An interval of random variables, depending on observed data, which, with a fixed probability, contain an unknown parameter of interest.

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11 views

Empirical confidence bands

Suppose I would like to evaluate how well, the following kernel density estimator $$\hat f (x) = \frac{1}{nh}\sum_{i=1}^nK\left(\frac{x-X_i}{h}\right)$$ works. I simulate data 1000 times and obtain ...
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0answers
10 views

Confidence interval of a function of Maximum Likelihood estimates

I have a probability density distribution for a variable $x$. This distribution is a function of another variable $Y$, that is $P(X=x \space |\space Y)$. I observe one $x$ value in nature (the ...
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1answer
31 views

How do I calculate required Sample Size to get useful confidence interval length for Bernoulli random variables?

I am pulling meta data fields from a population of 100M documents. These meta fields include things like Author Name, Author Location, Keywords, etc. Some documents have all of these meta fields, some ...
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1answer
7 views

Combining the confidence intervals of beta and OR values

I'm doing Mendelian randomization by hand as my supervisor wants me to practice. Based off a paper I'm learning from there is an intermediate phenotype (IP|G): SD increase of iron due to a mutation = ...
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0answers
14 views

95 confidence interval for data with a log trendline

I have a data set which a logarithmic trendline fits and I am trying to create 95% confidence interval lines for the trendline. Any suggestions? y = 0.1818 * ln(x) + 0.5268 X 1 1 1 1 1 1 1 1 3 6 7 ...
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6 views

Computing a confidence interval, understanding the estimated standard error

I'm currently learning about estimators and confidence intervals. I thought I understood the theory so far but when I run a simulation it doesn't work. Here is my understanding: Suppose I observe $n$ ...
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0answers
12 views

Confidence intervals for multinomial mixed models

I am using the ordinal package in R to create a multinomial mixed model using the clmm2 function. However, I cannot find a way to get confidence intervals for the coefficients; confint() does not work ...
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1answer
38 views

Paired samples or independent sample hypothesis test for two time periods

I want to know if employees in an organization are surveyed in 2013 and again in 2014 if the samples from the two time periods are considered related and dependent or independent if they are asked the ...
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0answers
19 views

Confidence intervals for chi square goodness of fit

I'm having trouble figuring this out. I know that you calculate the confidence interval same as you would for a proportion, $p_i= P \pm 1.96 \sqrt{(P(1-P))/N}$, but in my notes it says: ...
2
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1answer
37 views

Why would I want to bootstrap when computing an independent sample t-test? (how to justify, interpret, and report a bootstrapped t-test)

Let's say I have two conditions, and my sample size for the two conditions is extremely low. Let's say I only have 14 observations in the first condition and 11 in the other. I want to use the t-test ...
3
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1answer
24 views

How to interpret confidence interval with accuracy phrase

Upon reading a peer reviewed article, I found this: A Chi-square test shows that the demographic characteristics of the sample represent Toyota GB’s hybrid customers (data obtained from the New ...
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1answer
36 views

Can confidence interval from hypothesis test inversion ever contain observed difference if that difference is significant?

My question concerns the method for constructing a confidence interval for a difference in means based on a randomization test (that can be found here , check under 'Confidence interval based on the ...
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1answer
45 views

Confidence interval for sample $\{x_1, x_2, x_3, x_4\} = \{5,10,6,7\}$

Suppose this sample is generated from a $N(\mu, 9)$ distribution, $\mu$ is unknown. The question asks for a 95% confidence interval sample for $\mu$. I think this is a pretty straightforward case of ...
5
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1answer
63 views

Error bars on log of big numbers

I am calculating a quantity of the following form: $\mu = \log( \frac{1}{n} \sum_{i=1}^{n} e^{\phi(X_i)} )$ via MC. $X_i$ are iid and I can sample them. I want to give error bars\ confidence ...
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1answer
39 views

Show the shortest confidence interval of a normal distribution

I'm having trouble formally showing a problem I have been given. It goes as so: Show that among all $(1-\alpha)*100$% confidence intervals of the form ...
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1answer
25 views

