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confidence intervals | Using binomial confidence intervals for multinomial confidence intervals? | https://stats.stackexchange.com/questions/333933/using-binomial-confidence-intervals-for-multinomial-confidence-intervals | <p>Below is sample code showing the widths of binomial confidence intervals (using a <a href="https://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Normal_approximation_interval" rel="nofollow noreferrer">simple normal approximation</a>) and multinomial "simultaneous confidence intervals" (from <a href=... | 600 | |
confidence intervals | Classical Confidence Intervals vs. Bootstrap Confidence Intervals | https://stats.stackexchange.com/questions/595103/classical-confidence-intervals-vs-bootstrap-confidence-intervals | <p>Suppose I have some data that includes height and weight measurements for 1000 people - I am interested in calculating the Correlation Coefficient to see if there exists some correlation between height and weight, and if this correlation is statistically significant.</p>
<p>I was curious in learning more about how t... | <p>Yes, you can bootstrap the correlation coefficient and get the confidence intervals you are looking for but:</p>
<p>you should random-sample joint observations (couples of observations i.e. weight,height) and not independently sampling from weight and height.</p>
<p>Even if this makes sense, I may suggest a differen... | 601 |
confidence intervals | Confidence intervals on model parameters | https://stats.stackexchange.com/questions/310056/confidence-intervals-on-model-parameters | <p>I have a very basic question about interpreting confidence intervals. Say I use R to fit a linear model to the Nile water flow time series (from the <code>datasets</code> package), like this: </p>
<pre><code># Flow of the Nile river (10^8 cubic metres per year) between 1871-1971
nile.ts <- data.frame(year = do.c... | <blockquote>
<p>Or, can I state that there is no statistically significant trend?</p>
</blockquote>
<p>Yes. The coefficient for <code>year</code> would be then not different from 0. </p>
| 602 |
confidence intervals | t-statistic confidence intervals vs wilson score confidence intervals | https://stats.stackexchange.com/questions/91612/t-statistic-confidence-intervals-vs-wilson-score-confidence-intervals | <p>I don't have too formal of a grounding in statistics, so sorry if this doesn't make much sense. But:</p>
<p>What are the differences between using a t-distribution to generate confidence intervals for small samples vs using a wilson score confidence intervals? Can they even both be used for this purpose, or am I mi... | <blockquote>
<p>Are t-intervals more appropriate in certain situations and wilson intervals in others?</p>
</blockquote>
<p>Precisely this. They apply to two different situations, the first being (at least approximately) normally distributed values, the second for proportions based on binomially distributed counts.<... | 603 |
confidence intervals | Interpreting confidence intervals | https://stats.stackexchange.com/questions/12321/interpreting-confidence-intervals | <p>Suppose I have a $95 \%$ confidence interval for $\mu$ with population variance $\sigma^{2}$ known. It will be of the form $$[\bar{X}-1.96 \sigma/\sqrt{n}, \bar{X}+1.96 \sigma/\sqrt{n}]$$ </p>
<p>The statistical interpretation of this is that $95\%$ of the confidence intervals will contain the true mean? I know ind... | 604 | |
confidence intervals | Minimizing 95% Confidence interval extent for bootstrapped confidence intervals | https://stats.stackexchange.com/questions/135058/minimizing-95-confidence-interval-extent-for-bootstrapped-confidence-intervals | <p>I'm new to CrossValidated so please excuse any shortcomings in my question.</p>
<p>Suppose I have a sample of 500, for a population of 500,000. I asked my sample of 500 what day of the week they go grocery shopping and assume I do not know the actual distribution of which day of week people go grocery shopping. Bec... | 605 | |
confidence intervals | Confidence Bands vs. Simultaneous Confidence Intervals | https://stats.stackexchange.com/questions/177110/confidence-bands-vs-simultaneous-confidence-intervals | <p>This may be a dumb question, but when talking about multiple regression analyses are "simultaneous" confidence intervals and confidence "bands" the same thing?</p>
<p>I'm still having trouble figuring this out and how to compute the two things, if in fact they are different. From what I can tell simultaneous confi... | 606 | |
confidence intervals | Are confidence intervals open or closed intervals? | https://stats.stackexchange.com/questions/15872/are-confidence-intervals-open-or-closed-intervals | <p>I have a question about confidence intervals.</p>
<blockquote>
<p>In general, are confidence intervals open or closed?</p>
</blockquote>
| <p>The short answer is "Yes".</p>
<p>The longer answer is that it does not really matter that much because the ends of the intervals are random variables based on the sample (and assumptions, etc.) and if we are talking a continuous variable then the probability of getting an exact value (the bound equaling t... | 607 |
confidence intervals | Are confidence intervals useful? | https://stats.stackexchange.com/questions/390093/are-confidence-intervals-useful | <p>In frequentist statistics, a 95% confidence interval is an interval-producing procedure that, if repeated an infinite number of times, would contain the true parameter 95% of the time. Why is this useful?</p>
<p>Confidence intervals are often misunderstood. They are <em>not</em> an interval that we can be 95% certa... | <p>So long as the confidence interval is treated as <em>random</em> (i.e., looked at from the perspective of treating the data as a set of random variables that we have not seen yet) then we can indeed make useful probability statements about it. Specifically, suppose you have a confidence interval at level <span clas... | 608 |
confidence intervals | Confidence interval for the confidence interval? | https://stats.stackexchange.com/questions/194499/confidence-interval-for-the-confidence-interval | <p>I'm studying confidence intervals, and I'm curious about how one might generate a confidence interval for the confidence interval, if that even makes sense.</p>
<p>For example, let's say I draw simple random samples of n=100 from some population, calculate sample means and standard deviations, and construct 95% con... | <blockquote>
<p>what can I say about the distribution of how often the intervals captures?</p>
</blockquote>
<p>Treating each interval containing the parameter as a <a href="https://en.wikipedia.org/wiki/Bernoulli_process" rel="noreferrer">Bernoulli process</a> with each trial having some coverage probability $p$, t... | 609 |
confidence intervals | 95% Confidence Intervals | https://stats.stackexchange.com/questions/439860/95-confidence-intervals | <p>Statistics textbooks go out of their way to say that 95% Confidence Intervals (CIs) do not mean that you can be 95% sure that the population parameter of interest is somewhere between the high and low end of the interval. Rather, if your sample was drawn an infinite number of times, 95% of the intervals would contai... | <p>The clue to all of this is realizing that the population paramter <span class="math-container">$\theta$</span> is a fixed, unknown number. And that (loosely speaking) the "randomnes" in all of this comes from the confidence intervals. Each confidence interval is linked to a sample, so for different samples, we get (... | 610 |
