# 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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### CLT and unknown probability of success of handing out flyers on the street

Suppose that I distribute flyers on the street and people, when approached, take them with the same probability $p$. On average, I need 5 hours to distribute 2500 flyers and with confidence 0.9 it is ...
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### Can confidence intervals be found for the difference in marginal probabilities from two different logistic models of the same sample?

So, I have two multivariable logistic regressions for the same sample. They differ in one independent variable: Model A has a dummy variable for membership in the top 50% (compared to the bottom 50%) ...
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### SUR regression gets error "LU computationally singular: ratio of extreme...": can work around but still concerned about error margins

I originally posted this to stackoverflow, and was advised by I_O that the question would be appreciated more here. I am not sure how to reformat this to be appropriate here, so I am copying it over ...
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### Confidence interval for normals of normal model

Suppose $X$ is a normally distributed random variable with unknown mean $\theta$ and known variance $\sigma_{X}^{2}$. Suppose that $Y_{1}, \ldots, Y_{n}$ are random variables that, conditioned on $X$, ...
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### Finding confidence interval given z-score and null hypothesis

I am working on a homework question and got stumped on this question. Suppose researchers perform a large-sample test of a population proportion where the null hypothesis is that the population ...
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### How to get most likely value with confidence interval or expected value from a set of observations

lets say I have a set of values (R-code below for creating a vector) ...
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### what is the formula for confidence interval of standard deviation of a sample where observations are proportions of people from different countries? [closed]

example of a sample. What is the formula for confidence interval of standard deviation of people, having an access to sanitation facilities, if taking this sample into account?
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### Error bar plot with bootstrap-based 95% confidence intervals on SPSS [closed]

I have 10 groups of non-normal data, and I would like to generate a plot with the mean of each group and associated the 95% confidence interval (CI) using bootstrapping. I can generate the plot using &...
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### Ratio Confidence Interval for Proportions

Wondering if Fieller's theorem is used for the 'ratio' value in the compare argument in ...
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### How can generate 95%CI for GAM model in Stata?

I am analyzing a dataset with generalised additive models(GAM) in Stata. I want to obtain 95% confidence interval(95%CI) for my result. I have read the documentation in Stata ("Help gam") ...
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### Do asymptotic statistics "solve" the Behrens-Fisher problem?

The Behrens-Fisher problem concerns comparing two means from independent (maybe multivariate) samples in a way robust to heteroskedasticity in the populations being compared. It seems that if one ...
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### Do confidence intervals make sense for win rates in sport?

Imagine we have 2 teams play 10 matches against each other with team A winning 6 of them I.e. 60%. In this setting do confidence intervals for the probability of winning make sense? On one hand I ...
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### How can I compute rectangular confidence regions for parameters using R?

Simultaneous confidence regions for multivariate parameters (say, a confidence region for multivariate mean, or for regression parameters) usually find an elliptical region when the parameters' ...
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### Proper way to report on Confidence Intervals for 2 Proportions means

Disclaimer: Stat noob Context: I'm trying to figure out the best way to report CI to a non-data/stat/math savy audience. I'm performing a two proportion z test for an experiment. Control: 0.3097 ...
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### Summing confidence intervals, given $[a_0, a_1]$ and $[b_0,b_1]$, and $c=a+b$, is $[c_0, c_1]$ where $c_0 = a_0+b_0$? [closed]

How can you sum confidence intervals? Basically the title: Given $[a_0, a_1]$ and $[b_0,b_1]$, and $c=a+b$, is $[c_0, c_1]$ where $c_0 = a_0+b_0$? These are 95% CI's. How can you show this? Given ...
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### Confidence intervals, doesn't the definition suggest that it has a probability of e.g. 95% of containing the true value of the parameter? [duplicate]

I'm learning about confidence intervals and it explicitly states that the confidence interval is not to be interpreted as that it has 95% probability of containing the true value of the parameter. ...
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### Does the "type" of standard error affect the relationship between the standard errors of standardized vs. unstandardized estimates?

While previous answers explain how to convert between standardized and unstandardized coefficients and their standard errors, it is not clear if this formula applies across different types of standard ...
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### Error bars or standard deviation around means from zero-inflated heterogenous data?

I've constructed a plot of mean values per group (year) solely for the purpose of examining my data and have been told to always include either standard error (S.E.) or confidence intervals (C.I.'s). ...
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### Find the confidence level used based on multiple intervals

I am given the following table of confidence levels for a $\mu$ of a $X\cap N(0,1)$. and I'm asked to find the level of confidence used. Initially I thought when I chose, for exemple, a 90% ...
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### What is the impact of duplicate data on the variance of regression coefficient? [duplicate]

What is the impact of duplicate data on the variance of the regression coefficient?. Does increasing the size of data always certainly decrease the variance of the model coefficients? Suppose I have ...
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### Confidence interval estimation in easy to understand way

I want to understand well estimation of the confidence intervals. If I perform the estimation of confidence interval this way: ...
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### How many values should one validate to achieve a desired confidence?

