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

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22 views

How to correctly understand confidence intervals and confidence level [duplicate]

I recently read an online discussion about confidence levels and confidence intervals. To be honest, I'm confused. What's the bottom line there? For a specific statement, say, Foobar is 3.45 ...
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1answer
55 views

100% confidence interval for mean

Is it possible to apply the law of the iterated logarithm (e.g. http://en.m.wikipedia.org/wiki/Law_of_the_iterated_logarithm) to derive non-trivial (i.e. bounded) 100% confidence intervals for ...
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1answer
23 views

How can I determine if two features, given a set of data, are the same feature or not?

Thanks in advance for the help. Suppose I have a set of data of the form [feature, rating]. For the sake of argument lets assume feature can be movie A or movie B and rating is a ranked, continuous ...
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0answers
16 views

Multivariate hypergeometric confidence intervals

Suppose you have an urn filled with money. You know there are $N$ total bills, and that each is either a \$1, \$10, or \$100. You draw $n$ bills without replacement from the urn, and wish to ...
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0answers
17 views

Is the situation discribed a suitable use of the wilsons interval? [on hold]

Hiya I am have a 'disscution' on some stats theroy and my friend wants to use the Wilson interval, Ive looked through my stats books but I can find nothing on this test. She wants to take small ...
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0answers
18 views

How do I add a “confidence rating” to something? [duplicate]

I have a bunch of survey responses from people all over the country. Each survey has one question: "How much do you like X?" (X isn't important here), where answers range from 0 (not at all) to 100 (a ...
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1answer
33 views

Confidence interval definitions

Wikipedia provides the following definition for a confidence interval for a parameter $\theta$: A confidence interval for the parameter θ, with confidence level or confidence coefficient γ, is ...
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2answers
155 views

Faith in an extrapolated result

I would like to be able to predict when I will exhaust a particular resource. My situation is analogous* to a water tank. Each day zero or more rain will fall, filling up the tank. I can not tell ...
0
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1answer
16 views

Confidence Interval Application to a time series

So I'm not sure if I 100% grasp confidence intervals. Say I have a huge data set of a bond prices from 1996 to present in MINUTES. Suppose I separate each data by day. If I were to use a Dickey Fuller ...
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2answers
20 views

Pivotal to estimate lambda of a exponential

I am studying interval estimation by the method of pivotal quantities. Let $X_1,X_2,...,X_n$ be a random sample from a p.d.f $f(x;\lambda)=\lambda e^{-\lambda x}, x>0,\lambda >0$. I have to ...
3
votes
1answer
70 views

Averaging binomial confidence intervals

I have a general statistical question. Three schools A, B, and C have 0.23, 0.56, and 0.8 fraction of female teachers. The upper and lower confidence intervals (CI) for the three schools can be ...
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1answer
47 views

Data transformation and confidence intervals for mean difference

I have a between-group independent variable with two level (A and B) and a dependent variable Y that I transformed in order to normalize the distribution of the residual. I used a Box Cox ...
3
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1answer
39 views

Would two different pivotal quantities of the same parameter give the same confidence interval?

I couldn't think of an example but it would be great if someone could give one.
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0answers
46 views

Confidence interval for the standard deviation of a Normal distribution with known mean

Suppose $\textbf{Y} = (Y_{1}, ... , Y_{n})$ is a random sample from the $N(\mu, \sigma_{0}^{2})$ distribution where $\mathrm{E}(Y_{i}) = \mu$ is unknown but $\mathrm{SD}(Y_{i}) = \sigma_{0}$ is known. ...
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0answers
8 views

How to get/calculate confidence intervals for slopes of the continuous*categorical interactions?

