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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Using the table, explain what the 95% confidence intervals mean for both age and sex.? [closed]

I just do not understand the ranges given for the 95% confidence intervals. For age, the range is 0.9 - 1.3. and for sex the range is 1.2-4.0. What does that mean?
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GLMER, GHAQ and marginaled coefficients

I am confused about the GLMM procedures and their reporting. I have tried to follow @Ben Bolker on mixed effect model. However, I am confused after the GLMAdaptive approach. I will lay out my problem. ...
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Confidence Interval of Coverage Probabilities

Does it make much sense to calculate confidence intervals for coverage probabilities? For instance, if a CI coverage probability is estimated to be 0.80, does computing an exact 95% binomial ...
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Bootstrap estimation of variance and C.I. in cases with small group of outliers

I have a given quantity, say $y_a$ which parametrically depends on $a$ value. I consider $N$ values for the $a$ parameter and, for each one take multiple measures of the corresponding $y_a$ (say $N_a$ ...
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Determining odds ratios and confidence intervals from R output of a proportional odds model (cumulative logit model)

I have a proportional odds model with R output as follows: ...
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How to correctly word a frequentist confidence interval

I am aware that there are many, many threads on this (e.g. this excellent thread). I may have missed it but I can't seem to find one that actually explains how to accurately report a frequentist ...
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22 views

Sample size determination and Confidence interval of a model

I am asked to determine the test sample size of some data in order to get a 95% confidence interval with width $w$ of a given loss function $L$. The formula in wikipedia is $$ n = (\frac{4\cdot1.96 \...
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Lower confidence with larger sample size? Tolerance interval for distribution-free data

I am trying to find the sample size required in order to establish a tolerance interval which contain 99% of the population, with 95% confidence. The results from Minitab for a sample size of 473 are ...
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Confidence interval for relative risk with uncertain incidences

The usual suggestion for computing a confidence interval for a relative risk estimate is to start from the variance: $$ \text{CI}_R = R \pm z \cdot \exp \sqrt{\sigma^2_{\log R}} $$ where $R$ is the ...
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44 views

Hypothesis Testing with a Bootstrap

I have a list of 1000 samples from a distribution. I can find the lower limit of the 95% CI as it is the 2.5% percentile. In this case, it is zero. I would like to also test the hypothesis that a ...
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How to generate a confidence interval for an adaboost prediction?

I have created a simple AdaBoostRegressor (sklearn) model which is trained on a feature set $X$ (house features) to predict a variable $y$ (house prices). The model can be used to create a prediction ...
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To test if correlation is above a threshold |rho| > th in absolute value, to see if the correlation is significant. Is a sigle or a two tailed test?

which type of hypothesis test should I use for each of these possible tests (single tailed or two tailed): H0: rho = th vs H1: rho != th H0: rho > th vs H1: rho < th H0: |rho| > th vs H1: |...
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Confidence interval for vector of percentages/proportions

How would/should one calculate a 95% confidence interval for the mean of a vector of percentages or proportions? For example if I had the following vector of percentages, how best would a 95% CI be ...
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How to calculate confidence interval of an MLE estimate for a Bernouli random variable

Let's say a coin has a probability of P=2/3 of landing on heads on any independent flip. After flipping the coin N=10000 times, you observe heads on F=60% of the flips. Suppose the width of the 95% ...
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Difference between coverage probability and confidence coefficient

In the book Casella, G. and R.L. Berger, Statistical Inference, there are two definitions about confidence interval. But they look exactly the same to me. To be more specific about my confusion, in ...
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Conf intervals on the dispersion coefficient of quasibinomial GLM or binomial GLMM with obs-level random effect

In this post I see how they calculate the confidence interval on the theta parameter of a negative binomial GLM: Confidence Interval for the Dispersion parameter of negbin distribution. I typically ...
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Re-weighting after sampling?

