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

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28 views

Why Removal of Outliers Does not Affect Confidence Interval [on hold]

I have a question regarding why confint(), a function in R which returns a 95% confidence interval when applied to a linear model, returns the same result even when I remove the single greatest or ...
4
votes
2answers
114 views

Comparing a linear model with a spline model

I try to figure out how to describe my continuous variable. Unfortunately, I did not understand all of the statistics. I would really appreciate I you guys would help me out here. To better illustrate ...
0
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1answer
11 views

Confidence measure/statistic for inferring a category with random independent sampling

Suppose there's a group of dogs and a set of people A,B,C,D. If I know that, in this hypothetical scenario, the person who owns the dog is the person who walks it ...
0
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1answer
33 views

Bootstrap confidence intervals for regression and correlation coefficients

Take an example of a linear regression, $Y= \beta X$ where X and Y values are z-score transformed ($\mu$ = 0, $\sigma$ = 1). In this situation the correlation coefficient $r$ equals $\beta$ ...
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0answers
10 views

Testing Proportions of People Over Time

Let's say we have two time points (2013 and 2014 for sake of argument). In 2013, 50% of customers who come to my shop buy milk (100 out of 200 customers). In 2014, 75% of customers who come to my ...
2
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1answer
43 views

What is the distribution of the absolute difference between two points sampled from a normal distribution?

I have a normally distributed random variable $X$. I sample two points $x_1$ and $x_2$, and I am interested in the absolute difference between these two sampled points: $d=|x_2-x_1|$. I repeat this ...
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1answer
25 views

How to combine 2 unpaired t tests that test the same effect

I have am studying an effect that degrades device quality and performed an independent sample test on two batches that had different initial quality. I would like to make the strongest statement ...
0
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1answer
16 views

What is the meaning of Confidence Intervals regarding Hold Out samples?

Let's say you have a regression model that estimates GDP. Your model has a Standard Error of 1%. So, you can readily build Confidence Intervals around your regressed estimates. Your 95% CI will be ...
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1answer
33 views

How do I define a confidence band for a custom (nonlinear) function?

I am struggling to calculate / define confidence bands to use with a custom function that I must fit to my data. I have seen plenty of examples for standard models (linear regression, log functions, ...
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0answers
22 views

Calculating probability of sale from auction data

I have some data representing the last 6 months of closed auction data from a particular website. The data I have includes market value of product, actual sale amount, and date sold. I have about 600 ...
1
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2answers
16 views

Confidence interval question when population SD known

Im trying to understand why we can have situations where when trying to find a confidence interval we can know the population standard deviation but not the mean ? If I know the standard deviation of ...
1
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0answers
12 views

Confidence intervals for Kendall's tau-b

I am working on some stats coursework, and have non parametric bivariate data. n=19, so small sample. There are a number of tied ranks, so I'm planning to use Kendall's tau-b rather than Spearman's, ...
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0answers
20 views

Confidence interval for a mean over hierarchical data

What is a good method for producing confidence intervals when computing a mean over hierarchical data? Specifically, I have the text messages sent by group of people and I want to compute the mean ...
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0answers
52 views

How to prove features are independent and can also be vector [closed]

I have samples strings where each one is composed of alphabets and numbers. Using variable 1 i calculated value of each string. similarly i generated a random string and computed its value using ...
2
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1answer
20 views

back transforming confidence intervals

Purpose: Construct a 95% confidence interval for $\theta$. A common strategy is to construct a confidence interval for $\log(\theta)$ and then exponentiate. Why is it valid? My concern is that ...
4
votes
1answer
23 views

Confidence interval for the odds ratio in a finite population

Does it make sense to estimate a confidence interval for the odds ratio / logistic regression model when the sample size is nearly equal to population size? For example, if the sample size is 50 and ...
4
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0answers
30 views

Confidence interval for GLM or the maximum of a function?

