An interval of random variables, depending on observed data, which, with a fixed probability, contain an unknown parameter of interest.
4
votes
2answers
131 views
Boston University School of Public Health web page on confidence intervals [duplicate]
I'm wondering about the correctness of the Boston University School of Public Health's web page on confidence intervals, particularly the interpretations. For example, specific interpretation ...
2
votes
0answers
53 views
Regression model where errors are not normally distributed
From a Physics equation I have the following model:
$$W=\beta_0+\beta_1Z$$
$\beta_0$, $\beta_1$ are fixed values for which I want to find a $1-\alpha$ confidence region.
I have ...
1
vote
0answers
26 views
A non-statistician reference for confidence-interval Vs credibility-interval interpretation
As a beginner statistician, discussing the need to be accurate with the interpretation of statistical results with non-statistician is not an easy task. In particular, I am trying to convince some ...
0
votes
0answers
28 views
Determining Confidence Intervals from Measured and Predicted Data
I'm a long time visitor to this site and first time poster. My question is pretty basic...
I currently have a proprietary regression model with measured laboratory data being used as the reference ...
3
votes
3answers
119 views
Given a 95% confidence level, how do I demonstrate 95% of the intervals actually contain the population mean?
Let me say first off that I'm consistently impressed with the quality of responses on this site. You folks have done a better job of explaining difficult concepts than most instructors or textbooks ...
1
vote
0answers
50 views
Linear Equation System with Random Coefficients
I want to find a 1-$\alpha$ confident region for a value $\left(\Gamma_1,\Gamma_2\right)$. (Which are not random variables)
I can obtain diferent $m_i$ and $b_i$ that satisfy ...
1
vote
0answers
35 views
Logistic regression, “sum” confidence interval
I have an existing fitted logit regression model.
Model:
$\hat{p}(x)=\frac{1}{1+e^{-\hat{\beta}x}}$
With parameter estimates $\hat{\beta}$, and observation $x$
Given a new set of datapoints ...
4
votes
1answer
32 views
68% Confidence level in multinormal distributions
I wanted to create some contour plot to give confidence level say at 68% and 95% of some 2-dim multivariate normal distribution. (later I will have to go to 3-dim). I was wondering whether there was ...
1
vote
0answers
64 views
How to test the accuracy of a predictive model?
I am trying to find the best way to test the accuracy of a predictive model for the outcome of a game between two random teams. The model presents a chance for each game that team A will win (win ...
2
votes
1answer
71 views
Inverting a hypothesis test: nitpicky detail
First timer here. I'm reviewing a section of Casella and Berger on inverting a hypothesis test to get a Confidence Interval (CI), and came across a proof which I believe is missing a tiny piece. ...
0
votes
0answers
40 views
Should I convert bootstrapped confidence intervals for logistic regression coefficients (betas) to CIs for odds ratios (ORs)?
I have bootstrapped my multiple logistic regression model. SPSS does report OR and its confidence intervals for a non-bootstrapped multiple regression, but when it bootstraps the same model, it just ...
2
votes
0answers
40 views
Combining confidence intervals
I have a collection of efficiency curves i.e. numbers between 0 and 1 as a function of a physical variable. Each efficiency point on the curve has an associated Clopper Pearson 1-sigma confidence ...
2
votes
0answers
37 views
Why do (a lot) fewer than 95% of my confidence intervals intersect the true parameter value in this simulation?
Why are my confidence intervals performing so poorly?
I have a data frame may of two variables $C$ and $F$. I perform a linear regression
...
0
votes
0answers
47 views
Finding the mean difference of two data sets in R, within a confidence interval
I'm analysing benchmark data for some of my R functions, and I'm trying to compute a statistic describing how many times faster my function - group_one - is than a control function - group_two - as a ...
2
votes
1answer
60 views
Confidence Interval for squared term evaluated at the mean in Stata
When running an OLS regression with a squared term,
$$
y = a + b_1(X) + b_2(X^2) + e
$$
I know that the partial effect of $X$ is $b_1 + 2b_2(\bar X)$ to get the overall effect of $X$ on $Y$ evaluated ...
2
votes
0answers
46 views
Confidence intervals for glmer() from lme4
I'm running a mixed model on some data. I want to calculate confidence intervals for my model.
For this I have adapted the following code section from Predictions and/or confidence (or prediction) ...
