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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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What is the best statistical measure tool or approach to resolve time series data?

I have a dataframe from different sources with this index and 1 column. My goal is to detect which source_i have a different counter behavior per time. The first thing I did simple prediction using ...
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12 views

General way to construct a confidence interval for a unknown constant to which a sample estimator converges

Assuming that a sample estimator converges to some unknown constant (a wild assumption to be sure) and without assuming the distribution of either the sample estimator or the variables from which it ...
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19 views

Bootstrap confidence interval for just-identified IV estimator

Assume we have a regression model \begin{equation} y_{i} = z_{i}' \delta + \epsilon_{i} \end{equation} with dependent variable $y_{i}$, L regressors $z_{i}$ and K instruments $x_{i}$, and assumptions ...
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22 views

Confidence interval from sample quantiles

Context I am running some stochastic simulations in R to determine appropriate sample sizes for a biological problem of interest to me. My method iteratively generates "accumulation" curves which ...
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32 views

UMAU confidence interval for $\theta$ in a shifted exponential distribution

Suppose $X_1,X_2,\ldots,X_n$ is a random sample drawn from the distribution $$f_{\theta}(x)=e^{-(x-\theta)}\mathbf1_{x>\theta}$$ It can be shown that there exist some $c_{\alpha}, d_{\alpha}$ ...
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31 views

On the bias of a confidence interval

I have that $n(\hat{f}(x)-f(x)) \sim N(\mu,\sigma)$ And $\mu$ cannot be estimated. Can I say that the bias of my confidence interval for $\hat{f}(x)$ is $\mu n^{-1} $?
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24 views

How to use bootstrapping to compare two non-normal datasets

I have two data sets - one control and one treatment. I wish to test whether the difference between their means is significant or not (approx 30 data values in each set). The distributions of both of ...
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22 views

Where is my potential flaw in my Z-test of Proportions?

I was working through this z-test of proportions example I found online. The online example solutions says that the difference between the groups is statistically significant, whereas I concluded it ...
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33 views

specific equation for modified wilson confidence interval

I recently read the Brown, Cai, Dasgupta paper on interval estimation for a binomial proportion where they propose the modified wilson method as a better alternative to the standard wald interval. I ...
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7 views

Rescaling Linear Impulse Response Functions, Innovations, and Confidence Bands

all. I am using a VAR model to do a bit of analysis. I obtain cumulative (linear) orthogonalized impulse response functions (COIRF). Because I am conducting similar analysis across different time ...
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15 views

Confidence Interval for accuracy - Binomial?

Imagine we fit the same data mining model on 100 different validation datasets and accuracy is always exactly 95%. If we now use the Binomial proportion confidence interval we would have a standard ...
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25 views

How should I calculate mean CI - from raw data or mean values?

I have experimenatal data from medical industry. In the experiment 4 observations were weighted, each one 2 times for more precise measurement. As a final weight, a mean from each pair is reported. ...
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How to account for low sample size when computing performance?

I am interested in analyzing user performance at a per user level. Users have the opportunity to engage with an app by answering trivia questions and can choose how many questions they want to answer. ...
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1answer
16 views

Valid way of determining spread of data

I’m trying to determine a valid method for quantifying the maximum spread of values I can statistically expect to see. I’ve collected 12 sensor values from 12 different sensors. I’ve calculated the ...
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21 views

Cannot replicate a 95% CI using: Beta ±1.96*SE [duplicate]

I am having a lot of difficulty figuring out why I cannot calculate a 95% CI by hand with one set of data; but I can using the same process with a different set of data. Drawing on OLS results; I am ...
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12 views

Combining point prevalence estimates and their confidence intervals

I have some health survey data from multiple years. This includes the estimated prevalence of a flu vaccination in a population, then number of people surveyed, and the high/low confidence intervals. ...
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Confidence interval of one tailed Z-test