After arriving at a sample size in order to achieve a population estimate with a 90% confidence interval, significantly fewer sample results were obtained. Is there any way to re-weight what was ...
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Negative binomial one-sided confidence interval?

Suppose someone was flipping a coin, and want to test the hypotheses: $$ H_0: p=0.5 \\ H_a: p>0.5 $$ First, assume they decided to run 20 trials. They observed 14 heads and 6 tails. We can create a ...
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Is the standard error of the mean the square root of the sampling variance?

I came across different approaches for calculating confidence intervals in two stats books. Both books multiplies Z by the standard error of the mean. But how they compute the standard error of the ...
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Conflict between OR confidence interval and p-value

I'm currently reading this study about the adherence to health checkups in Austria. Table 2 displays some Odds Ratios for attending health checkups between groups of different educational statuses. I ...
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Coverage of a Bootstrap Confidence Interval for a Change in a Binomial Proportion

How can I estimate the coverage of a bootstrap confidence interval for a change in a binomial proportion please? For example, if the results from two tests (A and B) are: ...
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Boostrap Confidence Intervals For 3 Distributions

I am having 3 distributions (A/B/C) and I would like to check if there is any statistical significance difference in their means. The goal is to choose the one with the higher mean if there is a ...
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How to control for sampling bias?

I have a theoretical question in regards to confidence intervals for simple regression. Say we a set of a data (x_i,y_i). Theoretically if we took a biased sample (i.e. we tried to determine the ...
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Distribution of errors

I am struggeling with a basic question and would be happy to get some pointers. I am trying to evaluate an algorithm $f$ which maps some sample $x$ onto a scalar $y\in\mathbb{R}$, i.e. $f(x) = y$. For ...
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Finding the maximum of an experimental parameter for ensured success

Summary of the problem I have an experimental setup on which I measure one parameter and either get success or failure for each experiment. I can execute as many experiments as needed. I want to find ...
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How do you add together confidence intervals when adding estimates together?

I struggle with statistics so this might be a stupid questions but can you explain to me in a 'for dummies' fashion if I can add together two estimates with confidence intervals and how to calculate ...
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zeta argument in lme4::confint.merMod(.) for likelihood cutoff in R

I am trying to utilise the argument zeta = from the confint.merMod(.) function in the lme4 ...
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1answer
36 views

What does it mean to have (or not have) convicing evidence in statistics?

I know how to calculate the confidence intervals for proportions and means at various confidence levels. I'm having trouble when I'm asked to say whether there is (or isn't) convincing evidence as to ...
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Understanding the approach of considering the 95% quantile value as the 95% Confidence interval upper limit

I'm confused from the statistical approach described below. I'm not from this field but I had to use this approach in my study. Any explanation would be great!. According to my understanding the ...
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Determine confidence interval in a 2D cross correlation map

My problem is as follows: I have a 2D image (u,v), with each pixel representing the value of the 2D cross correlation function (ccf) at that place. I am trying to determine to what degree I can be ...
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67 views

Confusion in Confidence interval and Hypothesis Testing

Consider a normal distribution $N(\mu, \sigma^{2})$ where $\sigma^2 = 9$ and we draw 100 samples from this distribution. Now, we set up a hypothesis testing problem: $H_{0}:\mu = 0$ against $H_{0}:\mu ...
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Sample of rates: mean, standard deviation, coefficient of variation

A performance test of a software application measures the maximum rate (operations per second), which this application can handle. The test is repeated multiple times each iteration yielding the ...
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Bootstrapping variance in R gives weird shaped distribution- how to obtain confidence intervals?

this is the first time I've used bootstrapping so it's quite basic! I'm trying to obtain confidence intervals for the standardised variance- defined as the variance over the square of the mean- across ...
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How to calculate confidence intervals for logistic regression predictions? How does `statsmodels` do it in `summary_frame`?