0
votes
0answers
34 views
Confidence Interval for the Population
My (basic) understanding of a 95% confidence interval is that it is the interval within which the sample mean would fall 95 times should you take 100 random samples from the population.
My query is ...
1
vote
0answers
49 views
Deriving a “confidence relationship”?
I understand the basics of confidence intervals, the central limit theorem, etc, to be able to know things like given N samples of random variable, we're 68/95/99.7 percent sure the variable is within ...
0
votes
0answers
7 views
Can parameter uncertainties be salvaged when the residuals are correlated? (Tweaked, reasking)
I have a nonlinear physical model for which I'm trying to determine parameter uncertainties using Monte Carlo. Instead of describing the nitty-gritty details, I will use a series of figures:
...
1
vote
0answers
19 views
How to determine the Forecast Interval beyond the next period.
I like to establish a confidence interval my custom-made forecasting model (not one of the standard ones in the forecast package, which include the interval). The ...
2
votes
0answers
54 views
Role of coefficients in model selection for logistic regression
I have a model that I am using to predict mortality and it gives me an AUC of 0.799. The R code that I am using would look something like this:
...
2
votes
1answer
41 views
Uncertainty from Box–Cox estimation
Consider the model
$$
Y_i^{(\lambda)} = \alpha+\beta x_i + \varepsilon_i,\qquad \varepsilon_i,\ (i=1,\ldots,n) \sim \mathrm{i.i.d.}\ N(0,\sigma^2)
$$
where
$$
\begin{align}
y_i^{(\lambda)} & =
...
0
votes
1answer
45 views
I study subpopulation so huge that chi-squares test insists it is not representative. How do I get confidence intervals for my population?
I want to get results about population A. But all I can study is subpopulation C of B, where B is a subpopulation of A (that is, C $\subset$ B $\subset$ A). Each member of A is classified into one of ...
0
votes
1answer
39 views
How do I use a mean and 95% confidence intervals to draw from a distribution? [duplicate]
I have a number of parameters for a model. The parameter values are presented as the mean and the 95% confidence interval. I am not provided with standard deviation or sample size.
I am using R. I ...
2
votes
1answer
61 views
Can Agresti-Coull binomial confidence intervals be negative?
According to http://www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm
Agresti-Coull intervals cannot be negative; however using the formula from Wikipedia as well as the binom.confint function ...
3
votes
1answer
60 views
Statistical tests when each variable in a sample is a percentage
I am performing a temperature preference test in mice. Mice are placed into a chamber with one half of a chamber having a cold floor and the other half having a warm floor. Mice spend a specific total ...
1
vote
1answer
56 views
Bootstrapping to find confidence intervals. Very small sample size
I am trying to generate confidence intervals for estimates of numbers of fish observed with a very small number of surveys. Most of the numbers of fish observed are very small as well.
The estimate ...
4
votes
1answer
99 views
Confidence error bars and “central point”: Should we emphasize the median?
Say I want to plot summary data with a point and a 95% confidence interval around that point. What should my point really be? Mean, mode, or median?
I know that mean = median for any symmetrical ...
0
votes
1answer
68 views
How to add prediction intervals to describe the variability in monthly samples of data?
The data analyzed here is a sample of individuals collected on a monthly basis. What would be the best way to compute "prediction intervals" for the monthly sample means, in order to indicate the ...
0
votes
0answers
42 views
Confidence interval for the difference between $X_1$ and $X_2$ or $X_3$
The question:
Find a 99% confidence interval for the difference in mean oxygen
consumption of an algae that is in 100% concentrated seawater with
algae that is not in 100% seawater (i.e., 50% ...
1
vote
1answer
70 views
How to calculate confidence intervals of $1/\sqrt{x}$-transformed data after running a mixed linear regression in stata?
I have run a series of mixed linear regressions in Stata, some with inverse-square-root ($1/\sqrt{x}$) transformations and others with square root ($\sqrt{x}$) transformations.
How do I calculate ...
3
votes
1answer
67 views
Nonlinear regression: Confidence intervals on transformed or untransformed parameters?
Suppose I am using a standard inhibition model to find biochemical parameters that fit my data. The equation is:
$y = \frac{A}{{1 + \exp \left( {\ln \left[ S \right] - \ln IC_{50}} \right)}} $
where ...