confidence intervals | Combining confidence intervals | https://stats.stackexchange.com/questions/60844/combining-confidence-intervals | <p>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 interval.</p>
<p>I now need to combine these to obtain a total efficiency as a function of said variable. This means I m... | 611 | |
confidence intervals | Difference Between Confidence Bands and Confidence Intervals | https://stats.stackexchange.com/questions/655191/difference-between-confidence-bands-and-confidence-intervals | <p>I've read other answers on this stackexchange for this topic, but I have a few questions I would like clarified:</p>
<p>Confidence bands are usually visualized as the connected lines ('bands') formed from confidence intervals throughout the regression. This leads me to believe (possibly incorrectly) that the confide... | 612 | |
confidence intervals | How important are confidence intervals? | https://stats.stackexchange.com/questions/520577/how-important-are-confidence-intervals | <p>I am writing a research paper about time series forecasting using neural networks. In my results I created tables containing error values (RMSE, MAE and RMSSE) for the predictions and made plots showing the predicted values over the original data.</p>
<p>Now, I have been told that I need to add confidence intervals... | <p>Consider you have some money to invest. Your bank says, that investment A will give a guaranteed annual profit of 2% whereas investment B will may give you a profit somewhere between -8% to +12% with an expected value of 2%. Will you throw dice over which investment to take, because both have the same expected profi... | 613 |
confidence intervals | Are 50% confidence intervals more robustly estimated than 95% confidence intervals? | https://stats.stackexchange.com/questions/248113/are-50-confidence-intervals-more-robustly-estimated-than-95-confidence-interva | <p>My question flows out of <a href="http://andrewgelman.com/2016/11/05/why-i-prefer-50-to-95-intervals/#comment-342062" rel="noreferrer">this comment</a> on an Andrew Gelman's blog post in which he advocates the use of 50% confidence intervals instead of 95% confidence intervals, although not on the grounds that they ... | <p>This answer analyzes the meaning of the quotation and offers the results of a simulation study to illustrate it and help understand what it might be trying to say. The study can easily be extended by anybody (with rudimentary <code>R</code> skills) to explore other confidence interval procedures and other models.</... | 614 |
confidence intervals | Topology of Confidence Intervals | https://stats.stackexchange.com/questions/200647/topology-of-confidence-intervals | <p>I hope this is the right site to post this.</p>
<p>The example I have in my mind is a GLMM model, where we infer random effects, and a random effect caterpillar plot (with confidence intervals):</p>
<p><a href="https://i.sstatic.net/R4Wu6.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/R4Wu6.png" al... | 615 | |
confidence intervals | Where two confidence intervals meet? | https://stats.stackexchange.com/questions/192756/where-two-confidence-intervals-meet | <p>I have two means that refers to two different samples of different populations. Let's say, for example, that the two means are 1.0 and 3.15. I can compute confidence intervals about these two cases and, logically, higher is the confidence interval, larger are the two intervals (they tend to infinite width).
So, the ... | <p>The exact answer depends on what are the intervals about and other circumstances but I'm going to made a couple of assumptions in the hope they fit your problem:</p>
<ul>
<li>You are computing confidence intervals on the mean.</li>
<li>Your samples are large (let's say, at least over 100). If that assumption is fal... | 616 |
confidence intervals | Are confidence intervals scale-invariant? | https://stats.stackexchange.com/questions/419406/are-confidence-intervals-scale-invariant | <p>Suppose I estimate a mean and construct some sort of confidence intervals (e.g. based on normal approximation or bootstrapped) around the mean. I now wish to rescale my mean from, say, the mean number of infections per hundred persons to the mean number of infections per thousand persons by multiplying the mean by 1... | <p>If you have a scale family everything works:</p>
<p>If the probability that a random interval <span class="math-container">$[a,b]$</span> includes <span class="math-container">$\theta$</span> is some value <span class="math-container">$q \geq 1-\alpha$</span> then the probability that a random interval <span class=... | 617 |
confidence intervals | Test of confidence intervals? | https://stats.stackexchange.com/questions/152750/test-of-confidence-intervals | <p>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 refit them using the same model many times. Lastly, I need to take 2.5% and 97.5% quantiles of them and compare with ... | 618 | |
confidence intervals | Confidence Intervals - What's going on? | https://stats.stackexchange.com/questions/480991/confidence-intervals-whats-going-on | <p>I'm looking for help with this figure.</p>
<p>Plotted are percentages and confidence intervals for each year (I didn't collect the data).</p>
<p>I am wondering, under what circumstances would the confidence intervals be the same as the percentage for that year... What's going on in the data that allows this to happ... | 619 | |
confidence intervals | Joint confidence intervals for probabilities | https://stats.stackexchange.com/questions/28605/joint-confidence-intervals-for-probabilities | <p>I have two probabilities $p$ and $q$. $p>q$, and they aren't correlated. I'm going to calculate $i$ such that $p^i=q$, which is easily done as $\log_p(q)$.</p>
<p>Now, I'd like to also calculate a confidence interval for $i$, which is necessarily going to be a function of both $p$ and $q$'s confidence intervals.... | <p>I think there is a confusion between <em>confidence interval</em> and <em>probability interval</em> here. </p>
<p>In the R code, you are indicating that $p\sim Beta(152,29)$ and $q\sim Beta(37,19)$, then you can calculate the distribution of $i=log(q)/log(p)$ using a change of variable and then obtain the correspon... | 620 |
confidence intervals | Interpreting overlap of bootstrapped confidence intervals | https://stats.stackexchange.com/questions/467331/interpreting-overlap-of-bootstrapped-confidence-intervals | <p>Assuming two samples of numeric values for two groups of unequal group sizes (e.g. 100 opinion scores collected from group A and 15 opinion scores collected from group B), I understand that non-overlapping 95% confidence intervals of the opinion scores indicate that there is a statistically significant difference in... | 621 | |
confidence intervals | Hypothesis testing: 95% confidence intervals of group means overlapping zero or 83% confidence intervals? | https://stats.stackexchange.com/questions/146342/hypothesis-testing-95-confidence-intervals-of-group-means-overlapping-zero-or | <p>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 the two group means to determine if confidence intervals overlap zero, and 2) 83% confidence intervals. I realise that ... | 622 | |
confidence intervals | Confidence interval for ratio between two values without confidence intervals | https://stats.stackexchange.com/questions/616113/confidence-interval-for-ratio-between-two-values-without-confidence-intervals | <p>I have two numeric variables (death rates), each without confidence intervals, and I want to calculate the CI of the ratio between the two values.</p>
<p>I was using the MOVERR method developed by Donner & Zhou but this was only applicable to values with confidence intervals.
