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

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1answer
189 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 ...
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0answers
9 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 ...
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0answers
15 views

Cost/Benefit of BootStrapping CIs for dependent samples, but unequal number of observations

In the experiment, subjects were equally exposed to two conditions: 100 of condition_a and 100 of condition_b. A pre-determined response criteria created an unequal number of observations. Thus, no ...
3
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1answer
27 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
6 views
1
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0answers
19 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
9 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 ...
6
votes
2answers
92 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
votes
1answer
67 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
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2answers
49 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
29 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 ...
3
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1answer
28 views

R - lm how to get standard deviation coefficients

I have a very simple problem but I cannot find the answer anywhere. I run a linear model with lm() and I want the standard deviation coefficients in order to compute the confidence interval. I know ...
3
votes
1answer
107 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 ...
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0answers
9 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 ...
18
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2answers
203 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
votes
1answer
116 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
33 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
32 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 ...
3
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1answer
51 views

Are 10 experiments measuring 1 random variable “similar” to 1 experiment measuring 10 independent random variables?

I have some teammates that like to "measure everything" and want to decrease confidence intervals. I'm trying to intuitively understand where things can go wrong with this approach. Assuming a 90% ...
2
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0answers
23 views

Graph bootstrapped joint CI of two statistics in R

I have estimated a mixed-effects logistic regression with glmer and want to draw a bootstrapped confidence-region for the mean predicted probability for two subgroups of the sample. I have a $1000 ...
2
votes
1answer
33 views

How to build a confidence interval with only binary test results?

What would be the most sensible way to build a confidence interval if I have no other information than a the number of successes and failures with an experiment ? Is it possible to make some ...
0
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0answers
11 views

How To Calculate and Print CDF and Lower Bound CDF value for some t (time) with Minitab (without examining the plot)

I'm a reliability engineer. Cumulative Distribution Function (CDF) in statistics stands for the unreliability (probability of failure at a time value) of the item being tested. Unreliability is very ...
0
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0answers
7 views

Hotelling's one-sample T2 statistic

I wanted to determine if a new sample is within reasonable bounds of the mean of an approximately normally distributed sample of points. I want to use Hotelling's $T^2$ statistic to obtain a ...
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0answers
23 views

Confidence Intervals of regression line when flipping x and y

If the origin doesn't enter the confidence interval of a regression line of y on x, will this always still be the case if I switch to x on y?
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0answers
24 views

Line chart with means and CIs in Stata [migrated]

I have a data set with effect estimates for different points in time (for 1 month, 2 months, 6 months, 12 months and 18 months) and its standard errors. Now I want to plot the means for each period ...
8
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2answers
167 views

Biased bootstrap: is it okay to center the CI around the observed statistic?

This is similar to Bootstrap: estimate is outside of confidence interval I have some data that represents counts of genotypes in a population. I want to estimate genetic diversity using Shannon's ...
3
votes
1answer
47 views

LDA, Tukey HSD: little questions from a chemist

As you may know, analytic methods like PCA or LDA are used everywhere in science. In my case, I'm a chemist, and I use it to differentiate molecules. I have 4 different systems (let's call them A, B, ...
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0answers
8 views

Geometric Mean Standard Error [duplicate]

I read from wikipedia that the geometric standard deviation is $$\sigma_g = \text{exp}\left( \sqrt{\frac{\sum_{i=1}^n\left(\frac{A_i}{\mu_g}\right)^2}{n}}\right)\,, $$ where $\mu_g$ is the geometric ...
3
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1answer
28 views

Confidence interval for exponential distribution

Let $X_1,...,X_n$ random sample of $X$~$exp(\theta)$. i) Find a exact confidence interval for $\theta$ with coefficient of confidence equal to $\gamma$ ii)Find a asymptotic confidence ...
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2answers
56 views

Find the confidence interval, uniform distribution

Let $X_1,..,X_n$ a random sample of $X$~$U[-\theta,\theta]$, $\theta>0$. Find the confidence interval for $\theta$. I'm trying to find a pivotal quantity with the maximum and minimum, but I ...
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0answers
30 views

Confidence interval for mean

At any given laboratory are built countless 95% asymptotic confidence interval for mean of some indicator. Suppose indepence between the samples for construct each of these intervals,what is ...
1
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1answer
41 views

Confidence intervals of coefficients of multiple regression

With following model of mpg vs other variables in mtcars dataset: ...
0
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0answers
12 views

How to assess accuracy of phone GPS in measuring distance run on a 400m track, at a given speed?

