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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4P logistic regression differences in methods

I am using 4 parametric logistic regression for ELISA, we have been using GEN5 software so far and we want to switch to PLA3 for the new analysis, while keeping all the historical data from GEN5. The ...
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What is the confidence interval of consecutive subsampling

I have a situation where I do consecutive subsampling from an original population and I'm trying to figure out what the final confidence interval would be. I know that Var(A,B) = Var(A) + Var(B) if A ...
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Best way to find confidence interval for a mean of a symmetric leptokurtic distribution?

I have a very symmetric distribution with kurtosis of 10 and sample size of more than 100. Here is the Histogram https://ibb.co/ws7vBjd This histogram was obtained by asking participants in the ...
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How to find 95% CI of CI of Mean?

We know that the 95% confidence interval around the population mean is calculated as x̄ ± 1.96* σ/√n, where x̄ is the sample mean, σ is the sample standard deviation and n is the sample size. On the ...
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Negative Binomial: Estimating r (# failures until stopping) when p (success probability) is known

I have a NB(r,p) distribution (let's say with the conventions of the wikipedia page). Suppose I know the success probability p, observe Y the number of successes, but don't know and want to estimate r,...
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Heavy tailed rather than normal distribution for a stock simulator

Have a program that simulates picking stocks 10000 times according to different parameters. I then look at the ending portfolio amounts, and the distribution is pretty heavy tailed. This doesn't ...
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Am I using confidence intervals correctly here?

I run a stochastic computer program. What I’m doing is testing one strategy against what might be considered a default strategy. At the start of a run, there are 100 individuals using the test ...
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Meaning of Statistical forecast

Let say I have a regression equation $Y = \beta_0+\beta_1x_1+\beta_2x_2+\epsilon$. Estimate of the response value can be obtained as $\hat{Y} = \hat{\beta_0}+\hat{\...
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Meteorites and Poisson parameter estimation

I heard that the number of meteorites of the given size that hit the Earth follows the Poisson distribution. I am wondering how to estimate the Poisson parameter $\lambda$ and its 95% c.i. if I have ...
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Evaluating randomized algorithms on randomized problem instances

Suppose we want to compare the performances of two algorithms — call them A and B — on a problem X. In particular, suppose that we want to evaluate the algorithms on random instances of X drawn from ...
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Cohrane armitage test

we performed a cochran armitage test using xlstat on a 10-year data for trend analysis. The results showed a p-value but did not show a confidence interval. Is there a way to get confidence intervals? ...
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Using s to estimate $\sigma$ when finding the sample size in confidence interval questions

I am trying to learn sample confidence interval for $\mu$ , in this topic , there is a subtopic which is finding the sample size. I know that if $\sigma$ is given (standard deviation of population) , ...
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How to calculate a sense of error for estimated number of events with known probabilities?

I have a long series of entities: x1, x2, x3, ... xn for each of which, there is a probability of an event occurring. The probability for each x may be different, ...
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Is it appropriate to use linear regression when the response has a confidence interval?

I am looking to predict a response, $\hat{y}$, and have some information about how the response is generated. I know, for example, that it's a score that is computed from an array of weighted factors. ...
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Likelihood-based CI is better than Wald CI?

The text I'm reading mentions the following: Let us consider a scalar parameter case. The likelihood-based approximate 95% cI is $$\left\{\theta,2\log\frac{L(\hat{\theta})}{L(\theta)} \le3.84 \right\}$...
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95 % CI for ratio of variables subject to measurement imprecision

An instrument used for measurements has a known measurement imprecision of $CV = 10 \%$. Thus, if the variable to be measured has a true value $x_{true}$, the range of possible measured values will be ...
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Computing p-value vs. constructing confidence interval from sample for proportions

Let's say D is a Bernoulli distribution with parameter $\mu = 0.6$ and we want to test whether or not $\mu=0.5$. So, Null hypothesis: $\mu = 0.5$ Alt hypothesis: $\mu \neq 0.5$. Suppose we have a ...
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How to apply Bonferroni correction to confidence intervals?

