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
22 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 $1-\alpha$ ...
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0answers
11 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
15 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
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1answer
19 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
10 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 ...
1
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0answers
34 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-$e^{-\lambda_{1}}$)}\\ ...
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1answer
95 views

How to calculate the relative risk based on two independent confidence intervals

Medicine A cures 30% of patients (95% CI: 17 to 45). Medicine B cures 15% of patients (95% CI: 10 to 20). So I can divide 30% by 15% and say that medicine A is twice as likely to cure the patients ...
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1answer
20 views

If a percent difference is (approximately) normally distributed, can I calculate the confidence interval of its mean with a t distribution?

I have measured the same variable at two time points. The variable is approximately normally distributed (this approximation is supported for the measures at both time points), and I have calculated ...
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2answers
73 views

Bayesian analysis: Estimate whether a parameter is 0 or not

I have the following problem: I need to assess whether a given parameter $B$ is equal to 0. Let's consider the following model (my problem is more complicated but I think that this example is ...
0
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0answers
14 views

Confidence interval for exponential moving average and variance

There are well known formulas for the exponential moving average and variance. Just for the completeness of the question, for each new x in a series of X(1..n) online EMA and EMVar can be estimated as ...
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0answers
29 views

Confidence interval, lower and upper bound

I am studying on confidence intervals, but I'm still with some doubts Let a random sample $X_1,..,X_n$ with density $f(x;\theta)=\theta e^{-\theta x}I_{[0,\infty]}(x)$. Find a confidence interval for ...
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0answers
26 views

Test of confidence intervals?

In one of my assignments I have to "test" if the confidence intervals (CIs) for a set of parameters in a mixed effect model is accurate. I'm asked to simulate from fitted parameters and after that to ...
2
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0answers
71 views

Confidence interval and probability

Suppose that $T_1$ is $100\gamma$ percent lower confidence limit for $\tau(\theta)$ and $T_2$ is $100\gamma$ percent uper confidence limit for $\tau(\theta)$. Further assume that ...
1
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1answer
41 views

Lower bound on the mean for an exponential distribution at a confidence level of 95%

for the life of me I simply cannot wrap my head around confidence intervals and upper/lower bounds on parameters. E.g $$ f(t;\tau) = \frac{1}{\tau} e^{-t/\tau}, \qquad t \geq0 $$ If $t=1$ (a single ...
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1answer
26 views

Confidence Interval, uniform distribution

Let $X_1,...X_n$ random sample from $f(x;\theta)=I_{[\theta-\frac{1}{2};\theta+\frac{1}{2}]}(x)$. i) Show that $(X_{(1)},X_{(n)})$ is a confidence interval for $\theta$.ii) find your ...
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1answer
26 views

coverage of confidence interval

I need to check the coverage of a confidence interval, but I don't know which one of the following approaches I should use. Approach 1: Estimate the regression parameter $\theta$ Use the sandwich ...
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0answers
53 views

Confidence interval of the mean for a beta distribution when alpha and beta are estimated [duplicate]

I have elementary knowledge in statistics. I'm trying to estimate the confidence interval for mean of a beta distribution as specified in this article using log likelihood estimation given alpha, beta ...
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0answers
37 views

Confidence interval or p-value? [duplicate]

I am working on an assignment and struggling with odds ratios and confidence intervals. I have the following data from a fairly dubious study about shift work and poor sleep quality: OR 1.2 95% CI ...
0
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1answer
14 views

How to scale up mean/variance and confidence interval of clinical trial for whole population

In a clinical trial I have 1000 patients with disease A. Their mean treatment cost is 1000$ per patient with a 95% confidence interval of [900;1100] for example. The whole population of country X is ...
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1answer
51 views

Confidence intervals vs. standard deviation

The 95% confidence interval gives you a range. The 2 sigma of a standard deviation also gives you a range of ~95%. Can someone shed some light on how they are different?
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28 views

Computing a single regression line with confidence intervals for multiple regression lines

I have multiple regression lines for individual groups (predicted values stored in a data set). I want to compute a single overall quadratic regression fit with confidence intervals for these ...
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0answers
24 views

Computing Required Sample Size to Control Type II Probability

Let $X_1, \dots, X_n$ be a random sample from $\mathcal{N}(\mu_0,\sigma^2)$, $\mu_0$ known, $\sigma$ unknown. Consider $H_0:\sigma^2=\sigma_0$ vs $H_1:\sigma^2=\sigma_1^2$ where $\sigma_1 < ...
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0answers
28 views

Find minimal value that is larger than true error

I have trained a classifier with a training set containing 1000 samples and tested the classifier with a test set of 1000 samples. I've also computed the following values: Test error: number of ...
0
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1answer
43 views

95% confidence interval for p in R

I have to construct a 95% confidence interval using R, but I'm completely lost :( This is the assignment: In a random sample of 200 claims filed against and insurance company writing collision ...
0
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1answer
24 views

Compute test error and std of a model

I would like to do the following: Train a classifier on a certain dataset Test the classifier on a certain test set Compute the test error and standard deviation Compute a 95% confidence interval ...
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19 views

Calculate Confidence Interval of Multiple Regression from Standard Error

From a multiple linear regression model I know the parameter estimates as well as the corresponding standard errors. I also know that the model is based on 96 data points. I'd like to calculate the ...
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0answers
12 views

Given an N-sided die, an error and a Z-value, how many throws do I need?