Imagine I have a set of (xi,yi) measures. I can show it on a scatter plot I want to choose the value of x that maximizes y, or I could fit a function and find the values of the parameters that ...
0
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0answers
33 views

confint.merMod: Wald, profile, and boot COMPLETELY disagree

So this is either going to be straight forward or else a huge mess. I am finding that bootstrap CI for my glmer models are really wacky-- in fact, they don't even include the point estimates from the ...
3
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1answer
64 views

Significance/confidence intervals for PCA or factor loadings - how can such be defined?

Current discussions here in SSE made me to reconsider the PCA and FA models and procedures. I got curious how one would determine confidence intervals for the components/factor loadings by assuming ...
0
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0answers
35 views

Application of probability-inequalities in machine learning. Hoeffding's inequality

I would like to know a illustrative example of Hoeffding's inequality in machine learning? Does it have something to do with confidence intervals? Thanks in advance!
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0answers
28 views

click through rate stats

I have a group of 10 users. Each user receives a daily notification for one week. Ideally, each user will click on all notifications received. At the end of the week I collect the number of clicks per ...
5
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0answers
67 views

How to compute and interpret the confidence interval on a QQ plot

I often see QQ-plots with a confidence interval: For my application, I have a QQ plot of test p-values against a uniform distribution. I want to add the 95% CI of the observed p-values on the plot, ...
2
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0answers
14 views

Hypothesis test based on (random) result of previous experiment: can I multiply confidence levels?

Consider an i.i.d. sequence of Bernoulli random variables $\{Z_i\}$ with Bernoulli parameter $x$. By a certain procedure (experiment A) I obtain a random set S such that $\mathrm{Pr}[x \in S] \geq ...
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1answer
35 views

How to use Hoeffding's Inequality to find a confidence Interval?

I want an example that shows how to use Hoeffding's inequality to find a confidence interval for a binomial parameter p (probability of succes). Thanks in advance!.
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0answers
15 views

Are there any circumstances under which a confidence interval can be interpreted as a likelihood interval? What are they?

I read the answers provided to the question "are all values in a 95% confidence interval equally likely?". These answers raise questions for me regarding interpretation. I have read that under ...
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1answer
79 views

Proof: $T \sim \chi^2(N-1)$

I'm a maths student, this is my first statics class and I'm studying Confidence Intervals. When it's time to estimate the CI for the mean of $\{X_i\}_{i=1..N}$ - gaussian random variables i.i.d. with ...
2
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2answers
98 views

Ratio of standard deviation to mean

Let's say that we have a confidence interval like this: µ ± σ, where σ is the standard deviation and µ is the mean. I want to know if the ratio σ/µ has any interpretation? Does it mean anything if we ...
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0answers
5 views

Mean accuracy confidence intervals with “corrected resampled t-test statistic”

I'm interested in calculating the expected prediction accuracy of my machine learning algorithm. My datasets only contain a small number of sample, so to do this, I repeat k-fold cross validation ...
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1answer
24 views

Do confidence levels' ranges have a high correlation with prediction error

I've created four linear regression models each with different variables. I looked at the error rate: (actual-prediction)/actual and also on the confidence levels (90%). I've noticed that there is ...
1
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1answer
16 views

Distance between Vectors with Confidence Intervals

I have a machine learning application where I extract numerical features $a_{i1}, a_{i2}, \dots, a_{ik}$ for each object $a_i$ to study. Objects are then compared using standard euclidean distance. ...
1
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1answer
20 views

Combining confidence intervals from several regression point estimates

I have 13 point predictions from 13 independent linear regressions, each prediction with a 95% confidence interval. I want to sum the 13 predictions and calculate the 95%CI for the summed value. ...
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0answers
26 views

What causes differences in estimates of 95%CI of the mean across subgroups in Stata?

In the small reproducible example, I'm calculating mean of a variable across three groups: ...
2
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1answer
206 views

Interpretation of a 95% confidence interval calculated via bootstrapping?

