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

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5 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
8 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
15 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
12 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
94 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 ...
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1answer
13 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. ...
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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 ...
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1answer
30 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
15 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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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
26 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
41 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. ...
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0answers
55 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
34 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
25 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
14 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
21 views

Linear Regression: Confidence Interval for X

So I'm working with the following data set. ...
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1answer
31 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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32 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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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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3answers
299 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
51 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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27 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
22 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
22 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
93 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
23 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
8 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
53 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
25 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
11 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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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 ...
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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 ...
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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 ...
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6answers
218 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
67 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 ...
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1answer
27 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 ...
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10 views

What does it mean for a function to be “contained in” a confidence band?

So I have this problem that asks me to generate 100 random samples from a standard normal, and I did. It asked me to find a 95% confidence band and I did, using the Python code ...
2
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1answer
36 views

Implementing Gibbs sampler in R from posterior distribution

I am referencing a follow-up idea from something I posted earlier (Zero-inflated Poisson and Gibbs sampling, proofs and sampling). I want to implement the Gibbs sampler, by generating a large ...
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0answers
5 views

Analytic determination of exact confidence intervals (without making approximations)

I would like to determine 95% confidence intervals for the mean of a negative binomial distribution. I have read a number of papers that use Gamma, Normal and Chi-squared approximations in order to ...
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2answers
127 views

Citation for Statistical test for difference between two odds ratios?

In a comment here, @gung wrote, I believe they can overlap a little (maybe ~25%) & still be significant at the 5% level. Remember that the 95% CI you see is for the individual OR, but the ...
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0answers
15 views

Boostrap confidence interval mixed model

I have have about 1000 data points (x,y,z). I am fitting a mixed model to the data, using lmer in R model = lmer(z ~ x + I(x^2) + (1|y)) I am interested in ...
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0answers
49 views

bonferroni and scheffé' simultaneous confidence interval graph in minitab

I need to calculate bonferroni and scheffé' simultaneous confidence interval by hand as a homework. However, I also want to add minitab outputs and graphs to my homework task. How can I plot these ...
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0answers
5 views

Poisson parameter lambda confidence interval [duplicate]

Based on x arrivals in time t, what is the alpha level Confidence interval for lambda?
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0answers
14 views

Better approach to determining parameter error bars than my Monte Carlo approach?

I have a certain astrophysical phenomenon currently described by a few different models. For a given model I can expect a certain number of particles passing by earth as a function of time. From this ...
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14 views

Process interpretation of confidence intervals?

Frick (1998) explains how statistical inference can be interpreted as making causal claims about processes, without resorting to random sampling and infinite populations. This view seems particularly ...