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

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25 views
+100

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 ...
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1answer
16 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
16 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
8 views

Compute confidence cutoff for scatterplot

I have data collected from two different individuals for different treatments, like this: ...
2
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0answers
48 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
357 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 ...
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1answer
22 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
43 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
6 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 ...
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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 ...
2
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1answer
28 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
22 views

Dealing with studies with no cases in meta-analysis

I am meta-analysising the following data by age range: ...
3
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3answers
133 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 ...
0
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1answer
14 views

Confidence Interval for 5% Lower Limit

For a normal distribution with a mean of X, and a standard deviation of SD, the 5% lower limit of the population is computed as X-1.645*SD. Meaning, 5% of the population will not reach that level. ...
2
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0answers
12 views

Hypothesis testing: 95% confidence intervals of group means overlapping zero or 83% confidence intervals?

I am trying to select between the following two methods to look for significant differences between two abundance estimates: 1) calculation of the 95% confidence interval for the difference between ...
3
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1answer
32 views

Distribution of pivotal quantity

I'm attempting to determine whether a pivot can be used to construct a confidence interval for $\theta$ given that observations are iid and from the distribution below. Specifically: $f(x \mid ...
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0answers
16 views

p-test for parameter

Statisticians, number magicians, I was wondering what the best way is to check for the equality of two parameters including possibly a confidence interval and p-value. $$H_0:\beta_1=\beta_2\vert\ ...
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0answers
14 views

How do I / should I calculate confidence interval for one set of data?

I am working with two very small sample sizes of 8 and 12 and I know the actual populations 15 and 40. Each population rec'd a survey where they answered a set of questions all focused on how much ...
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0answers
45 views

What is the name of this distribution family?

I am trying to identify this probability density function so I can read up on it to find confidence intervals for $\theta$: $$f(x;\theta,v)=\frac{\theta v^\theta}{x^{\theta+1}}I_{[v,\infty)]}(x);\ ...
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0answers
27 views

Confidence Intervals of a Given Width

I'm working through some questions on confidence intervals. My answer doesn't match the book, but the book's answer was a number I had a few steps before the end. I have ten numbers which are a ...
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0answers
42 views

Dependent Bernoulli trials confidence interval

I would like to know if there is a way to build a confidence interval, for a random variable which has a Bernoulli distribution, based on its history. I mean if the order of its states is 11100 (i.e. ...
1
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0answers
59 views

95% CI in nonlinear mixed-effect model {lme4} with two or more crossed random effects

I have fisheries-independent data and am interesting in estimating maturity patterns across 50 lakes that are sampled (with bias) by 4 types of gear-collections. The sampling pattern is very ...
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0answers
35 views

Stability of boostrap confidence intervals

As a word of background, I want to show that certain result is stable when averaging over a large number of simulations, but could be just a lucky draw with a small number of simulations. I have a ...
3
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0answers
29 views

Confidence interval of the mean response from nonlinear model

My problem (question at the end) is to calculate confidence interval (CI) (NOT prediction interval) of the response of a nonlinear model. I am working with R but this question is not R-specific. I ...
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0answers
16 views

Confidence intervals and functions of an estimator

Im studying non-parametric estimators for survival functions and for the Nelson-Aalen estimator we have that the estimator for the survival function is exp(-Y_hat) (i.e. exponential of negative "y" ...
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0answers
22 views

Linear Regression: Confidence Interval for X

So I'm working with the following data set. ...
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1answer
35 views

Equation for Confidence Interval of Linear Regression

I've done a multivariate linear regression. The results specify each parameter and the 95% confidence interval for each parameter. I did this using Python and StatsModels (not that it matters), and ...
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0answers
33 views

How likely is it, that a value belongs to a given distribution?

I'm struggling with this question: I created 100 random data sets and the results are normal distributed. This data will be my null hypothesis. Now I want to check, if an observed value belongs to ...
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0answers
24 views

The theory behind Confidence Limits [closed]

In class we've just started on the topic of Confidence Limits. Now I know what confidence limits are and how we can find them on a set of data (Normal data, Random Sampling). Now I just don't know the ...
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4answers
318 views

Confidence intervals when the sample size is very large

My question could be rephrased as "how to assess a sampling error using big data", especially for a journal publication. Here is an example to illustrate a challenge. From a very large dataset ...
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0answers
52 views

Relative size of p value at different sample sizes BUT same odds ratio

Will the relative size of the p-value increase or decrease with the increase of sample size? My guess is that it will decrease, however, would it be the same case if they both have the same odds ratio ...
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0answers
30 views

Calculating probability that a future observation falls within a given interval

I am brushing up on statistical theory to keep my mind active, and I have a question about confidence intervals. Given a normal distribution with unknown mean $\mu$ and known variance 1, I know that ...
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1answer
23 views

How are sample size and confidence related when calculating Sample mean?