Not sure if this should be in Stack Exchange or here, but here goes. I have a linear mixed model in SPSS, and I want the confidence intervals for slopes of the continuous*categorical interactions. ...
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0answers
21 views

CI of a ROC/AUC in MATLAB

How can I calculate the confidence interval of my ROC curve (and relevant AUC score) in MatLab? FYI: I'm using the plotroc function The data gets classified in one of two classes via a linear ...
0
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1answer
44 views

Confidence intervals for predictors in multivariate logistic regression

I've got a question. I am dealing with medical data which contain 5 predictors and 1 binary outcome. When I try to classify the data using all 5 predictors I get 0.84 area under roc-curve which is ...
3
votes
1answer
104 views

Calculate a 95% confidence interval and p-value for the change in C-statistic using bootstrap with R

I am using boot() and boot.ci() to furnish confidence intervals for the difference in the $c$-statistic (AUC) between models ...
0
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0answers
14 views

Is Monte Carlo simulation more appropriate than parametric tests for constructing confidence intervals for weighted means?

A colleague suggested that Monte Carlo simulation should be preferred for constructing confidence intervals for weighted means calculated from a sample. How and why exactly might Monte Carlo perform ...
3
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3answers
66 views

What is the most likely meaning of a confidence interval?

I'm using a service (Optimizely, as it happens), which show a confidence interval but doesn't explain what it is. I'm assuming it is a Binomial Confidence Interval, but I have no idea what the % ...
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0answers
11 views

Confidence interval calculated from values with different numbers of sample

I'm trying to calculate the estimated win probability between two players whose ratings (assume it's something like Elo rating in chess) are known. E.g. given player A's rating of 2000, player B's ...
2
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1answer
31 views

Comparing proportions in the same sample

I gathered 11 responses to a question where the options were A, B, or C. 9 people answered A. 2 people answered B. 0 people answered C. Using Clopper-Pearson 95% confidence intervals, I obtained ...
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25 views

Recovery of Standard Errors of Random Effects in Lmer

I'm analysing data with a nested structure with the lmer-function of the Lme4 package in R. I'm interested in the estimation of the confidence intervals of the random effects (is the score of class1 ...
3
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1answer
63 views

Estimating Uniform distribution endpoints using data with errors

Suppose I have a random variable $X$ ~ $Unif(0,\theta)$ where I want to estimate $\theta$. I draw a sample $X_1,...,X_n$.One way is to get a point estimate using e.g. maximum likelihood estimation ...
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0answers
17 views

Why are BCa bootstrap confidence intervals second order exact?

I've just come across a statement in Good, P. I.: Resampling methods. Springer, 2001 and wondered if someone could explain it to me. If you want to construct a 95% confidence interval for, let's ...
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0answers
28 views

confidence interval using median

I have a model where time is the response variable. I'd like to generate confidence intervals for the estimates. I have established that the error in the estimation is roughly normally distributed (it ...
2
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1answer
52 views

Calculation of confidence interval for estimation of demand curve - how many degrees freedom?

I'm trying to understand how uncertain an estimation of a demand distribution of a good is. If I take a random sample of n people from the representative consumer population who give me their personal ...
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0answers
17 views

Inverse prediction of percentile

Suppose we consider a linear normal regression $y\sim$Normal($\mu,\sigma$) and $\mu=a+bx$. I have seen documentations for methods for obtaining a confidence interval for $x$ for a specific mean value ...
4
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1answer
78 views

Confidence interval for a proportion estimated through stratified sampling

When estimating the confidence interval for a binomial proportion $p$, with $\hat{p}$ near 0 or 1, one has to use something other than the Wald interval to get a reasonable estimate (see for instance ...
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0answers
17 views

Calculate extreme tails of distribution

This is how my empirical distribution look like: I have calculated a genetics index of fixation in populations, called FST. My values have the maximum value of one. This gives me an empirical ...
2
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1answer
75 views

Justification for the Bootstrap Percentile Interval

The following is a proof of the validity of the (bootstrap) percentile interval taken from Larry Wasserman's "All of Statistics". $\theta^*_{\alpha/2}$ and $\theta^*_{1-\alpha/2}$ denote the ...
3
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1answer
40 views

Error Bars for Monte Carlo Experiment

Suppose we have a random variable $X$, where $\mathbb{E}(X)$ and $\text{Var}(X)$ are known. I have computed $N$ number of MC-type samples from the distribution of $X$. Let $\bar{x} = \frac{1}{N}\sum ...
2
votes
1answer
39 views

