0: \mu = ...
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Confidence interval for $R^2$ in a panel VAR

I know it is possible to compute the confidence interval for $R^2$. An answer to this question on CrossValidated references this blog post with the Equation: $$ SE_{R^2} = \sqrt{\frac{4R^2(1-R^2)^...
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Calculating difference in means confidence interval using only standard errors, sample sizes, and means

I use a complicated survey-corrected estimator to calculate a mean and standard error for one year and then redo the process to calculate a mean & se for another year (using IEA education data ...
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Confidence regions from a Gamma distribution

Let a random variable with posterior distribution be given by $X \sim \textrm{Gamma}(10,12)$. This is the result of Jeffreys prior $\pi_J(\lambda)$ multiplied by the Likelihood of i.i.d. $X_1,...,X_n \...
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Computing C90 ellipse area for two dimensional time series data

I am trying to determine the area of the ellipse which contains the true mean of $(X_n, Y_n)_{1\leq n \leq N}$ with a probability of 90%. The 90% confidence ellipse area, or C90 area. The sample ...

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