I want to apply the Bonferroni correction to the following confidence interval: Since $\alpha _{Bonf}\:=\:\frac{0.05}{k}$ and I have two groups, should I just substitute $\alpha$ above with $\frac{0....
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Kaplan Meier using survfit confidence interval of the median

In R, I am trying to produce a survival analysis using Kaplan Meier. I have previously used SPSS. I am trying to compare my results but R is producing a 95% confidence level of the median, whereas ...
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Approximating the 2-likelihood region in R

By following the distribution I provided here on stackmathematics Q. A biased die favours the number 2. It's rolled 4 times and 2 comes up twice. It's rolled again 4 times and 2 comes up once. ...
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get CI bands on predicted fit from nls/nlme(r) models in R with subscripted parameters

I have a dataset with different groups (bacterial strains) with a continuous response variable result to which I want to fit a non linear model. Initially, the parameters of this model need to be ...
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Differing confidence intervals between ggpredict() and ggemmeans() when REML = TRUE in glmmTMB beta regression

I am using the package ggeffects to estimate marginal effects and confidence intervals for a beta regression model fit with glmmTMB. I notice the estimates differ ...
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Compare two confidence intervals calculated from same sample

Problem: We have distance between user and a static device(in meters). We have lab tested data where user is actually standing away from device(actual values). Based on these we try to determine what ...
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Confidence interval for summation of time series

I have three time-series of denoting forecast means with confidence intervals around them. I want to add these three models and get a confidence interval for the final model. How should I approach ...
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How to minimize confidence intervals on $\beta_o$,$\beta_1$ and $\sigma^2$ given data

If I have 20 data points and a linear model ${\displaystyle y=\beta _{0}+\beta _{1}x\ +\varepsilon}$ where $\epsilon$ is normally distrubuted with Expected value=0, variance $\sigma^2.$ If I want to ...
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How to calculate a confidence interval for a variable that is based on multiple samples?

Let's say there are multiple (ex: 3) coaches who are each recording the speed of the same sprinter over a constant distance multiple times (ex: 10). In order words, coach 1 will record the speed of ...
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Small Sample - Confidence Interval Mean

I have a sample size of 14 and I plan to measure confidence intervals for the mean of different characteristics. I can say this about my data: ...
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Infer from Confidence Interval of Two Sample's Mean whether they are different

Background: I have 2x8 conditions. I can visualise the 8 different cases on a continuous line (x-axis) and now want to plot the mean and confidence intervals for the 2 different treatments. The CIs ...
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Skewed - Unknown Distribution - Median Confidence Interval [duplicate]

I am trying to compute the confidence interval of the median for my data. Sample size: 14 Skewed Unknown Distribution To my understanding, I can use non-parametric ...
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Native method to calculate confidence upper bounds for the mean of a Poisson Distribution

Reading about how to calculate confidence intervals for Poisson distributions, one says that if the unknown mean is high you can use the Normal distribution approximation and use $\widehat\lambda\pm c\...
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Confidence interval for variables with multiple categories - estimation of difference

I have performed a chi-squared test on two categorical variables - one is a dichotomous variable (eg survived, died), whereas the other has multiple sub-categories (location A, location B, location C ...
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Constructing a confidence interval around a regression slope for hierarchical data and/or from a nonrandom sample

I know it is possible to construct a confidence interval for an estimated regression slope from a linear regression estimated via OLS estimator (y = b0 + b1x + e). But is it also possible (and correct)...
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Chi-squared confidence interval for variance

When constructing, for example, a $90\%$ confidence interval for the population variance using the chi-squared distribution, we have: \begin{align} & P\left(a<\frac{(n-1)S^2}{\sigma^2}<b\...
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A basic question about hypothesis test and rejection region

If we want to test the hypothesis $H_0$: $\mu = 0$, where $H_a$: $\mu \neq 0$. Then the t statistic is $t=\bar{y}/(s/\sqrt{n})$ and 95% confidence interval is $\bar{y} \pm t_{.975}s/\sqrt{n}$ by t-...
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Why use confidence interval for survival estimates?