<a href="https://rdrr.io/cran/pairwi... | 623 | |
confidence intervals | Boxplots vs. Confidence Intervals | https://stats.stackexchange.com/questions/137543/boxplots-vs-confidence-intervals | <p>I designed a heuristic that solves a problem concerning network graphs. It was tested on thousands of different instances that have various different characteristics: Topology, template, number and position of users, capacities, ... It produced more than 300000 results that also depend on the random seed that was us... | <p>Choosing box plots means that you print the 25th and 75th percentiles. Why not choose to print 2.5 and 97.5 percentiles? At n=300000 and unknown distribution that would be the most sensible definition of a confidence interval. You might even consider printing both in just one plot.</p>
<p>The purpose of the data ev... | 624 |
confidence intervals | Confidence intervals for multinomial proportions | https://stats.stackexchange.com/questions/569073/confidence-intervals-for-multinomial-proportions | <p>I know that there are a lot of methods to find the confidence intervals for binomial proportions using methods like Agresti-Coull, but is there any important papers mentioning to find confidence intervals for multinomial case?</p>
| <p>Not sure about important papers, but there's the obvious traditional <a href="https://en.wikipedia.org/wiki/Conjugate_prior#Table_of_conjugate_distributions" rel="nofollow noreferrer">conjugate Bayesian updating</a> option (using a Dirichlet prior for the multinomial parameters).</p>
<p>In the binomial case there's ... | 625 |
confidence intervals | Do likelihood-based confidence intervals avoid general criticisms of confidence intervals? | https://stats.stackexchange.com/questions/539413/do-likelihood-based-confidence-intervals-avoid-general-criticisms-of-confidence | <p>In the literature, I see post-sample criticisms of frequentist confidence intervals — but the usual targets are intervals that use somewhat weak methods such as assumed normality or other long-run/asymptotic methods.</p>
<p>However, Bayesian credibility intervals simply average over a number of likelihood intervals.... | 626 | |
confidence intervals | Simple example of confidence intervals | https://stats.stackexchange.com/questions/119805/simple-example-of-confidence-intervals | <p>I'm looking for an example for confidence intervals similar to the following but has only one continuous interval. The following confidence interval is two separate set each of which only contain one value, which seem rather odd for being confidence interval:</p>
<p><img src="https://i.sstatic.net/Nivwo.png" alt="... | 627 | |
confidence intervals | Confidence Intervals for ICC | https://stats.stackexchange.com/questions/578301/confidence-intervals-for-icc | <p>I was wondering if anyone might know of a way to calculate confidence intervals around an ICC(1) value? I'm running a multilevel model using the lmer() function in lme4 where I'm interested in seeing if there is a significant amount of within-person variation in a particular construct. I've run a null model for the ... | 628 | |
confidence intervals | QAP regression and confidence intervals | https://stats.stackexchange.com/questions/663864/qap-regression-and-confidence-intervals | <p>I've run a Poisson QAP (quadratic assignment procedure) regression in R on my network data. As expected, the output provides permutation-based p-values, but not standard errors or confidence intervals.</p>
<p>To communicate the uncertainty around my estimates, I’d like to explore whether it's possible to derive conf... | 629 | |
confidence intervals | When are confidence intervals useful? | https://stats.stackexchange.com/questions/3911/when-are-confidence-intervals-useful | <p>If I understand correctly a confidence interval of a parameter is an interval constructed by a <em>method</em> which yields intervals containing the true value for a specified proportion of samples. So the 'confidence' is about the method rather than the interval I compute from a particular sample. </p>
<p>As a use... | <p>I like to think of CIs as some way to escape the Hypothesis Testing (HT) framework, at least the binary decision framework following <a href="http://j.mp/awJEkH" rel="noreferrer">Neyman</a>'s approach, and keep in line with theory of measurement in some way. More precisely, I view them as more close to the reliabili... | 630 |
confidence intervals | Confidence intervals calculated from other confidence intervals (binomial problem)? | https://stats.stackexchange.com/questions/616470/confidence-intervals-calculated-from-other-confidence-intervals-binomial-proble | <p>In a binomial experiment, I have an estimate for the probability of 3 independent events A, B & C, each with a 95% confidence interval.</p>
<p>(Trivial example values)</p>
<p><code>P(A) = .12 (.05, .29)</code><br />
<code>P(B) = .16 (.08, .25)</code><br />
<code>P(C) = .06 (.02, .14)</code></p>
<p>I need to calc... | <ul>
<li><p>You have estimates <span class="math-container">$\hat{q}_a$</span>, <span class="math-container">$\hat{q}_b$</span> and <span class="math-container">$\hat{q}_c$</span>, which are (presumably) approximate independent estimates of the probabities for the independent events 'no A', 'no B' and 'no C'.</p>
</li>... | 631 |
confidence intervals | Monte-Carlo error Confidence Intervals | https://stats.stackexchange.com/questions/287939/monte-carlo-error-confidence-intervals | <p>I am constructing 95% confidence intervals on some metric of interest using MC simulation. These intervals can be constructed for example using bootstrapping. </p>
<p>Does it mean that if I repeat the same MC simulation 100 times with a different seed, 95% of my results should be inside the confidence interval? </p... | <p>$[a,b]$ is a 95%CI if probability that true vaule of your metric lies between $a$ and $b$ is 95%. </p>
<p>In statistics, we believe that a thing called 'true value' actually exists (given by God, Nature, Spaghetti Monster or who/what-ever). We are aware that we can never tell exact value of it, but we try to approx... | 632 |
confidence intervals | Confidence interval and confidence region | https://stats.stackexchange.com/questions/138603/confidence-interval-and-confidence-region | <p>Could you please tell me what is the difference between confidence interval and confidence region in the following sense? </p>
<p>For example, we have s multiple linear regression model. For individual confidence intervals, we use $t$-statistics to find individual confidence intervals for regression parameters but... | <p>As @NBrouwer says, a confidence interval is for an individual variable, so it is a (one-dimensional) interval. This is the case for e.g. the confidence interval for an individual regression coefficent. </p>
<p>However, if you build 'confidence intervals' for more than one variable at a time, i.e. for a multivariat... | 633 |
confidence intervals | Different methods, different confidence intervals | https://stats.stackexchange.com/questions/191133/different-methods-different-confidence-intervals | <p>A <a href="http://en.wikipedia.org/wiki/Confidence_interval#Statistical_theory" rel="nofollow">definition</a> of a confidence interval could be:</p>
<blockquote>
<p><strong>A confidence interval</strong> for the parameter θ, with confidence level or
confidence coefficient γ, is an interval with random endpoints... | <p>First 95% Confidence Interval: Symmetric 2-sided, so sample mean +/- 1.960 * (standard error)</p>
<p>Second 95% Confidence Interval: Upper 1-sided: [$-\infty$, sample mean + 1.645 * (standard error)]</p>
| 634 |
confidence intervals | Are Prophet's "uncertainty intervals" confidence intervals or prediction intervals? | https://stats.stackexchange.com/questions/619860/are-prophets-uncertainty-intervals-confidence-intervals-or-prediction-interva | <blockquote>
<p>By default Prophet will return uncertainty intervals for the forecast <code>yhat</code>.</p>
</blockquote>
<p>Unfortunately, <a href="https://facebook.github.io/prophet/docs/uncertainty_intervals.html" rel="noreferrer">the documentation</a> about those "uncertainty intervals" is extremely vagu... | <p>From digging through the code as you suggest it seems that they are prediction intervals. Specifically the model is fit by sampling a posterior with Stan (line 1249-1266 in <a href="https://github.com/facebook/prophet/blob/374676500795aec9d5cbc7fe5f7a96bf00489809/R/R/prophet.R#L1249" rel="noreferrer">prophet.R</a>) ... | 635 |