I am fitting a logistic regression in Python's statsmodels and want a confidence interval for the predicted probabilities. This has been easy to get using ...
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Sigmoid confidence curves in logistic regression

I have a logistic regression model that predicts the probability of an outcome based on one input variable. I am able to plot the curve just fine and show my group how the probability is predicted to ...
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Confidence Limits for normal vs rayleigh distributed random variables

I have a device to measure a coordinate in one axis, the measurement error is $\Delta x$, which is specified that $3\sigma < thr$, where thr is say 1 nanometer, and the average is not specified. ...
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Calculate 95%CI for cumulative survival rate

For a research project, I am calculating a cumulative survival rate using the following formula: Cumulative survivalt = survival proportiont-1 * survival proportiont So for example if we have a ...
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29 views

Confidence intervals with sums of transformed regression coefficients?

I have an index that is formulated as follows, for party $j$, group $s$, where $w$ indicates weight of party or group as share of population : $$ \lambda =\sqrt{\sum^J\sum^S w_j w_s(\alpha_j+\beta_{js}...
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Confidence intervals for multinomial models

I'm trying to figure out an extension to the answer given here the Effect() function only seems to work given 1 type of multinomial specification, where each row/...
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How to adjust (bootstrapped) confidence intervals for multiple testing in R?

I am comparing effects of different resources by comparing slopes implemented by interaction terms in (generalized) linear mixed effects models e.g. with a negative binomial distribution and a log-...
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1answer
28 views

Confidence intervals for mean response do not agree using predict.lm() in R

I have $n$ data points $y_i,x_i$ and the model $y_i=\alpha x_i^\beta + \epsilon_i$ where $\log{\epsilon_i} \in N(0,\sigma^2)$. Thus, I define $z_i=\log{y_i}$ and $w_i=\log{x_i}$ and my normal linear ...
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1answer
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Estimating population parameter from bootstrapped sample distribution, other than mean value

I'm a rather novice to statistics, so my terminology here might not be totally correct. But I will do my best to explain my question clearly. My question is about understanding whether it is making ...
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fitting methods for data with bootstrap uncertainities

I have a set of dataset of $N$ couples , say $\{z\}_{i=1}^N$; $z_i = (x_i, y_i)$. The $\{x\}_{i=1}^N$ set has no uncertainities, while the $\{y\}_{i=1}^N$ set has, for each member an uncertainity ...
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Confidence intervals of positive parameters reaching into negatives [duplicate]

Suppose I want to estimate the proportion parameter for a binomial distribution, and my method for constructing a 95% confidence interval (e.g. MLE +- 1.96 SDs) gives an interval of let's say (-.1, .3)...
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Determine stratified sample size $n$ with confidence level 95%, if required $SE $ of the estimated mean is given

I need to calculate sample size $n$, so that $SE$ of the mean would be 4 points. There are $55$ units in total in the $I$ group. $N_2 = 80$ in the $II$ group and $N_3=65$ in the $III$ group. The ...
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Interval Estimation for a Change in a Binomial Proportion

I'm not sure how to estimate the confidence interval (CI) for a change in a small sample size binomial proportion using the same sample set both times. I have two methods that I would like to compare (...
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Why can't we say that the probability of the true parameter being within a 90% confidence interval is 90%? [duplicate]

I've been reading a bit about the confidence intervals on Wikipedia. The section on misunderstandings says: A 95% confidence level does not mean that for a given realized interval there is a 95% ...
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Numerical integration of the exact distribution of the product of two random gaussian variables

I am trying to implement this function in R, which is equation (2) in this paper by Cui et al. (2016), which is the exact distribution of the product of two random gaussian variables. ...
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Bernoulli trial confidence intervals

I am working through an example in my notes and I am not sure how they arrived at the solution. The question reads: "7 successes are observed in 20 trials. Find a 95% confidence interval for p&...
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comparing differences between quartiles at two different conditions

I have calculated the difference between two independent groups in their quartiles and calculated the 95% confidence interval of that difference. These calculations have been performed twice (in the ...

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