In an intelligence test of boys and girls, the question has asked to find if the boys and girls are equally intelligent against the alternative that girls are more intelligent than boys. While I have ...
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16 views

How to adjust confidence interval

I am reading a journal where it is written "Time series are based on annual-mean translation speeds from 1949-2016. Trends are estimated by linear regression. The P values of the regression are based ...
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14 views

Binary survey confidence

A simple one question Yes/No survey was sent to about 250 people from a population of 481. 135 responses received showed about 80% “Yes” and 20% “No”. How do I calculate my 95% and 99% confidence ...
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20 views

Confidence interval for reciprocal proportion ($\frac{1}{p}$) [duplicate]

Is there a "nice" closed-from expression for the confidence interval (CI) of the reciprocal binomial proportion, $\frac{1}{p}$? I'm actually looking for a CI for $\frac{N}{p}$, which will be a simple ...
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13 views

Chi-Square - difference in modeling of CI and Chi-square test

If i have a 2x2 table, and i have to calculate the 95% CI for the difference of proportions, and calculate the chi-square test for a 2X2 table For example Learning habits : conventional, e - learning ...
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43 views

Is the sampling distribution of a complete sufficient statistic free from relevant subsets?

Let $T_{\theta}(\mathbf{x})$ be a complete, sufficient statistic $T_{\theta}: \Omega \mapsto \mathbb{R}$, where $T_{\theta}$ is indexed by the parameter $\theta \in \mathbb{R}^n$. Is it true that the ...
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1answer
24 views

Margin of error for a specific question on a survey?

Background: We want to find the margin of error, at a 95% confidence interval on a particular question in a survey. If there are 10 questions in the survey, this question is towards the very end. ...
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36 views

Index accuracy based on sample size out of population size

Suppose I have people who work at different companies and I am interested in seeing their view on some topic. In order to do this, I decide to conduct interviews on people from each of the different ...
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How can I calculate confidence for a multiplicative (growth) dataset?

I have a dataset of daily price changes, represented as decimals. Perhaps: 0.5, 1.5, 2.0. That's to say it lost 50%, then it gained 50%, then it gained 100%. I'd like to know how confident I should ...
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3answers
48 views

How to interpret this Confidence Interval?

I'm currently writing a critique on an RCT and my essay should include a report on the findings of the study. I have very minimal knowledge on interpreting statistics and papers. I'm confused on how ...
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1answer
47 views

Formula used in confidence intervalle on R's lm function

Does someone know how confidence interval on factor values are computed on R (lm function), here is a simple example : data ...
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1answer
35 views

Bootstrap confidence interval of an estimated function

I have a model whose estimation is a function (finite number of points) over an intervalle. I am looking at the sum of each estimated point of the function : $\hat{\theta} := \sum_{i=0}^k \hat{f}(i)$ ...
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1answer
34 views

One sided hypothesis testing with two-sided interval

So, I have a population which is believed to have $H_0:\mu = 4620$ and I should test for $H_1: \mu < 4620$. Given a sample of $n=81, \bar{X}=4450, S=900$, the p-value is: $pv=\Pr\left(\frac{\bar{X}-...
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Understanding STD, SEM and CI

Trying to understand the difference between std and sem: ...
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25 views

Heteroskedasticity robust confidence interval

I have used Chebyshev's Inequality to construct confidence intervals. I know that Chebyshev's Inequality works for any distribution as long as the second moment exists. But I have got a comment that ...
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R-studio: confint(). When using this code, the output shows 'Sig01', 'Sig02', 'Sigma' and '(Intercept)'. How do you know what the 'Sig..' stands for?

De data is from PIRLS-research about how much students 'Like reading' and 'confident in reading'. There are three levels, and we added the levels IDSCHOOL and IDCLASS the third level students are ...
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Sorting By User Ratings - Overlapping Wilson Confidence Intervals

I'm working on a personal project to rank user ratings on a 5 star scale and have implemented Evan Miller's often-referenced Wilson Score Interval calculation with the help of this comment. My data ...
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Use of 50% confidence interval to detect marginally-significant fixed effects in linear mixed models?

