# 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.

2,921 questions
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### confidence interval for the variance with unknown distribution

Let $X_i \sim \text{iid}(\mu, \sigma^2)$ (the question does not specify whether or not $\mu$ and $\sigma^2$ are known). I have to show the confidence interval for the variance. Since $X_i$ is not ...
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### Bootstrap Confidence Bands for Linear Regression (in R)

I am looking for a way to implement non-parametric bootstrap to confidence bands around my regression line for my linear regression model. I am, however, new to bootstrap, therefore I am unsure how to ...
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### How to compute confidence intervals from *weighted* samples?

Imagine we have a webserver, which serves a total of N static URLS. There are users visiting the URLs every day. At the end of each day, we have data like this: ...
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### How to check if a distribution is different from uniform distribution using the values only?

I have a discrete empirical distribution, where the values D1 = {1,2,3,7,9,15,16,17,18,19,20} occurs with some different frequencies. The frequencies are not of interest to me. I am interested in how ...
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### significance of difference smooths

I am working to understand what is represented by the standard errors and confidence intervals of smooths of ordered factors. In this toy example, I wish to determine (1) the overall form of the trend ...
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### Find confidence interval of mean without knowing sample size?

In our calculation, we have only $\mu$ and $\sigma$ values. Is that possible to find the confidence interval of $\mu$ and $\sigma$, without knowing the sample size? As per our idea, we can calculated ...
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### Confidence intervals

How do you determine the confidence interval of the quotient of 2 numbers, each of which has its own confidence interval? I have a numerator and denominator. Each has a confidence interval, i.e., the ...
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### How should I determine the CI of my classifier counts?(i.e. 95% confidence at least 30 objects are present)

I have built a classifier that detects a disease based on the presence of certain particles and the amount of said particles. An uninfected person would have 0, light infection is less than 50 ...
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### How to calculate a permutation confidence interval?

Mara Tableman, Minh Nguyen, and Michael D. Ernst note The idea behind a permutation confidence interval is well known and fairly straightforward (Ernst 2004). The confidence interval is simply the ...
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### How to compare predicted accuracy and actual accuracy? [duplicate]

Consider a classifier that, given an input vector ${\bf x}$ outputs both a prediction $y'$ whose accuracy ($a \in \{0, 1\}$) can be measured, as well as a predicted accuracy that corresponds to the ...
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### How does fisher.test calculate the confidence interval for the odds ratio in R?

The fisher.test function in base R by default returns a confidence interval for the odds ratio in a 2x2 contingency table. For example: ...
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### Can we calculate a confidence interval using a permutation testing approach?

Tim Hesterberg's "What Teachers Should Know about the Bootstrap" is excellent. On page 77 he writes: "We cannot use permutation testing to obtain confidence intervals." Is that correct? If so, can ...
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### Find number of elements to check for finding false negative rate

I have 3500 pictures that were classified in four different possibilities of match: very low (16%), low (1%), high (30%), very high (53%) All labels are not known, i.e., I don't know if they were ...
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### What are the confidene intervals when plotting the forecast function in R?

So I have forecasted with the 'forecast' function in Rob Hyndman's "Forecast" package using R. But when plotting it I am in doubt what the blue and grey area in the graph means. I assume that the blue ...
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### Seeking a general solution to confidence intervals around ranks

Often test takers are ranked based on their test scores (e.g., people taking a civil service exam) and often those test scores are rounded before being ranked, producing many ties). How might I go ...
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### Confidence Level and Interval probability [duplicate]

I understand that the confidence level denotes how reliable is my test and the confidence level is not the probability associated with the confidence interval. This is well explained on Wikipedia:...
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### Question about the equality of variances of two populations

When finding the confidence interval for the mean difference between two groups of sample, under which assumption about the equality of their population variances should we take if no information ...
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### Calculate proportions and CI [closed]

My data is in two columns: sample, and disease, and 380 rows. How can I calculate the proportion of disease and the 95% CI for each row in R
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### Can the variance of a U-statistic be of the order $O(\frac{1}{n^2})$?

