# 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 ...
1 vote
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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 ...
1 vote
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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 $X$, ...
23 views

### 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%) ...
305 views

### Confidence Intervals for the Parameters of a Logistic Growth Curve

I'm using the growthcurver library to estimate the parameters from some bacterial growth curves. It fits a logistic equation of the following form: This returns ...
23 views

### 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") ...
8 views

### 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 ...
194 views

### How to calculate confidence intervals for a generic (non-normal) pdf

In particular, this is a question about distributions with some skew and/or where the mean, median and mode might all be different. For any pdf, it's possible to find multiple different domains within ...
61 views

### 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) ...
26 views

### 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 ...
259 views

### Bayesian update of a confidence interval

How does one update a confidence interval using Bayes rule? Say, for example, an experiment shows that the mean lies in [A, B] with 95% confidence. Later, a colleague says they ran a similar ...
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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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### 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: ...
35 views

### Ratio Confidence Interval for Proportions

Wondering if Fieller's theorem is used for the 'ratio' value in the compare argument in ...
325 views

### Confidence interval on binomial effect size

Suppose I have a binomial test, with 9 successes in 12 trials, expected p=1/3. In other words, in R you might do: binom.test(9,12,p=1/3) Now, I'm under the ...
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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 &...
136 views

### Non-self-referential interpretation of confidence intervals?

Interpreting what a (say) 95% confidence interval actually means is obviously tricky, especially when you are trying to teach it to students just beginning to learn stats. One of the biggest ...
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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 ...
39 views

### 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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### 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' ...
10 views

### 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 ...
10 views

### 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. ...
96k views

### Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?

It seems that through various related questions here, there is consensus that the "95%" part of what we call a "95% confidence interval" refers to the fact that if we were to exactly replicate our ...
133k views

### Why does a confidence interval including 0 mean the difference is not significant?

Could someone please explain why zero being inside or outside the confidence interval tells you whether or not the difference is significant?
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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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### 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% ...
19 views

### 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). ...
17 views

### 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 ...
1 vote
57 views

### error code in finding confidence interval? [closed]

I optimized parameters from a function using mle2 from bbmle package. After I got the values, I tried to find profile likelihood ...
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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 ...
27 views

### 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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### 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. ...
1 vote
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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 ...
269 views

### (rqpd) How to obtain the confidence intervals of a quantile regression model on panel data?

I had to adjust a quantile regression model on panel data and I used the rqdp package, however, when I needed the confidence intervals, I realized that the package does not provide the item in ...
1 vote
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### Non-parametric bootstrap not normal distributed

I am trying to derive the confidence intervals through bootstrap for some parameters I have calculated for a model via maximum likelihood estimation. I have also used profile likelihood to determine ...
4k views

### Why are confidence intervals and p-values not reported as default for penalized regression coefficients

I have been using the R package glmnet to do penalized regression. As part of this the package does not produce confidence intervals or p-values with regression ...
169 views

### Confidence interval for GLM or the maximum of a function?

Imagine I have a set of (xi,yi) measures. I can show it on a scatter plot I want to choose the value of x that maximizes y, or I could fit a function and find the values of the parameters that ...
322 views

### Correct Interpretation of Survival Curves

I am interested in learning about how decisions (e.g. prioritization of treatment) can be made in the real world based on Survival Curves (e.g. Kaplan-Meier). To illustrate my example, I simulated a ...
363 views

### Confidence of Mean Squared Error

Let $X \sim \mathcal{N}(\mu, \sigma^2)$, where $\mu$ and $\sigma$ are unknown. I would like to estimate $$\mathbb{E}\left[(X - a)^2\right]$$ where $a$ it is a known constant. For this purpose, I ...
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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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### 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-...
2k views

### How to calculate the confidence interval with weighted data?

I've done some search for similar questions, but they're not the same as what I'm trying to get. Assume that there's a server that handles requests $r$ and returns a set of items $I_{r}$ of random ...
89 views

### Paired multiarm bandit

I have a set of independent experiments with different distributions and I'm trying to determine which has the highest mean payoff. I would like to treat this as a multi-arm bandit problem, but the ...
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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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### 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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### 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 ...