Maybe I'm getting ahead of myself and I should just keep reading my textbook, but I'm getting confused about something. Let's say a friend gives me 10,000 integers that he claims are normally ...
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1answer
23 views

Confidence Interval For Mean By Bootstrapping

The standard deviation in my original sample is very large, about 100 or so. I took many bootstrap samples, found the mean of each bootstrap sample and then took the mean of these means. I found the ...
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2answers
98 views

difference between qt and qnorm

Can you tell me what is the difference between qt and qnorm? From my understanding, qt is used for small sample, and qnorm is use for large sample. Am I correct? If yes, how do I know whether my ...
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1answer
24 views

Comparison method for curves using percentiles

I have a question regarding the use of quantiles for determining the enveloppe of a curve. This is what I am doing: I have a continuous variable ("var") that I turned discrete using cut ("var_cut"), ...
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0answers
13 views

Randomization test inversion for completely randomized design versus AB phase design

I am trying to write R code to invert a randomization test in order to produce a confidence interval for the employed test-statistic. The code is quite similar to what can be found here: ...
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1answer
56 views

Confidence intervals for ordered probit [closed]

I'm attempting to compute confidence intervals for an ordered probit. I am a graduate student and it was suggested as one of the tasks to add to my final paper. I have found a few papers discussing it ...
2
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1answer
36 views

How can I compute the lower and upper bounds of a confidence interval in a linear regression problem?

I am completing a university statistics assignment on the Mathematica program, and this is the initial question: "The Medical Research Council wanted to evaluate the effects of different dosages of a ...
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1answer
27 views

Confidence interval for correlation

I know the confidence interval of an estimated correlation can be calculated after performing Fisher transformation. But I never figured out why. I also couldn't find the explanation online. Can ...
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0answers
12 views

How to determine how many simulations to run, in order to illustrate “extreme-valued statistics”?

As an engineer trying to learn statistics, I wonder if someone could please recommend references / a statistical method that may assist with determining the number of simulations that need to be ...
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0answers
5 views

Ancillary statistic in exact tests

I have been reading about use of ancillary statistic in hypothesis testing. For e.g. To test variance the test statistic is chi sq distributed and is independent of variance. (Please correct me if I ...
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0answers
30 views

What impact does a higher $R^2$ have on the precision of the CI?

I attended a seminar today at which the presenter mentioned that a higher $R^2$ would, all other things being equal, produce a narrower confidence interval. Is that true, and if so then why? Google ...
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1answer
27 views

Can a proportion confidence interval be thought of as error of estimation?

One interpretation of a confidence interval for a mean is that the most plausible position of the mean (given no more information) is in the middle of the confidence interval, and the plausibility ...
0
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1answer
37 views

Apparent paradox about using a pilot study to determine sample size

I'm using some pilot data to determine the necessary sample size for an upcoming study. The primary goal of this study is to measure the correlation between two variables, A and B, and to determine ...
2
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0answers
40 views

drawing confidence interval graphs [migrated]

I've made regression model with 4 variables. And I have gotten the following regression equation $$ Y= 0.0761 - 0687X_1 - 3.46X_2 - 1.937 X_3$$ I calculated Confidence intervals for these four beta ...
7
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6answers
226 views

What are good examples to show to undergraduate students?

I am going to teach statistics as a teaching assistant for the second half of this semester to CS-oriented undergraduate students. Most of the students took the class has no incentive to learn the ...
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1answer
68 views

Why do we need confidence intervals?

I am following a video lecture on Statistics, which introduces the concept of confidence intervals in the following way: "A bank vice president is interested in the average checking account balance ...
2
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1answer
29 views

confidence intervals around lines from glmer in lme4

I have spent a large amount of time trying to figure out how to generate a desired plot, and was wondering if any one can help. The plot is to illustrate an interaction between 'time' and 'group' on a ...