I've been thinking about what exactly a 95% confidence interval means when it is calculated via bootstrapping. The formal definition of a 95% confidence interval is something like this: "if the ...
1
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0answers
10 views

How to calculate effect size confidence interval with multiple replications at multiple sites?

Let’s say we have an experiment at one location evaluating the effect of some sort of treatment on a control condition (n=4). We calculate the effect size as (Treated – Control)/Control*100. So for ...
3
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1answer
31 views

Is there a method to form a CI based on an MLE which is not the mean

I know how to find confidence intervals for parameters based on sample means. I want to know whether there exists a method for finding confidence intervals based on MLE's which are not sample means. ...
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0answers
7 views
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0answers
20 views

Plotting cumulative average means in ggplot2 [closed]

I want to depict the result of several replications (mean, confidence interval) ...
1
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0answers
12 views

Generating predicted mean values and CIs across different groups in lme4

I’ve run a mixed-effects model with crossed random effects in glmer and ultimately want to show a bar graph depicting mean predicted values (and associated confidence intervals) across years within ...
8
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2answers
101 views

Interpretation of confidence interval

Note: apologies in advance if this is a duplicate, I didn't find a similar q in my search Say we have a true parameter p. A confidence interval C(X) is a RV that contains p, say 95% of the time. Now ...
5
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1answer
74 views

Are group effects in a mixed effects model assumed to have been picked from a normal distribution?

Say we're interested in how student exam grades are affected by the number of hours that those students study. We sample students from several different schools. We run the following mixed effects ...
5
votes
2answers
51 views

How do I include measurement errors in a Bernoulli experiment?

I would like to understand how to combine a known measurement error in a Bernoulli experiment with the confidence interval in order to calculate error bars. I am performing an experiment that has two ...
1
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1answer
35 views

Using Fieller's theorem to calculate the confidence interval of a ratio (paired measurements)

If you have two means (with their own confidence intervals) and want to represent them as a ratio, how do calculate the confidence interval for the ratio? An answer that was given to me, mentions ...
4
votes
2answers
52 views

How to generate confidence bands for $\hat{Y}$

Suppose I run a linear regression model. I am interested in generating prediction intervals. The predicted values are easy to compute, but how can I compute the standard deviations for each of the ...
3
votes
1answer
122 views

Confidence Interval of a Lognormal Random Variable

Just learning some stats, so please forgive if this is simple but I couldn't find a good explanation. Let $X \sim \mathcal{N}(\mu,\sigma^2)$ and $Y = e^X$. To find an approximately 95% confidence ...
2
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0answers
14 views

Calculating and plotting confidence interval for Theil-Sen estimator

I'm using Wilcox's R functions (specifically, regplot) to plot a Theil-Sen estimator with a single predictor. However, regplot ...
20
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2answers
215 views

confidence intervals' coverage with regularized estimates

Suppose I'm trying to estimate a large number of parameters from some high-dimensional data, using some kind of regularized estimates. The regularizer introduces some bias into the estimates, but it ...
9
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1answer
120 views

How can I compare 2 means that are Laplace distributed?

I want to compare 2 sample means for 1-minute-stock returns. I assume they are Laplace distributed (already checked) and I split the returns into 2 groups. How can I check whether they are ...
1
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1answer
42 views

How can a 95% confidence interval not overlap with my trendline forecast?

I used holt winters in excel to forecast 12 moths ahead based on 40 months of historic data. Then I ran a monte carlo simulation to create 1000 scenarios and computed upper and lower bounds to create ...
1
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1answer
34 views

How accurate is my simple description of a confidence interval?

Here's my simple words-only description of a 95% confidence interval for the mean. How accurate is it? the sample mean comes from a distribution of possible sample means the sample mean might have ...
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0answers
36 views

“Luckiness” measure for series

I have the following game: One player drops a coin N times. The probability of heads for each experiment is different and equal Pn. All probabilities are known(Actially there are only 10 different ...