Just read How to assess accuracy of phone GPS in measuring distances? and I was wondering in anyone fancies taking it a bit further and propose a solution for estimating the intervals / error expected ...
2
votes
2answers
74 views

Lagrange multipliers and confidence interval

Suppose $X_1,...X_n$ is a random sample from $X$~$N(\mu,\sigma^2)$, with $\sigma^2$ unknow. If $$[\overline{X}+z_{a_2}\frac{\sigma}{\sqrt{n}};\overline{X}-z_{a_1}\frac{\sigma}{\sqrt{n}}]$$ ...
3
votes
1answer
69 views

R: glm(…,family=poisson) plot confidence and prediction intervals [closed]

I could not find many information on how to plot a confidence interval and a prediction interval for a Poisson regression (for example with glm()). What are some ...
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0answers
41 views

Constructing 95% confidence intervals of coefficients in ARIMA model

For the recurrence relation below I simulated it in R with arima.sim and used arima.sim(data, order=c(2,0,2)) to estimate the coefficients. $x_t = x_{t-1} - \frac 13 x_{t-2} + w_t + \frac 14 ...
0
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0answers
20 views

Confidence Versus Prediction Intervals using Quantile Regression / Quantile Loss Function

If you fit a quantile regression for the 5th and 95th percentile this is often described as an estimate of a 90% prediction interval. This is the most prevalent it seems in the machine learning domain ...
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0answers
44 views

How to construct a 95% confidence interval without knowing the number of successes?

I apologize if this question has been asked before, but I did not see any similar. Problem: "A production line is supposed to operate with a mean filling weight of 16 ounces per container. Since ...
3
votes
1answer
44 views

Confidence interval on point biserial correlation coefficient

How can I calculate the confidence of a point biserial correlation coefficient? I'm calculating the point biserial correlation between a continues variable (score on a test), and a dichotomous ...
0
votes
1answer
39 views

Fitted Confidence Intervals Forecast Function R

I am using the forecast function in R written by Rob Hyndman. I am trying to determine the best way to determine confidence intervals for the historical fitted values. I would like to plot how often ...
0
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0answers
11 views

Obtaining wide Confidence Intervals from a fitting of a model with 2x2 Crossover trial data. Where am I going wrong?

I am doing an analysis of a 2x2 crossover experiment with ordinal output. And it seem that the effect of the treatment (trt) is statistically significant. However my CI are very wide [1.05, 364.23]. ...
3
votes
1answer
58 views

R lmer confint: theta values not the same as summary values

I've been using lmer's confint procedure to compute bootstrapped confidence intervals for random effects. I noticed that extracting the theta values using "getME" produces estimates that are slightly ...
1
vote
1answer
36 views

Largest or smallest confidence interval at $\pi_{i}=0.5$ in logistic regression

A binomial GLM can be written as: $Y_{i}\thicksim B(1,\pi_{i})$ $\mathrm{E}(Y_{i})=\pi_{i}$ and $\mathrm{var}(Y_{i})=\pi_{i}\times(1-\pi_{i})$ ...
2
votes
1answer
39 views

Confidence interval for known non-normal estimation?

Assuming I know the density of my random sample - for example: $$ f_\Theta(x) = \frac{e^{-x/\Theta^2}}{\Theta^2} $$ (but I care about general single parameter case) How can I obtain $1-\alpha$ ...
0
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0answers
19 views

Confidence interval for the difference of two proportions from small sample size

Suppose I have two trials with small sample sizes such that the event rate for the first trial is $p_1=2/25=0.08$ and for the second trial $p_2=3/20=0.15$. I am wondering what may be the best way to ...
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0answers
17 views

Interpretation of confidence intervals [duplicate]

CI(p) = (a, b) People sometimes interpret this interval by saying that there is a 95% probability that the true p belongs to (a, b) The statement is incorrect (there is no probability ...
0
votes
1answer
26 views

Confidence intervals for percentage share of multiple response

If I have a sample of 100, who give responses to a set of multiple response variables, say for example, the brands they have purchased in the last 12 months. How can I calculate the confidence ...
2
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0answers
15 views

Confidence and credible interval: cases

I am having difficulties in understanding these two approaches. Let's say given the data I compute both confidence and credible interval, then what is the intuition/interpretation of having: Big CI ...
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0answers
40 views

Confidence interval for function of the parameter - small sample size

I am trying to come up with a solution for this problem. Consider the following set of random variables: \begin{align*} X_{11},...,X_{1n_{1}}\quad &\text{i.i.d. Bernoulli(1-$e^{-\lambda_{1}}$)}\\ ...