If I have a set of 100 values which have been programmatically calculated and I would like to validate those calculations by performing them manually, how many manual calculations would I need to do ...
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### Estimate the Numbers of samples required for each variable

I am tasked to help with organizing the driving experiments for a robot. The goal is that for each Terrain Class like forest, wet-meadows, dry-meadows we will measure the time it takes the robot to ...
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### Confidence Intervals and Hyptothesis testing

Iam currently reading up on basic statistics and Iam somewhat confused about the computation/inference of confidence intervals and hypothesis tests. As far as I have understood there are several ...
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### 95% confidence interval for the goodness of fit scores in regression

I see the following computation available online in classification setting. ...
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### Error-Propoagation: Combine confidence intervals of two subsequent regressions

I have two subsequent regressions and want to combine the results of these two regressions. But I also want to show the increased uncertainty by somehow combining the confidence intervals of these two ...
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### Testing and conidence interval in a clinical trial

In a clinical trial, let's say I want to test $$H_0: \mu_1 \leq \mu_2$$ $$H_1: \mu_1 > \mu_2$$ $\mu_1$ belongs to the placebo group and $\mu_2$ belongs to the trt group. I used an independent two-...
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### Computing sample size for a sample to estimate binomial distribution when point estimate of proportion is 0

For example, I have a estimate of p = 0 (95% CI: 0, 0.01), and I want to know the sample size for this sample. For $p\not =0$, I can compute the s.e. by $\sqrt(p(1-p)/n)$ to get the $n$, but not sure ...
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### Risk score uncertainty quantification

I am working on various risk score estimation problems. I assume individual subjects are associated with a true risk $$r_i = f(x_i) + \varepsilon_i$$ where $x_i$ is some available information about ...
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### Number of confidence intervals for Binomial Distribution

Consider the random variable $X$ to denote the event that the confidence interval cover the unknown parameter or not. Thus, X will follow the Bernoulli distribution with a parameter $θ$, i.e. $X~Be(θ)$...
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### What does it mean if my confidence interval includes zero with a significant p value in linear regression analysis?

I performed linear regression analysis to assess the associations between continuous variables. I found a significant p-value but my confidence interval includes zero. What does it mean? Here are the ...
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### Confidence interval for population maximum

I am sampling an arcsine distribution, with probability density function $F(x) = \frac{1}{\pi\sqrt{(x - a)(b-x)}}$ which is defined between $a<x<b$. I want to estimate $a$ and $b$, that is, the ...
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### Establish convergence to normal area

I will try and make my question abstract, since I have two problems of the same overall type. I am given a time series $Y_t$, t=1,...,T. I know that this time series has a (slowly) changing ...
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### Reconciling differences in CI calculated between SAS and R on same dataset

I have been given a brief of replicating statistical analysis which was done previously to verify results. Data being collected are body weights of male and female mice over 20 weeks, given a ...
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### Bootstrapping with quantiles of data instead of SD*z?

I have recently been bootstrapping the confidence intervals of a neural network model estimated to data. I execute the following psudo-code, which seems similar to previous bootstraps I have done: ...
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### Intuition for confidence intervals vs prediction intervals for linear regression

I am having a bit of trouble understanding the difference between a confidence and prediction interval in the context of linear regression, and in what scenario we would use either of them. I've posed ...
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### How to test overlapping confidence intervals to see a significant difference between groups in a COX propotional model

Cox proportional models have been done with this result. The two groups (C, B) had overlapping confidence intervals, while the p-value was significant at p<0.001. I have used this code to get the ...
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### confidence interval: A/B test - unable to decide what to use

I am new to A/B test; I am interested to generate confidence interval in python language. At the moment I have ratio (proportion), for instance, ratio of add to cart to the total sessions in control ...
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### Meaning of endpoints of ONE confidence interval

From wiki, we should understand the confidence interval by: in large repeated samples, 95% of the realized confidence intervals (computed from samples) can cover the true value of the population ...
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### Are there possibilities to determine 95% confidence interval for right skewed data?

The dataset that I'm using for my thesis is right skewed. It is about lead times (days) I tried log10 transforming it in SPSS but it still does not meet the requirement p>0,05 (Shapiro-wilk). So ...
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### Effect of size of data on the confidence on the coefficients in Linear regression? [duplicate]

What is the impact of size data on the confidence (p-value) of model coefficients?. Does increasing the size of data always improve the confidence in the model coefficients? Suppose I have 100 data ...
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### Back-transformation of confidence intervals

I have read that I can simply back-transform my confidence intervals from my (mixed) linear models, which seems very handy for model interpretation. What I don't understand is why log-transforming the ...
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### confidence interval formula of gamma distribution? [closed]

i want a help can someone tell me the formula for confidence interval of gamma distribution? for alpha and beta Parameters i couldent find them? and there also this problem i dont know which pdf of ...
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### Correcting repeated measures data to display error bars that show within-subjects differences

I have some data containing within-subjects observations for two factors: y as a function of timepoint (300 'levels') and ...
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### Distribution-free prediction intervals in linear regression

I've found some literature on the subject, but it is rather difficult to read. I am wondering if the following simplified method makes sense. My question is what part is correct in this methodology, ...
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### Lower confidence interval for quantile function [duplicate]

I have a real-valued, unknown distribution $\mu$ and would like to find the largest threshold $t \in \mathbb{R}$ such that $\Pr_{X \sim \mu}\left[X \leq t\right] \leq q$ with high probability \$1-\...
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### Looking for a way to analyse results of a poll and compare them to expected results

I will be conducting a poll on 5 to 10 people. I will have each of them score about 100 samples from 0 to 10 and then I will compare their answers with the expected values of those samples. I am ...
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### Confidence interval for incidence rate if multiple events per person is possible

I assume that most of the sources about incidence rates are assuming that there is only one event per person. In a medical context (e.g. cancer) this make sense. I am able to compute the incidence ...
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### Translate Excel's NORM.S.INV function to Python to calculate confidence interval of an incidence rate

I have an Excel-sheet with some formulas which are able to calculate the confidence interval of an incidence rate. The formulas not from me but they work. Beside some other stuff the Excel-sheet use ...
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