confidence intervals | Confidence intervals for integer parameters | https://stats.stackexchange.com/questions/579228/confidence-intervals-for-integer-parameters | <p>I'm interested, purely out of curiosity, in what methods can be used to calculate confidence intervals for discrete integer model parameters.</p>
<p>As an example, consider the model (which I can flesh out with code if needs be)</p>
<p><span class="math-container">$$
y \in [0,1]; \\
P(y_i = 1) =
\begin{cases}
.25 \... | 636 | |
confidence intervals | Confidence intervals for autocorrelation function | https://stats.stackexchange.com/questions/368404/confidence-intervals-for-autocorrelation-function | <p>Given a time series data sample I have computed autocorrelation coefficients for various lags, the result looks something like this</p>
<p><a href="https://i.sstatic.net/VEDsn.jpg" rel="noreferrer"><img src="https://i.sstatic.net/VEDsn.jpg" alt="enter image description here"></a></p>
<p>How do I compute the confid... | <p>A quick google search with "confidence intervals for acfs" yielded</p>
<p><a href="https://books.google.fi/books?id=WLaLBgAAQBAJ&pg=PA38&dq=Confidence+intervals+for+acfs&hl=fi&sa=X&ved=0ahUKEwiTvrPqotPdAhUriaYKHRUFDmAQ6AEIJjAA#v=onepage&q&f=false" rel="noreferrer">Janet M. Box-Steffensme... | 637 |
confidence intervals | Given Two 95% Confidence Intervals | https://stats.stackexchange.com/questions/41141/given-two-95-confidence-intervals | <p>Suppose we have given a two $95 \%$ confidence intervals for $X_1$ and $X_2$. They are normally distributed. From this how would we get a $95 \%$ confidence interval for $X_{1}/X_{2}$?</p>
| <p>I dont think you can get the 95CI of mean(x1/x2) just by their separate 95CI.
Maybe you can do a simulation to get the empirical distribution of (x1/x2) if you also get the correlated relationship between x1 and x2 </p>
| 638 |
confidence intervals | Confusion regarding Confidence Intervals | https://stats.stackexchange.com/questions/461378/confusion-regarding-confidence-intervals | <p>Suppose we have <span class="math-container">$2$</span> independent population parameters <span class="math-container">$p_1$</span> and <span class="math-container">$p_2$</span>, such that the <span class="math-container">$90$</span>% ( symmetric ) confidence intervals for <span class="math-container">$p_1$</span> a... | <p>When we say that an interval has confidence 95% we mean that in repeated sampling we would find that intervals constructed in the same way would cover the true value of the parameter about 95% of the times: the confidence is the probability
of coverage in repeated experimentation.</p>
<p>Now, I do not think you can... | 639 |
confidence intervals | Particle Filter: Confidence Intervals | https://stats.stackexchange.com/questions/271099/particle-filter-confidence-intervals | <p><strong>Context</strong></p>
<p>This is a basic question about confidence intervals. So the standard way to estimate a confidence interval.Assuming we have a set of $N$ random variables $\{X^i\}$ such that all of them are i.i.d. We know that the mean of is converges to the central limit of a $N(\mu,\frac{\sigma^2}{... | <p>You might want to check your formulas for the sample means and sample standard deviations once you start talking about particle filters. Also, the particles are not independent if you are resampling. But they are identical. I think you have that backwards. </p>
<p>Otherwise, if you weren't resampling, you would jus... | 640 |
confidence intervals | Confidence intervals for ordered probit | https://stats.stackexchange.com/questions/144636/confidence-intervals-for-ordered-probit | <p>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 but I'm not sure if this has to be done manually. I am using Stata.</p>
<p>The confidence intervals are for the pre... | <p>This is a partial solution, but maybe it will be useful start.</p>
<p>The usual way of doing this is with <code>predictnl</code>'s <code>ci</code> option, which will give you predicted probability and a confidence interval for each observation. But this will give you some CI endpoints that fall outside [0,1] interv... | 641 |
confidence intervals | Confidence intervals for population | https://stats.stackexchange.com/questions/442655/confidence-intervals-for-population | <p>These might be slightly basic questions for confidence intervals but I can't think exactly how to resolve them.</p>
<p>Considering an example where I have access to the entire population e.g. the annual revenue for a company over the last decade <span class="math-container">$R_i, i\in{1,..10}$</span> where revenue ... | 642 | |
confidence intervals | Monte-Carlo Quantile Confidence Intervals | https://stats.stackexchange.com/questions/287710/monte-carlo-quantile-confidence-intervals | <p>I am looking at a Monte-Carlo engine with N simulations. This Monte-Carlo engine builds a distribution from which I would like to read the 99%-tile (called the VaR). The problem can be interpreted as Monte-Carlo VaR (value at risk). I use a confidence interval on this quantile obtained with 2 different methods:</p... | 643 | |
confidence intervals | Confidence Intervals Around a Mean: biased (non-centered) confidence interval? (an exercise using R) | https://stats.stackexchange.com/questions/115554/confidence-intervals-around-a-mean-biased-non-centered-confidence-interval | <p>I've been playing around with the module "Confidence Intervals Around a Mean" (meanCI) from statsTeachR (www.statsteachr.org), authored by Eric A Cohen (unfortunately, author's contact information was not available).</p>
<p>It "focuses on understanding and calculating confidence intervals around a sample mean. This... | <p>First of all, I agree with the comments left by heropup. I'll add some details.</p>
<p>The reason why your simulation breaks down may be a little subtle. At least I spend some time reading your code to find the source of the problem. Please notice, that you only simulate once for each of the cases. Then your CIs fu... | 644 |
confidence intervals | Confidence intervals in beta regressions | https://stats.stackexchange.com/questions/656994/confidence-intervals-in-beta-regressions | <p>I am using a mixed-effects beta regression model in my study because my values are bounded between 0 and 1. When I run the same analysis using a linear mixed-effects model, I obtain similar results (predictors have the same directions and are significant). In the linear model, the confidence intervals remain within ... | <p>Beta regression models typically use a logit link, which means that the effects (parameter magnitudes or CIs) can't easily be translated to the probability scale without picking a baseline value (unlike identity-link models or log-link models such as Poisson regression). That's why epidemiologists spend so much time... | 645 |
confidence intervals | Standard error and confidence intervals | https://stats.stackexchange.com/questions/647158/standard-error-and-confidence-intervals | <p>About theoretical concepts... We use confidence intervals to do an inference to extrapolate results from study to similar sample. Is this true?</p>
<p>Which is the difference between a confidence interval, and dividing the result by <span class="math-container">$\sqrt{n}$</span>, how does the standard error occur?<... | <p>We use confidence intervals to estimate where the true parameter of a point estimate might be. Technically, the confidence interval has a certain coverage, e.g. 95% Think that asymptotically in 95% of the cases you compute a confidence interval, the true value is in this estimated interval).</p>
<p>The standard erro... | 646 |
confidence intervals | Two questions about confidence intervals | https://stats.stackexchange.com/questions/368347/two-questions-about-confidence-intervals | <p>I am learning about confidence intervals, but don't think I understand them very welll.</p>
<p>Assume <span class="math-container">$$(\mu - \hat{\mu}) \sqrt{\frac{n}{\sigma(\mu)}}$$</span>
is asymptotically standard normal.