I have a random variable with an almost-but-not-quite iid distribution mapping to N different values. I wish to use the empirical distribution from k samples as the "true" distribution, and have ...
0
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1answer
13 views

Autocorrelation and Statistically Independent Samples

I'm trying to do an error analysis and I was asked to calculate the confidence intervals but was told that I need to calculate the true number of statistically independent samples for doing this. I am ...
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0answers
16 views

Data Interval Determination

I run a TV programme for 30 mins. That TV programme has, say 5 keywords, associated with it. I then measure the number of clicks those keywords received over that 30 min time window. The problem is ...
0
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1answer
31 views

Which of the following when performing a statistical test is NOT a Random Variable?

For a test for my stats class, we were asked, "When performing a statistical test on a sample, which of the following is NOT a random variable?" A) The Test Statistic B) the p-value C) The power of ...
2
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1answer
29 views

How would I create a 95% confidence interval with log-transformed data?

I have data for insulate material and fail times and need to create a 95% confidence interval for the mean failure of each material. However the data is log-transformed because the residuals were not ...
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1answer
35 views

Layman's explanation of bootstrap confidence intervals for a regression with percentile method

First of all, I am not a statistician. I only how to interpret stats and to do them with R, my understanding of the math/formulas behind them is virtually zero. With this said, I am looking for a ...
0
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1answer
41 views

Reporting pseudo p-values for bootstrap-estimated linear regression coefficients

I've just received peer reviews for an applied paper that reported a table of multiple linear regression coefficients. While I reported 95% confidence intervals for these coefficients, a reviewer has ...
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2answers
63 views

What is a Highest Density Region (HDR)?

In statistical inference, problem 9.6b, a "Highest Density Region (HDR)" is mentioned. However, I didn't find the definition of this term in the book. One similar term is the Highest Posterior ...
1
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1answer
36 views

Prediction uncertainty intervals for predictions of machine learning algorithms

Assume I have a regression problem. I fit models on a train data set and tune their hyperparameters using CV. I then run the models on the test set. What is the best way to calculate prediction ...
0
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0answers
14 views

Confidence interval odds-ratio matched case control

Consider having a list of pairs of binary data denoting observations from a matched case control study. The list may be used to set up a contingency table and an odds-ratio can be calculated by ...
0
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1answer
78 views

False Coverage Rate for confidence intervals of positive likelihood ratios of multiple dependent tests

I want to calculate confidence intervals of positive likelihood ratios of multiple dependent tests. To adjust the confidence level for the 'problem of multiple comparisons', I believe I should ...
1
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1answer
20 views

Finding z-scores from z table relating to confidence intervals

I'm having trouble finding the proper $z$ score so that I can find the $99\%$ confidence interval. $\bar{x} = 6.01231$. with an $s$ of $1.96833$ and $n$ of $26$, and I got $2.575$ for ...
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0answers
21 views

Estimating confidence intervals on count data from classifier output on varying populations

I have a widget factory which produces a varying number of widgets each day. Every day, I need to report the number of faulty widgets. But the proportion of faulty widgets is expected to change every ...
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0answers
14 views

Compute confidence cutoff for scatterplot

I have data collected from two different individuals for different treatments, like this: ...
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0answers
97 views

How to plot the confidence interval from boot.ci output of nonlinear regression in R?

I have a data.frame with two columns (x and y) for which I have obtained a nonlinear least squares fit: -a/(b+exp(-x)). Now I'm trying to plot the 95% confidence interval for y. My best attempt so ...
4
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1answer
378 views

95% confidence intervals and the null hypothesis

I have performed an unpaired t-test comparing the means of two groups. My hypothesis was that the stroke group mean would be significantly higher than the control group mean. However, the t-test ...
0
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1answer
26 views

A higher odds ratio but a broader confidence interval

I have derived two logistic models. one has just the predictor. Other has the predictor adjusted for few co-variates. The odds ratio of the predictor in the first model is 4.6 (1.39-16.70) and the ...
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0answers
20 views

Confidence interval syntax in frequentist probability [duplicate]

Let $\theta$ be an unknown population characteristic (say average height). A confidence interval written as $P(\hat \theta - \delta < \theta < \hat \theta + \delta) = 1 - \alpha$ makes perfect ...
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1answer
47 views

Confidence Interval Formulas

We are doing the topic confidence interval in class and I just wanted to confirm if my concept about it was clear. Single Population: $x \pm Z*$ $\frac{\sigma}{\sqrt{n}}$ Now this is used when we ...
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0answers
8 views

profile likelihood when a parameter is constrained to be non-negative

I would like to use the profile likelihood method to generate confidence intervals for a model with several parameters which are constrained to be non-negative. I was wondering if there is an easy way ...
0
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1answer
10 views

Deriving Confidence Interval from pivotal statistic

Using the pivotal statistic $T = \frac{Y ̄ −μ}{s/\sqrt{n}}$ derive the $(1 − α)100%$ confidence interval for the mean $μ$, where a random sample of size $n$ is taken from a very large population and ...
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1answer
38 views

Exploring a two-way interaction in multi-level regression, why do I get significant contrasts when the confidence intervals overlap on the graph?

I'm exploring a significant two-way interaction in a multi-level random-effects regression. The graph (below) appears to show the interaction is driven by differences at low X, and that at high X the ...
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2answers
27 views

Dealing with studies with no cases in meta-analysis

I am meta-analysising the following data by age range: ...
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3answers
269 views

How to interpret negative 95% confidence interval?

I have performed an unpaired t-test on two groups of data: Group 1 (control): mean = 0.087 (n = 15) SD = 0.028 Group 2 (treatment): mean = 0.115 (n=12) SD = 0.042 The t-test ...