It is not that easy to find estimators $T_n$ such that $\mbox{Var}[T_n] \sim O(n^{-B})$ with $B = 2$. In most cases, $B=1$.Here $n$ is the sample size. It seems, according to this paper on U-...
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### Find $k \in R$ such that $P\left(\max\left\{\frac{{S_x}^2}{{S_y}^2}, \frac{{S_y}^2}{{S_x}^2}\right\} > k\right)= 0.05$

Let $\overline{X}$ and $\overline{Y}$ sample means and ${S_x}^2, {S_y}^2$ unbiased estimators for the variance of 2 independent random samples of size 7 with normal distribution with mean unknown and ...
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### Finding a confidence interval for shifted exponential distribution

Let $X_1,\ldots, X_n$ are i.i.d. random variables such that: $$f(x;\sigma ,\theta)=\frac{1}{\sigma}e^{\frac{-(x-\theta)}{\sigma}}, x\gt \theta$$ where $\sigma \gt 0$ and $\theta \in R$ . a) if ...
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### If $X_i \sim U(\theta-\frac{1}{2};\theta+\frac{1}{2})$, show that $[X_{(1)},X_{(n)}]$ is a confidence interval [closed]

Let $X_1,...X_n$ random sample from $f(x;\theta)=I_{[\theta-\frac{1}{2};\theta+\frac{1}{2}]}(x)$. a) Show that $[X_{(1)},X_{(n)}]$ is a confidence interval for $\theta$. b) Compute the ...
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### Assistance with statistics question please [closed]

If anybody is able to assist me with the following question it would be greatly appreciated. Thank you.
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### Statistical significant difference between two regressed models with use of confidence intervals

I wonder how to decide if two regression models are significantly different at a location X. Here is an artificial example, $\hat{Y}=a+b\cdot X+c\cdot X^2$. The graph shows the (artificial) measured ...
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### Calculate SD for a given problem specification (see Body) with python

I am new here as you can tell. I have the following problem for which the SD has to be adjusted in order to fit said problem. Problem: Say I have 500 balls which I deliver to a customer and if more ...
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### Comparing assault rates at one facility with two other facilities

Assaults on staff are fairly uncommon in our facilities with between 70-140 in a year at a given facility. Time, similar to 'person years' in epidemiology, is tracked as 'number of bed days' (i.e., ...
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### Confidence intervals for predictions from linear discriminant analysis

I wan't to draw 95% prediction area of an LDA model. I can draw the prediciton area, however with no information on the confidence. ...
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### Confidence interval for population variance and chi-square distribution [closed]

At present, i am reading the e-book by Robert L. Mcdonald(Professor of Finance,Northwestern University's Kellogg school of Management) named $"Derivatives Markets" 3rd Edition.$ In that book, I didn'...
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### Understanding the Confidence interval

I'm trying to figure this out and either I am completely missing the point or I am in fact correct. (I am a student). The null hypothesis is "There is no significant difference between time taken to ...
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### Estabilishing an upper bound for the probability of an impossible event, by sampling [duplicate]

Lets suppose there is an event that gives a random outcome each time it happens. The set of possible events is finite, but their probabilities differ, sometimes by orders of magnitude. (imagine a ...
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### Confidence interval for extrapolated value?

I have data that is modeled according to the equation: $$\tag{1} \frac{\Delta p}{L} = \frac{\mu}{k}\frac{q}{A}+\beta \rho \frac{q^2}{A^2}$$ The variables $\Delta p, L, \mu, q, A$ and $\rho$ are all ...
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### Finding confidence interval for a Poisson parameter that varies over time

I have data as $t=[0, 1 ,2 ,3,4,5,6]$ and $X(t)=[395000,500000,400000,300000,300000,250000,300000]$ and I am fitting to these data assuming $X(t)$~Poisson$X_0e^{-\theta t}$ to estimate the parameter ...
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### Confidence Interval's equivalence to hypothesis tests

Theoretically, I was having a debate with my friend about confidence intervals and I got confused. So, my understanding is the whole confidence interval is essentially the same as a two-tailed ...
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### confused about effects vs. means parameterization in R - which is right for Anova?