So I guess we can say that a 95 % CI is <span class="math-container">$\hat{\mu} \pm 1.96 \s... | <p>The whole game is about learning something about <span class="math-container">$\mu$</span>, so you're right in your first question: the starting point is that <span class="math-container">$\mu$</span> is unknown and you want to use data and an estimator to learn about it. Using a given dataset, you can form an estim... | 647 |
confidence intervals | Understanding lincom confidence intervals (STATA) | https://stats.stackexchange.com/questions/231067/understanding-lincom-confidence-intervals-stata | <p>I'm trying to understand confidence intervals for linear combinations of parameters (lincom command in STATA). Let's say I'm interested in whether smoking is associated with low birth weight (using the lbw dataset, see example in help logit).</p>
<pre><code>webuse lbw
logit low age lwt i.race smoke ptl ht ui
age ... | 648 | |
confidence intervals | Calculating group mean and confidence interval from single-subject means and confidence intervals | https://stats.stackexchange.com/questions/205359/calculating-group-mean-and-confidence-interval-from-single-subject-means-and-con | <p>I have a sample of 20 subjects. I have two continuous variables, <strong><em>X</em></strong> and <strong><em>Y</em></strong> which are linearly related. I use linear regression to estimate the regression coefficient relating <strong><em>X</em></strong> and <strong><em>Y</em></strong>.</p>
<p>For each subject, I est... | <p>In cases as yours two extreme approaches can be taken: (a) calculate <em>independent</em> models for each of the individuals, or (b) calculate <em>aggregate</em> estimate for the whole sample, ignoring the individual variability. Unfortunately, both approaches can give you misleading results. When you calculate inde... | 649 |
confidence intervals | Regression: Mean Response Confidence Interval vs Confidence Intervals of Each Predictor | https://stats.stackexchange.com/questions/83951/regression-mean-response-confidence-interval-vs-confidence-intervals-of-each-pr | <p>I have a regression of costs on volume and some interactions (costs ~ volume + volume:year + year)</p>
<p>Often times when I do a regression, I expect a negatively sloped relationship and the model validates that. I can add up the volume coefficient and the associated interaction term for a given point and get a n... | 650 | |
confidence intervals | Confidence Intervals Intuition | https://stats.stackexchange.com/questions/73875/confidence-intervals-intuition | <p>I am new to statistics and have run into some trouble understanding computing confidence intervals and am seeking some help. I will outline the motivating example in my textbook and hopefully someone can offer some guidance. </p>
<p>Example </p>
<p>There is a population of mean values and your goal is to figure ou... | 651 | |
confidence intervals | Difference between confidence intervals and prediction intervals and data set | https://stats.stackexchange.com/questions/336736/difference-between-confidence-intervals-and-prediction-intervals-and-data-set | <p>I read <a href="https://stats.stackexchange.com/questions/16493/difference-between-confidence-intervals-and-prediction-intervals">Difference between confidence intervals and prediction intervals</a> and <a href="https://www.graphpad.com/support/faq/the-distinction-between-confidence-intervals-prediction-intervals-an... | 652 | |
confidence intervals | confidence intervals for dependent observations | https://stats.stackexchange.com/questions/97638/confidence-intervals-for-dependent-observations | <p><a href="https://stats.stackexchange.com/questions/61266/why-is-dependence-a-problem">The answer to this question</a> discusses problems associated with calculating P-values for dependent observations. Let's say you have observations from two different groups that are dependent. You consider carrying out a t-test to... | <p>No. Since confidence intervals convey the same inferential information as $p$-values ($\mu_0 \in \mathrm{CI} \iff p_{H_0:\mu_0=\mu}\geq \alpha$), they also share the same difficulties dealing with dependence.</p>
| 653 |
confidence intervals | Calculating confidence intervals for two samples | https://stats.stackexchange.com/questions/86509/calculating-confidence-intervals-for-two-samples | <p>Let's say I have two samples and I want to calculate confidence intervals for the means of each sample.</p>
<pre><code>x = rnorm(10)
y = rnorm(10)
</code></pre>
<p>Using the t.test command I'm able to get the following output.</p>
<pre><code>> t.test(x, y)
Welch Two Sample t-test
data: x and y
t = -0.01... | <p>Your question leave some considerable doubt about what, exactly, <em>this</em> in 'mimic this' consists of. You should be more explicit.</p>
<p>Do you want one sample confidence intervals for the means? </p>
<p>Then <code>t.test</code> can do it easily, by doing it one sample at a time.</p>
<pre><code>t.test(x,co... | 654 |
confidence intervals | Confidence Intervals and Hyptothesis testing | https://stats.stackexchange.com/questions/575615/confidence-intervals-and-hyptothesis-testing | <p>Iam currently reading up on basic statistics and Iam somewhat confused about the computation/inference of confidence intervals and hypothesis tests.