I noticed that in most cases people use point estimate + 95%CI to describe survival estimates like the 3-year survival probability. Mean +/- SD is also a popular method to describe data, why do I see ...
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What can we conclude when the confidence interval for a regression line slope contains 0?

If my confidence interval, say $(-.4, .7)$, for a regression line slope contains $0$, I am looking for the strongest conclusion that I can make from that. Can I conclude that "there is no ...
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Comparing margins of error of confidence intervals before and after new data is collected

Consider the following question: I have calculated: margin of error for the first 50 jumps is 0.127, margin of error for the last 10 jumps is 0.248, margin of error for all 60 jumps is 0.156. The ...
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Two possible definitions of confidence regions: which one to choose?

Let's say you have a parameter vector $(p,q)$ consisting of two proportions, and you want to find a confidence region for the estimator $(\hat{p},\hat{q})$. Define \begin{equation} H(x,y,p,q)=\frac{n}{...
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How to calculate P-value and 95% confidence interval in R for cross-sectional table

I am a newbie to statistics and R. Need someone's help to understand how to get a 95% confidence interval and p-value from the above data to test the null hypothesis that there is no difference in FUS ...
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max subscription of 2 quantiles

I saw in literature the : $x^i_{\max(1-\alpha=0.01;\alpha=0.99)}$ which states that "is the maximum $(1-\alpha)$-quantile derived from the standardized empirical distribution of the same vector ...
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What is the relationship between confidence intervals that are build with bootstrapping vs t-distributions?

I've seen a few resources online that construct confidence intervals (CI) in different ways. One is through bootstrapping which essentially samples with replacement from a group of measurements and ...
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What approaches does R use to find confidence interval for proportion? [duplicate]

I am wondering what approaches are used in R to find the confidence interval for proportion? For example, in prop.test, it provides a confidence interval which is different from $\bar{p}-+z_{\alpha/2} ...
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Meaningfull spread or confidence interval for percent value?

I have for some items booleans value, let's just say it's a product and the boolean represents returned or not.. For example: item1 = [0, 0, 0, 1, 0, 1, 0, 1, 0] ...
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How to construct a confidence interval for the average of discrete values between 0 and 1?

I have data where each person can take 5 potential values of $(0, 0.25, 0.5, 0.75, 1)$. Each person is part of a larger group of 3 people, so that the reported value for each group is the average of 3 ...
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confidence interval interpretation for new parameters

In the book "all of statistics" the author brings the following interpretation of confidence intervals with the following exmaple: Interpretation: "On day 1, you collect data and ...
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Why aren't these sentences about confidence intervals equivalent?

Yes, I'm aware that there's similar/duplicated questions already open: Aren't these statements about confidence intervals equivalent? Why does a 95% Confidence Interval (CI) not imply a 95% ...
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mean + 95 % confidence intervall versus boxplots

I am wondring about the use of boxplots versus mean with 95 % in a figure? A boxplot will give you median and you can add a notch to show the 95 % CI for the median so it is quick and easy to compare ...
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Calculate probabilities with confidence intervals of integers exceeding certain values from a negative binomial regression model

I'm fairly new to negative binomial regression models, so I hope my question makes sense. So far, I already found this answer to this old question (https://stackoverflow.com/questions/22213315/how-to-...
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Comparing model performance accounting for variance in sampling and training

I'll give an example of the problem to make things concrete. I'm using machine learning to tackle a classification task. I have a sample of data which I can use for training and evaluation. I'm using ...
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Hypothesis testing: Fisher's exact test and Binomial test

My first post in this community. My knowledge of statistics is limited, and so I am seeking advice on the following problem. (Sorry for the long post, and thank you in advance for your help). I have a ...
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