2
votes
0answers
27 views
Can parameter uncertainties be salvaged when the residuals are correlated?
I have a nonlinear physical model for which I'm trying to determine parameter uncertainties using Monte Carlo. Instead of describing the nitty-gritty details, I will use a series of figures:
...
2
votes
1answer
50 views
Change in binomial proportion confidence interval
I'm having trouble calculating 95% confidence intervals for a change in binomial proportion. For example, in group $A$, there are $4$ successes out of $n =20$. In group $B$, there are $12$ successes ...
0
votes
0answers
55 views
Is there evidence to say with 99% confidence that the proportions are different?
A college placement service interviewed 1,100 graduates to determine if they were satisfied with the teaching they received. Of the 400 who had taken statistics, 225 said they were satisfied. Of the ...
1
vote
1answer
58 views
How to estimate true value and 95% bands when distribution is asymmetrical?
I have a set of results of independent measurements of some physical quantity. As an example I give here real expermental data on methanol refractive index at 25 degrees Celsius published in ...
3
votes
0answers
186 views
Ratios of means - statistical comparison test using Fieller's theorem?
I would really appreciate any suggestions with the following data analysis issue. Please read till the end as the problem at first may appear trivial, but after much researching, I assure you it is ...
0
votes
2answers
76 views
Why do we refer to our estimates in terms of precision?
Open any statistics textbook and it will urge the need to check the 'precision of our estimates'.
Take the following random variable:
...
0
votes
0answers
15 views
Assigning weights in crowdsourcing or voting system
In Multi-weighted voting system, how is each individual worker is assigned with a weight? What is the concept behind it?
1
vote
1answer
48 views
Error in estimation with continuous data
Is there a way to correlate error in a fit (MSD) to the error of the a calculation performed with the parameters associated with the fit? My specific problem is dealing with spectroscopic data. I ...
1
vote
0answers
23 views
Duality between acceptance region of testing and confidence region in terms of optimality?
The duality theorem between acceptance region of testing and confidence region is about their validity (i.e. satisfying the significance level of the former and the confidence level of the latter sum ...
1
vote
0answers
34 views
Does pivoting a discrete CDF provide a pivot?
In Section 9.2.3 of Casella's Statistical Inference,
they base their confidence interval construction for a parameter $\theta$ on a real-valued statistic $T$ with cdf $F_T(t| \theta)$.
They first ...
1
vote
0answers
50 views
Computing a bootstrap confidence interval for the prediction error with the percentile and the BCa method
I have two related questions regarding the computation of a non-parametric bootstrap confidence interval for the prediction error.
Setting: I have a sample S from a data population P and a learner L, ...
2
votes
1answer
83 views
confidence interval for classification error---binomial assumption vs. bootsrap resampling
I am developing a classifier using a set of N patterns, where N~1000. I am using K-fold cross-validation (with K=5) and computing the probability of classification error p (typical value is p=0.03). ...
0
votes
0answers
25 views
How are confidence intervals constructed from point estimates?
Wikipedia gives a brief description on constructing confidence intervals from point estimates, and in particular points out three ways, "the method of moments", "likelihood theory" and "the estimating ...
0
votes
0answers
21 views
Meaning of following statement about confidence intervals
From Wikipedia
Confidence intervals are an expression of probability and are subject to the normal laws of probability.
I was wondering what the normal laws of probability means? Are they the ...
1
vote
0answers
46 views
In testing, do we need to make the area of an acceptance region as small as possible?
One criterion to access a confidence interval is that the smaller its area, the better.
For hypothesis testing, I was wondering if it is also that the smaller the area of the acceptance region, the ...
0
votes
0answers
31 views
How do you construct confidence interval (by the method of pivots)?
From a note
Many derivations of confidence intervals can be described in terms of
... (pivot). ... The best choice is often suggested by looking at what statistic a good hypothesis test ...
2
votes
1answer
84 views
What does it imply when an estimate is not inside its 95% confidence interval?
What does it actually imply when a 95% CI does not contain an estimate (coefficient or parameter). Is there some model assumption that has not been satisfied? Or it means something else?
I know when ...
0
votes
0answers
153 views
marginal effects (and confidence interval) for interaction variables (Stata)
I'm trying to calculate marginal effects (and their confidence intervals) for an interaction variable.
I'm using Stata and have panel data (pooled cross-sectional time series). I am using the ...