How to Get this Confidence Interval

One example in Maronna, Martin and Yohai's Robust Statistics (2006, p.2) is as follows. Given 24 measurements of certain quantity (see below) and their sample mean 4.28 and sample standard variation ...
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1answer
37 views

Calculating means and confidence intervals when most data points are 0

I am looking at data set that has four groups. In each group, the data is mostly, 99+% of time, composed of zeros, but, when it is not zero it can be any float number (e.g., 0.01 to 921.2, with most ...
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0answers
10 views

Constructing confidence intervals for mean of means, using standard errors [duplicate]

Is it possible to construct confidence intervals for a mean of weighted means using standard errors? I have 4 different weighted means ($p_t = \sum_{i=1}^{n} w_ip_i $ where $w_i$ is the respective ...
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12 views

Confidence interval before the first event in a Kaplan–Meier curve

The confidence intervals for Kaplan–Meier curves in survival analysis only exist for times after the first (non-censored) event. Example R code: ...
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10 views

Weighted mean: Inverse of individual values's confidence interval as weight?

This seems to be a very basic question, however I could not find a satisfactory answer throughout the web, yet. I have, say, N values, whose I know the N respectives 95% confidence intervals (said ...
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0answers
17 views

Confidence intervals for maximum likelihood estimator with constraints

Let us suppose I have a maximum likelihood estimator for a multivariate parameter $\vec{\theta}$. The parameter is subject to the following constraints: $\theta_i \in [0,1]$ $\sum_i \theta_i = 1$ ...
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1answer
21 views

Confidence interval for the variance when we know the mean of the population

We have $n$ random samples from a population which has normal distribution, and the mean of the population is known. How do we change the procedure of finding a confidence interval for the population ...
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1answer
73 views

How many individuals must be measured to determine the true mean?

I saw this was asked earlier, but I also have the same question. This was the question: "Anatomy: The human height is the distance from head to toe. When populations share a genetic background and ...
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16 views

Adjust confidence ribbon in regression plot in ggplot2(R) [migrated]

I am plotting a regression line with confidence intervals in ggplot2. How can I adjust the code (see below) that there is no shaded area indicating the confidence interval but just a dotted line for ...
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1answer
39 views

Scientifically reasonable or not ? exclusion of very, very uncertain values from statistical analysis

I have 5 treatments A1 .. A5 and 4 independent individuals per treatment, whose parameter X is of interest to me. My objective is to compare X among treatments, and see if one or more treatment ...
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59 views

Estimating the 95th percentile of nitrate data using non-parametric Weibull method, with associated confidence intervals in R

I am currently involved in a project where I have to estimate the 95th percentile of nitrate data from different sample points, using the non-parametric Weibull method, to see if it breaches the ...
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16 views

Getting a confidence interval for a predicted value in regression

So I have this table of statistics which I'll try to reproduce below. It is meant to be a summary of a multivariate regression of "PolityIVScore" against log foreign aid and a dummy variable for ...
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1answer
41 views

confidence intervals best through direct calculation or R's confint funtion

I am interested in pairwise comparison of means, through the calcul of confidence intervals (CI) of the difference between two given sample's means. However, CI calculated directly from each sample, ...
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31 views

Bootstrapping to create confidence interval

I have about 50 or so observations of x,y pairs. The relationship I am trying to learn is a quadratic relationship between x and y. While fitting the quadratic, I am also interested in learning ...
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1answer
30 views

confidence interval of a difference of variables

Let's say I got two samples from two unknown random variables: $(x_i), (y_i)$ At this stage I don't know (or don't want to assume) that they come from a similar process or not. I want to compute a ...
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23 views

approaches for computing confidence band and prediction band for general regression analysis and predictive models

In linear regression model, the predict in R is able to calculate the confidence band and ...
0
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1answer
11 views

Constructing CI for log OR based on OR

I have in my data the mean OR and its standard deviation (computed by Delta method). I have a question about constructing a 95% CI for the log OR based on this data (based on asymptotic normality ...
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21 views

difference between confidence interval and prediction interval in the context of regression analysis and predictive modeling

When building prediction models, I always see the following concept 1) Confidence interval for regression model 2) Prediction interval 3) Confidence interval for predicted value I can understand ...
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1answer
83 views

Confidence interval for a proportion

Let's say I want to built a confidence interval for a proportion ($p$). I have seen that many times this is made from the standard error: $p\pm 1.96\times SE(p)$ taking SE from ...
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39 views

Does Hoeffding's inequality apply to sampling from finite populations?