I'm running a few GLMs and using the effects (e.g. glm(var1~var2...) ) and then means parameterization (i.e. glm(var1~-1+var2...) -- the one without the intercept). I understand that effects gives you ...
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### Multiplying with standard error for population estimate

I need to calculate a population estimate from slightly mismatched data. I have the average (±SEM) density of apartments in different areas of a city (2200±120 per km2, n = 12) collected in 2012, and ...
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### Confidence interval of Poisson distributed MLE using chi squared

There is a variable distributed as $X$~Poisson$(X_0 e^{-\lambda t})$. The value of $\lambda$ was estimated through maximum likelihood by fitting to the data $t=0,1,2,3,4$ and $X=[5000,3000,100,10,1]$. ...
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### When to use a one tailed or two tailed confidence interval

I'm currently doing a project for my AP Stats class. I performed a 2 sample t test for difference of means with an alpha value of .05. I rejected my null hypothesis that the means of two populations ...
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### Complementary log-log or log-log transformation when combining estimates from multiple imputation after cox regression

Can anyone give me an argument for or against using the complementary log-log transformation as opposed to the log-log transformation on survival estimates after cox regression in multiple imputation ...
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### How to find if people's preference is significant

I am trying to find out the wheither people prefer ads on Instagram or Facebook. As in are they more likely to choose x or y? Each person is given if you had to choose from and they pick x or y. ...
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### Likelihood of an event based on Confidence limits

A simple problem I can't figure out. Suppose at confidence level 99.9, there is a likelihood of loss in a 1 in 1000 years. What is the likelihood of loss if confidence level is 60? Any idea how to ...
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### Standard error or confidence interval of a weighted average

I am calculating a weighted average according to, $f = \sum_{x=1}^{3} a_{x} \sum_{i=1}^{10} d_{x,i}w_{x,i}$, where $d_{i}$ are the values being weighted and $w_{i}$ are the weights. $a_{x}$ is ...
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### Error estimates for coefficients of a non-negative quantile regression

I am looking for a way to provide an error estimate for coefficients obtained from a non-negative quantile regression. The complicated part aside from positivity constraints is that my observations ...
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### Confidence interval given sample size?

Let's say I have a normal distribution of N ~ (1,0.01) I pick 10 observations from that normal distribution. Is the confidence interval the same for 10 observations as it is for 100 observations? Or ...
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### estimate confidence interval of empirical percentile [duplicate]

Suppose $n$ samples are generated from an unknown distributions and the empirical percentile is estimated. In python: ...
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### name for histogram of nominal p-values under the null

To evaluate a statistical test or means of generating frequentist confidence intervals, it makes sense to repeatedly simulate data for which the null is true and then compute the nominal p-value, and ...
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### Why $\alpha$-level confidence interval consists of hypotheses under which p-value is larger than $1 - \alpha$?

I have read in an old paper that "Typically, an $\alpha$-level confidence interval consists of those hypotheses under which the $p$-value for the experimental outcome is larger than $1 - \alpha$". If ...
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### Resampling technique to compare genetic diversity indices

I would like to know what would be the more appropriate way to compare two gene diversity indices by resampling or bootstrap methods. The data are as follows. In the first sample, I have 23 ...
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### Distribution of $XY$ when $(X,Y) \sim BVN(0,0,1,1,\rho)$

The question is pretty much in the title, I need to find an approximate distribution of $XY$ when $(X,Y)$ follow a Bivariate Normal Distribution where $X$ and $Y$ are each $N(0,1)$ distributed and \$...