As far as I have understood there are several techniques for both confidence interval estimation and hypothesis testing:</p>
<p>confidence interval are computed:</p>
<u... | 655 | |
confidence intervals | Calculating confidence intervals for mode? | https://stats.stackexchange.com/questions/240563/calculating-confidence-intervals-for-mode | <p>I am looking for references about calculating confidence intervals for mode (in general). Bootstrap may seem to be natural first choice, but as discussed by Romano (1988), standard bootstrap fails for mode and it does not provide any simple solution. Did anything change since this paper? What is the best way to calc... | <p>While it appears there hasn't been too much research into this specifically, there is a paper that did delve into this on some level. The paper <a href="https://link.springer.com/article/10.1007/PL00003988" rel="nofollow noreferrer">On bootstrapping the mode in the nonparametric regression model with random design</... | 656 |
confidence intervals | Confidence Intervals for Non-normal data? | https://stats.stackexchange.com/questions/140481/confidence-intervals-for-non-normal-data | <p>I have a dataset where the response is the number of successes and I have two factor variables A, B (A has 6 levels and B has 4 levels) and a quantitative variable H (H is hours so it is non-negative). The number of trials is fixed for different levels of A -- A1 always has 20 trials, A2 always 12, etc). The datas... | 657 | |
confidence intervals | Confidence intervals for mean correlation | https://stats.stackexchange.com/questions/497609/confidence-intervals-for-mean-correlation | <p>What is the correct way to define confidence intervals for the mean of multiple correlations? I understand how to calculate CIs for individual correlation coefficients, I also understand how to calculate the mean correlation through Fisher's transformation. But what are the confidence intervals for this mean correla... | <p>Actually, what you describe is just fine.</p>
<p>If <span class="math-container">$\bf{x}$</span> <span class="math-container">$= [x_1, x_2, \dots, x_n]$</span>, your set of data points, is approximately normally distributed, <span class="math-container">$\text{mean}(x) \pm \alpha \times\text{se}(x)$</span> produces ... | 658 |
confidence intervals | Calculating confidence intervals | https://stats.stackexchange.com/questions/28809/calculating-confidence-intervals | <p>Body mass index was compared for two groups, people with elevated triglycerides (above 1.7 mmol/L) and people with normal triglyceride levels. The 10 people in the group with elevated triglyceride had body mass index mean = 26.1 and standard deviation = 3.72 and the 15 people in the normal group had body mass index ... | <p>What part are you stuck on? Try to solve it one step at a time.</p>
<p>The data is: </p>
<p>$\overline x_1 = 26.1, s_1 = 3.72, n_1 = 10\\
\overline x_2 = 24.3, s_2 = 3.45, n_2 = 15$</p>
<p>Find the confidence interval for $\mu_1$. Then, separately, find the confidence interval for $\mu_2$.</p>
<p>The next part... | 659 |
confidence intervals | Confidence intervals for exponential smoothing | https://stats.stackexchange.com/questions/43501/confidence-intervals-for-exponential-smoothing | <p>I'm using exponential smoothing (Brown's method) for forecasting. The forecast can be calculated for one or more steps (time intervals). Is there any way to calculate confidence intervals for such prognosis (ex-ante)?</p>
| <p>Exponential smoothing methods as such have no underlying statistical model, so prediction intervals cannot be calculated. However, when we do want to add a statistical model, we naturally arrive at state space models, which are generalizations of exponential smoothing - and which allow calculating prediction interva... | 660 |
confidence intervals | Confidence intervals for repeatability | https://stats.stackexchange.com/questions/11898/confidence-intervals-for-repeatability | <p>I have calculated the repeatability of individuals' responses to a stimulus using the methodology of <a href="http://www.univet.hu/users/jkis/education/Kutatastervezes/Lessells_Boag_Auk_87_Unrepeatable_repeatabilities_-_a_common_mistake.pdf" rel="nofollow">Lessells & Boag (1987) Auk 104:116</a>, where repeatabil... | <p>I would go for bootstrap to compute 95% CIs. This is what is generally done with coefficient of heritability or intraclass correlation. (I found no other indication in Falconer's book.) There is an example in the <a href="http://cran.r-project.org/web/packages/gap/index.html" rel="nofollow">gap</a> package of an han... | 661 |
confidence intervals | Why are confidence intervals valid? | https://stats.stackexchange.com/questions/650430/why-are-confidence-intervals-valid | <p>Recently, I began my statistics journey to understand the field better. Previously, my experience with statistics consisted of memorizing formulas, conditions, and applications of the latter. While one can often get away with such a superficial understanding, I overlooked the intuition behind most statistical practi... | 662 | |
confidence intervals | Transformation of Confidence Interval = Confidence Interval of Transformation? | https://stats.stackexchange.com/questions/439994/transformation-of-confidence-interval-confidence-interval-of-transformation | <p>I am wondering about the following situation: I have a confidence interval estimator <span class="math-container">$\delta(x)=[lb, ub]$</span>, which returns valid a%-confidence intervals for a value <span class="math-container">$\theta \in \mathbb{R}$</span> (not necessarily a parameter). How can I obtain a confiden... | <p>Assuming <span class="math-container">$f$</span> is strictly monotone, this method works:</p>
<p><span class="math-container">$$lb < \theta < ub \implies f(lb) < f(\theta) < f(ub)$$</span></p>
<p><span class="math-container">$$\theta \in [lb, ub] \implies f(\theta) \in [f(lb), f(ub)]$$</span></p>
<p><... | 663 |
confidence intervals | Excel using confidence intervals when forecasting | https://stats.stackexchange.com/questions/618679/excel-using-confidence-intervals-when-forecasting | <p>My understanding is that when forecasting if you want to quantify the level of uncertainty of your model, one would typically use predictive intervals. However in Microsoft Excel, when using the 'Forecast Sheet' tool, it appears to be expressing uncertainty using confidence intervals instead.</p>
<p>Are confidence i... | 664 | |
confidence intervals | Confidence Intervals for Normalized Random Variables | https://stats.stackexchange.com/questions/596267/confidence-intervals-for-normalized-random-variables | <p>I think I have a pretty simple question about constructing confidence intervals for normalized random variables.</p>
<p>If I have i.i.d random variables <span class="math-container">$X_1, X_2, X_3, ..., X_n \sim F$</span> for some distribution <span class="math-container">$F$</span>, and say i have the standard mean... | 665 | |
confidence intervals | pooled proportions with confidence intervals | https://stats.stackexchange.com/questions/316083/pooled-proportions-with-confidence-intervals | <p>I have some data like:</p>
<pre><code> Var1 Var2
Study1 20/23 3/23
Study2 30/34 4/34
Study3 1/30 29/30
</code></pre>
<p>I would like to calculate pooled proportions with confidence intervals using R.</p>
| 666 | |
confidence intervals | Confidence intervals for glmer() from lme4 | https://stats.stackexchange.com/questions/60448/confidence-intervals-for-glmer-from-lme4 | <p>I'm running a mixed model on some data. I want to calculate confidence intervals for my model. </p>
<p>For this I have adapted the following code section from <a href="http://glmm.wikidot.com/faq" rel="nofollow">Predictions and/or confidence (or prediction) intervals on predictions (lme4)</a>. The problem is that I... | <blockquote>
<p>the code then calculates the confidence intervals it says prediction +/- 2*sqrt(pvar1). Shouldn't it be the t.crit value or 1.96 for a normal distribution?</p>
</blockquote>
<p>This is correct. 1.96 is a more accurate critical value, however, statistical inference in mixed models is plagued with problem... | 667 |