Based on Hoeffding's theorem, one could easily find the minimum number of samples required for the inequality $\Pr \left(|\bar{X} - \mathrm{E} [\bar{X}]| \geq t \right) \leq \delta$ to hold as ...
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69 views

How to calculate confidence limits for various scenarios when drawing random cards from a pack?

I'm designing an experiment that involves a subject attempting to determine various attributes of a playing card drawn at random from a standard 52 card pack. The experiment is in four phases: ...
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63 views

Can Chebyshev inequality be used to bound the error of the sample mean?

Can the probability of error of the sample mean, i.e., $\Pr(|\bar{X}-E[X]| \geq \epsilon)$, be bounded using Chebyshev inequality (or something similar)? $X$ is a discrete random variable with an ...
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2answers
364 views

Does high number of values outside of 95% Confidence Interval imply non-normality?

I am looking at the errors of my model, i.e. difference between predicted outputs and actual values. Finding a mean and standard deviation, I found that many values (sometimes more than 50%) are ...
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0answers
19 views

What is the confidence interval for model that is supposed to have mean of 'zero'?

I'm trying to analyze some dataset. I have a model. This model predicts some values. There are real values also known. I calculated the differences between the predicted and real outputs. Ideally, the ...
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0answers
36 views

Using classical methods to explain bayesian approach to confidence interval estimation

I'm using bayesian techniques on R to calculate a 50% confidence interval for a parameter lambdastar which has a prior distribution gamma(alpha,alpha). I am simulating 10000 random samples of size 10 ...
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30 views

Tukey HSD, insignificant p-value when the confidence interval does not contain 0?

I am using TukeyHSD to do multiple comparisons. I am seeing strange results for some of the pairs: the adjusted p-value is greater than the specified significance level but the corresponding ...
0
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1answer
38 views

What is the formula for a normal-theory confidence interval of the mean?

A psychologist is collecting data on the time it takes to learn a certain task. For $55$ randomly selected adult subjects, the sample mean is $10.5$ minutes and sample standard deviation is $3.25$ ...
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1answer
28 views

Forming confidence interval using a sampling distribution

I know the relation between the distribution of sample means (for a given sample size) and the population parameters, from which samples are taken. My question is, how exactly do we use this relation ...
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39 views

Bootstrapping with bootstrap sample greater than original sample

My original sample has 350 observations drawn randomly from a population of 60,000 people. My independent variable is Default, with 35 observations with value of ...
2
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1answer
153 views

Mann-Whitney U-test: confidence interval for effect size

According to Fritz, Morris, and Richler (2011; see below), $r$ can be calculated as an effect size for the Mann-Whitney U-test using the formula $$ r = \frac{z}{\sqrt N} $$ This is convenient to me, ...
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0answers
12 views

Confidence interval from kaplan meier survival table

I have been able to creat kaplan meier survival plots for group of patients with a cancer diagnosis. The table give me proportion people surviving at specific time points e.g. 5 years with SE, how can ...
0
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0answers
21 views

Upper confidence interval for the variance using chi squared distribution

It is needed how to estimate the upper confidence interval for variance. I have the equations here from a document. I attach a photo of one page. I do have the raw data and hence the mean values, ...
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38 views

How to pool the interquartile range for an arbitrary distribution?

Let's say that I want to estimate the temperature in an annulus-like region. I split the annulus into four equal sectors (sectors 1,2,3, and 4) with $n_i$ being the number of measurements in sector ...
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1answer
50 views

Confidence intervals vs P-values for two means

I know in studies where relative risk or odds ratio is calculated, if confidence interval overlaps 1, then the P-value is not significant. Is similar relation true for following situations as well? ...
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1answer
82 views

Explain confidence intervals in simple terms

For one newly handling statistical analysis, please can you explain in the simplest of terms, with an example, what is a confidence interval?