Hypothesis testing for multiple choice quiz

I am trying to determine whether students perform better than chance on a quiz with $q$ multiple choice questions. Each question as 4 possible responses; one is correct and 3 are wrong. A correct ...
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0answers
9 views

Normality Testing of Productivity Data

I have a series of measurements from a construction production study I've been carrying out. I essentially measured the output rate of workers in terms of output/hr. The measurements varied each day ...
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0answers
8 views

Quantify possible model improvement given samples X in Y dimensions and Z% accuracy in a random forest model

I've been doing some Machine Learning as a hobby and am playing around with Random Forest models and basically trying to apply that towards predicting things in my own life. So I have a series of ...
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2answers
42 views

Confidence interval for Population proportion

I've a small query and really confused as how to solve such problems. $n$ people are question about internet connection 87 of them have high speed connection. We are given confidence interval(CI) of ...
2
votes
1answer
25 views

How to define Confidence Intervals from a distribution of 1000 t-statistics?

I have a vector of length 300 containing some kind of values (say, scores of a math test). The distribution is not normal. I want to test if the average score of a small group (30 samples) is ...
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1answer
18 views

Picking the top 10 answers from a survey

I ran a survey on a population of advisors in all the different recruitment centers of in a country. I had 1410 text written entries (not multiple choice) I took a sample of 284 to see what are the ...
3
votes
1answer
54 views

Wald test and Likelihood ratio test, where do the confidence intervals on the regression coefficients come from?

So I'm trying to build my own Wald test and likelihood ratio test code within a machine learning pipeline. I can get the final fitted logistic regression coefficients from liblinear. I'm coding in ...
8
votes
2answers
135 views

Understanding shape and calculation of confidence bands in linear regression

I am trying to understand the origin of the curved shaped of confidence bands associated with an OLS linear regression and how it relates to the confidence intervals of the regression parameters ...
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0answers
53 views

Why are confidence intervals for predicted values so large?

The data for this question can be downloaded with this code: ...
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2answers
85 views

Drawing pair of cards. Did my brother play fair or unfair?

The Game There is a pool of $n$ cards that are marked either by a A or by a B. There is a proportion $p$ of the cards that are ...
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0answers
12 views

Is it possible to calculate the confidence intervals of eta-squared manually

Could you give me a set of formulas which I can use to calculate the confidence interval of eta-squared manually? I found some formulas in this paper: http://www.jstatsoft.org/v20/i08/paper (pages 12 ...
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0answers
10 views

Testing presence of one outcome over another

I have what I think is a simple problem, but I can't seem to think of how to test it. I have a sample of 2649 patients, of whom 125 have a specific disease. The disease is classified into "early" ...
0
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0answers
45 views

Confidence Intervals for AUC using cross-validation

I am analyzing the performance of a predictive model with the AUC, area under the ROC curve. I repeat several times cross-validation, and I have different estimations of the AUC in each folder. For ...
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0answers
30 views

Confidence interval in EVT

I'm working through a Power-Point presentation about extreme value theory with application to finance. My question is about a technique to calculate the confidence interval of a $k$ $n$-block return ...
4
votes
1answer
75 views

Why not always use bootstrap CIs?

I was wondering how bootstrap CIs (and BCa in barticular) perform on normally-distributed data. There seems to be lots of work examining their performance on various types of distributions, but could ...
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vote
2answers
63 views

Large overlap between confidence intervals, although z test for difference was significant

I have calculated a z test to examine the difference between two proportions. I found differences to be significant. The formula I used was: $$z = (p_1-p_2)/SE$$ where $$SE = \sqrt{ p ( 1 - p ) ( ...
2
votes
1answer
60 views

Confidence Interval for Percentile for Empirical Distribution

I have a bunch of raw data values that are dollar amounts and I want to find a confidence interval for a percentile of that data. Is there a formula for such a confidence interval? Thanks for any ...
4
votes
2answers
84 views

Why do the 95% confidence limits in ARIMA models widen at the forecasts?

Can someone please explain why when I do an ARIMA model the forecast's 95% confidence interval widen?