confidence intervals | Confidence Interval - Revisit | https://stats.stackexchange.com/questions/539778/confidence-interval-revisit | <p>I've read in many articles about Confidence Interval as below</p>
<p>One such article link: <a href="https://www.statisticssolutions.com/misconceptions-about-confidence-intervals/" rel="nofollow noreferrer">https://www.statisticssolutions.com/misconceptions-about-confidence-intervals/</a></p>
<ol>
<li><p>[FALSE] - T... | <p>I view this as a philosophical question with no uniformly satisfactory answer.</p>
<p>Consider a 95% CI for <span class="math-container">$\mu$</span> based on a random sample of size <span class="math-container">$n$</span> from <span class="math-container">$\mathsf{Norm}(\mu, \sigma),$</span> where <span class="math... | 668 |
confidence intervals | Confidence intervals vs sample size? | https://stats.stackexchange.com/questions/38676/confidence-intervals-vs-sample-size | <p>I am totally new to stats and the field of confidence intervals. So this might be very trivial or even sound stupid. I would appreciate if you could help me understand or point me to some literature/text/blog that explains this better.</p>
<p>I see on various news sites like CNN, Fox news, Politico etc about their ... | <p>In addition to Peter's great answer, here are some answers to your specific questions:</p>
<ol>
<li><p>Who to trust will depend also on who is doing the poll and what effort they put into getting a good quality poll. A bigger sample size is not better if the sample is not representative, taking a huge poll, but onl... | 669 |
confidence intervals | What are "ABC" boostrap confidence intervals? | https://stats.stackexchange.com/questions/545316/what-are-abc-boostrap-confidence-intervals | <p>I am reading the <a href="https://astrostatistics.psu.edu/su07/R/html/boot/html/abc.ci.html" rel="nofollow noreferrer">documentation</a> of <code>boot::abc.ci</code> and feel I am missing something. It sounds like the "ABC" method is just an approximation of BCa bootstrap confidence intervals.</p>
<p>Is th... | <p>Basically, there are situations where BCa intervals can become quite computationally expensive and ABC intervals offer a more feasible alternative. With the computational power usually at hands nowadays, I don't think there is so much need for ABC intervals anymore, though.</p>
<p>As reference, there is a brief stat... | 670 |
confidence intervals | R Confidence Intervals for quantiles from Generalized Lambda Distribution | https://stats.stackexchange.com/questions/518733/r-confidence-intervals-for-quantiles-from-generalized-lambda-distribution | <p>I'd like to compute confidence intervals in R for quantiles from generalized lambda distribution.</p>
<p><a href="https://www.sciencedirect.com/science/article/abs/pii/S0167947309000437" rel="nofollow noreferrer">Steve Su (2009)</a> introduces below 2 ways to calculate confidence intervals. I think I could understan... | <p>Here, I'm going to reproduce example 3.1.1 in Su (2009) where he calculates 95% confidence intervals for the 99th quantile for the speed of light data from Michelson 1879.</p>
<p>It basically boils down to implementing the formulas (4), (5) and (6) from Su (2009). In the following <code>R</code> code, I used the <a ... | 671 |
confidence intervals | Ranking by score with confidence intervals | https://stats.stackexchange.com/questions/182405/ranking-by-score-with-confidence-intervals | <p>I am using simulation to compute a unique score for every college basketball team, and ranking these teams based on that score.</p>
<p>I am sensitive to the fact that the score sometimes differs by a tiny amount (1 part in 1,000), which is unlikely to be meaningfully different. Therefore, I am planning to use permu... | <p>Not disagreeing with @Kontorus, but putting in some more context.</p>
<p>You are making "multiple comparisons"; A with B, A with C, B with C. In such circumstances overlapping groups are common, often indicated by grouping symbols e.g.</p>
<pre><code> value Grouping
1 (Team A) ... | 672 |
confidence intervals | Family-wise confidence intervals | https://stats.stackexchange.com/questions/1972/family-wise-confidence-intervals | <p>I have a bunch of variables organized into 10 different levels of a grouping factor. I'm doing some ANCOVA on particular variables and also plotting the data using boxplots. I'd like to add 84% confidence intervals to all the groups (since non-overlapping 84% CIs indicate a significant difference at alpha .05 - at l... | <p>It sounds a reasonable solution <strong>if this is what important for you to present in the plot</strong>.</p>
<p>What this will give you (besides many questions, in case you are working with people who like statistics less then you), is a CI that is applicable to your situation which requires correction for multi... | 673 |
confidence intervals | visualizing confidence intervals in longitudinal models | https://stats.stackexchange.com/questions/597869/visualizing-confidence-intervals-in-longitudinal-models | <p>I have a longitudinal dataset with continuous variables for 6 different time points nested within each ID. I prepared a longitudinal Poisson model with ID as a random effect for the intercepts, which in itself is working fine. In preparing the figures for the report, I prepared a figure with the predicted values for... | <p>The question is whether you want to display "the uncertainty of our measurements over time" (essentially the raw data) or the uncertainty of the <em>model estimates</em> over time.</p>
<p>If all you have is a simple Poisson model of counts versus time and random intercepts for individuals, and you have com... | 674 |
confidence intervals | Confidence Intervals for Dice Rolls? | https://stats.stackexchange.com/questions/600395/confidence-intervals-for-dice-rolls | <p>Suppose I roll a 6-sided die 100 times and observe the following data - let's say that I don't know the probability of getting any specific number (but I am assured that each "trial" is independent from the previous "trial").</p>
<p>Below, here is some R code to simulate this experiment:</p>
<pre... | <p><em>See also link in @jbowman comment, method 5.</em></p>
<p>Are you willing to entertain a Bayesian approach? If so, you could specify a uniform prior on the five-dimensional surface <span class="math-container">$\sum\limits_{x=1}^{6} p_x = 1$</span>, sample from the posterior distribution, and identify the <span ... | 675 |
confidence intervals | Confidence Intervals and Probability Relationship | https://stats.stackexchange.com/questions/340257/confidence-intervals-and-probability-relationship | <p>Suppose that 20 students visit a farmer's market and each pick (a random sample of) 25 oranges, weigh them, then create a 95% confidence interval for the true mean weight of an orange at the market. What is the probability that 5 of these intervals contain the true
mean weight of an orange at the market and the rest... | <p>I think the confusion comes from how we interpret frequentist confidence intervals. There is NOT a 95% probability that the true mean lies in the interval. In a frequentist approach, the mean is fixed and not random. The interval is the random aspect. For a given interval, the true mean is either in the interval or ... | 676 |
confidence intervals | ARIMA forecast confidence intervals | https://stats.stackexchange.com/questions/431467/arima-forecast-confidence-intervals | <p>Can someone explain how confidence intervals for ARIMA forecasts are derived? I can't seem to find any good explanation of it. From what I've read it seems like because an ARIMA process can be expressed as an infinite valued MA process then the forecast values are normally distributed. If this is true then how do yo... | <p>For reference, let your model be:</p>
<p><span class="math-container">$$X_t=\phi X_{t-1} + \epsilon_t$$</span></p>
<p>Say you have data from 1 to <span class="math-container">$T$</span>. So your point forecast for <span class="math-container">$X_{T+1}$</span> would be <span class="math-container">$$E(X_{T+1}|\{X_t... | 677 |