I read this research paper today: Fates of trees damaged by logging in Amazonian Bolivia. In my understanding, the authors used the following approach to determine if fixed predictors in an LMM are ...
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Difference - Probability-To-Exceed (PTE) and $\chi^2$ distribution

I would like to understand the difference between the $\chi^{2}$ distribution and the Probability-To-Exceed ? I have to compare 2 data sets A and B and in the article I am reading, they talk about ...
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62 views

Confidence interval in R lm function with factors values

Does lm R function handle factors value 'correctly' when computing confidence interval ? I read that confidence interval formula are different in case of discrete or continuous variable. Thanks. ...
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21 views

Calculating CI's using bootstrapping on the holdout test dataset

I’m trying to calculate 95% confidence intervals for the sensitivity and specificity of a decision model that I’m building. I’ve split my dataset into 90/10 train and test sets. I’ve used the 90% ...
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50 views

Confidence interval with only one observation

How could one create a 95% lower confidence interval for the expectation of a exponentially distributed r.v. with only one observation of the r.v., say 5555?
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54 views

How do I get an odds ratio with McNemar's test?

I have pre and post test data evaluating the effectiveness of a lesson about how to help friends who are being bullied. I am trying to see if more students know how to help a friend being bullied ...
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Magnitude of the effects using confidence interval [closed]

I have an assignment (doing regression) and one of the tasks is "Check the magnitude of the effects using confidence intervals.". How can I check this and how to report it in a paper? Using SPSS.
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22 views

Get relative risk ratio and confidence interval from logistic regression

There are many examples on these forums of people calculating risk ratios from logistic regressions, but none of them seem to match my situation. I have two predictor variables - one continuous and ...
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1answer
64 views

Calculating confidence interval for ratio of sums

I have a problem where I need to calculate a confidence interval for a ratio of two sums. I have code below which calculates this stat using a bootstrapping method, but I would much prefer a closed ...
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How are confidence intervals calculated for lm in R using predict?

Here, a simple linear model, given x = 98, yields a predicted value of 24.47 with 95% confidence interval [23.97, 24.96]. ...
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22 views

Discussing regression results in a frequentist framework

There have been excellent debates about how to discuss treatment effects in a frequentist framework, for example: Language for communicating frequentist results about treatment effects What about ...
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How to correctly summarize a confidence interval in a sub--sample using linear regression?

This is probably a stupid question but I'll ask it anyway. So here it goes. Consider an ordinary linear regression setting. Assume you are using a relevant set of regressors, there is no sign of ...
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1answer
78 views

How to compute variance/confidence intervals from Fisher information matrix. Mistake in this document?

https://www.stat.umn.edu/geyer/5931/mle/mle.pdf In this document (by the great Geyer nonetheless!) it calculates confidence intervals using the Fisher matrix: But the standard deviation is not the ...
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16 views

Significance testing of signal-to-noise ratio

I have three 18-second, 32-channel resting state EEG time series sampled at 500 Hz using dry EEG electrodes (condition 1) and three more 18-second, 32-channel resting state EEGs also sampled at 500 Hz ...
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1answer
27 views

Calculating 95% confidence intervals for GLMM additive coefficient - count data estimates

I am running a GLMM on some data where the response is count data, using the glmmADMD package in R. I would like to plot the results giving estimates for the response variable with certain explanatory ...
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2answers
44 views

How can I estimate the confidence interval of correlations possibly dependend with time?

I have a multivariate problem (with solar data from different meteorological stations) that I am working on my engineering master thesis. I would like to estimate the correlations of different ...
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1answer
26 views

Confidence Intervalls

H, I have a question where I am not sure if what I calculated is correct. So there are two therapies, A and B with 48/60 and 25/40 being healed respectively. I shall calculate the 95% CI I now ...