confidence intervals | Confidence intervals for beta regression | https://stats.stackexchange.com/questions/234254/confidence-intervals-for-beta-regression | <p>I have used the betareg package in R to fit a regression. My question is: how do I calculate confidence intervals for betaregression in R? </p>
| <p>The beta likelihood is not a regular exponential family, so constructing interval estimates for such two parameter families is not easily done. I think Zeileis was wise not to implement any de-facto methods for <code>confint</code>. The cited article Ospina suggests that bootstrap interval estimates perform best. Th... | 678 |
confidence intervals | Alternatives calculus for proportions confidence intervals | https://stats.stackexchange.com/questions/184908/alternatives-calculus-for-proportions-confidence-intervals | <p>I have two related questions:</p>
<p>a) Is there any other way to calculate a confidence interval for the proportion, in addition to the "classical" form?</p>
<p><a href="https://i.sstatic.net/egPJM.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/egPJM.png" alt="enter image description here"></a></p... | <p>One explanation could be that the survey uses clusters and weights, so effectively your n is smaller now because of the correlation of people within a cluster. That is they are similar people within a group, so not independent. If n is smaller then your confidence intervals are wider.</p>
<p>One good thing about th... | 679 |
confidence intervals | Confidence intervals for cross-validated statistics | https://stats.stackexchange.com/questions/69831/confidence-intervals-for-cross-validated-statistics | <p>How does one calculate confidence intervals of cross-validated estimates?</p>
<p>For an epidemiological paper we use cat. and cont. NRI, IDI, and difference in C index for comparison of two Cox models. The reviewer suggested showing only cross-validated estimates <strong>and their 95% confidence intervals</strong>.... | <p>For our <a href="http://www.sciencedirect.com/science/article/pii/S0377221711009064" rel="noreferrer">credit risk paper</a> on predicting loan defaults, a reviewer also suggested we produce confidence intervals for cross validation estimates and in particular recommended bootstrapping of the resampled mean.</p>
<p>... | 680 |
confidence intervals | Confidence intervals - how to interpret and report | https://stats.stackexchange.com/questions/303970/confidence-intervals-how-to-interpret-and-report | <p>Just to state that I don't belong to the statistics field or something related (I am medical scientist). I've been trying to understand more about the confidence interval and how to interpret it for biological studies (in case of biological experiments). In this case, I was advised to report confidence intervals in... | 681 | |
confidence intervals | Combining multiple confidence intervals | https://stats.stackexchange.com/questions/555302/combining-multiple-confidence-intervals | <p>Suppose that we have 10 90% confidence intervals resulting from 10 large samples showing the percentage of 3rd-graders who don't know how to sum. Means, sample sizes and other statistical data are not given.</p>
<p>(1.10, 1.12)
(1.01, 1.04)
(1.01, 1.15)
(1.11, 1.12)
(1.03, 1.04)
(1.04, 1.07)
(1.05, 1.20)
(1.08, 1.17... | <p>One possible approach:</p>
<p>These ten CIs may be of the form <span class="math-container">$\hat p \pm 1.645\sqrt{\frac{\hat p(1-\hat p)}{n}},$</span> where <span class="math-container">$\hat p = x/n$</span> for <span class="math-container">$x$</span> arithmetic deficient students in <span class="math-container">$n... | 682 |
confidence intervals | confidence intervals in linear regression | https://stats.stackexchange.com/questions/263115/confidence-intervals-in-linear-regression | <p>I am trying to understand the confidence interval for linear regression parameters. At this link <a href="https://stats.stackexchange.com/questions/88461/derive-variance-of-regression-coefficient-in-simple-linear-regression">Derive Variance of regression coefficient in simple linear regression</a> an answer is provi... | <p>I am from a different domain, and use somewhat different language, but maybe this will help.</p>
<p>Imagine doing an experiment. $x$ is a set of given values, an "independent variable". Not random. For each of these values you measure a dependent variable, $y$. Presumably, $y$ depends on $x$ in a deterministic (non... | 683 |
confidence intervals | Are confidence intervals useful for fitting data? | https://stats.stackexchange.com/questions/442521/are-confidence-intervals-useful-for-fitting-data | <p>I recently directed to a very good explanation on the difference between an error band and a confidence intervals, <a href="https://stats.stackexchange.com/questions/217374/real-meaning-of-confidence-ellipse/217377#217377">here</a>.</p>
<p>My question arose from the context of using error bars/bands or confidence i... | <p>It depends on what the error estimates represent: errors in the measurements going into the model, or expected errors in predictions from a fitted model. For terminology, it's simplest to discuss in terms of the error variance estimates (which for a given study size bear a one-to-one relationship with the confidence... | 684 |
confidence intervals | Question about confidence intervals and prediction intervals | https://stats.stackexchange.com/questions/517730/question-about-confidence-intervals-and-prediction-intervals | <p>Considering following linear multiple regression model:
<span class="math-container">\begin{equation}
y=X\beta + e,
\end{equation}</span>
where observations <span class="math-container">$y\in\Re^n$</span>, coefficents <span class="math-container">$\beta\in\Re^p$</span> and <span class="math-container">$e\sim N(0,\si... | 685 | |
confidence intervals | Cox multi-state model - CIF confidence intervals | https://stats.stackexchange.com/questions/638037/cox-multi-state-model-cif-confidence-intervals | <p>Is it possible to get confidence intervals for the estimated CIF from a <code>survival::coxph</code> multi-state model?</p>
<p>This code produces the cumulative incidence function, but there are no options to get confidence intervals:</p>
<pre><code>library(survival)
# 0 = Censored, 1 = Relapse, 2 = Death
rotterdam... | <p>I am not familiar with this stuff, so I'm really not sure of what I do below. See <a href="https://cran.r-project.org/web/packages/survival/vignettes/compete.pdf" rel="nofollow noreferrer">the competing risks vignette</a> and <code>?finegray</code>. Below I follow the <code>?finegray</code> example.</p>
<pre class="... | 686 |
confidence intervals | Forecast confidence intervals from multiple realizations | https://stats.stackexchange.com/questions/477167/forecast-confidence-intervals-from-multiple-realizations | <p>I have a forecast which involves sampling a probability distribution and therefore each time I run the forecast there is some random variation between results. If I run the forecast many times, how do I compute the expected forecast, 5% and 95% confidence intervals using the ensemble of results?</p>
<p>Two options I... | <p>If I have understand the question correctly, this is a case of <a href="https://en.wikipedia.org/wiki/Ensemble_forecasting" rel="nofollow noreferrer">Ensemble Forecasting</a>, and I believe the goal is to find <em>Prediction</em> rather than <em>Confidence</em> Intervals. Given a set of <span class="math-container">... | 687 |
confidence intervals | Why do we need confidence intervals? | https://stats.stackexchange.com/questions/143772/why-do-we-need-confidence-intervals | <p>I am following a video lecture on Statistics, which introduces the concept of confidence intervals in the following way:</p>
<p>"A bank vice president is interested in the average checking account balance for all personal accounts. A random sample of 500 accounts is selected, and the average is calculated. What lev... | <p>You forget that accuracy comes at the cost of effort. He'd need to gather all the data from thousands of accounts. And what if five accounts have billions while the rest are in the hundreds? The confidence interval is a faster way to give you a reasonable answer in a reasonable amount of time.
Confidence interval is... | 688 |
confidence intervals | Confidence intervals for group means (R) | https://stats.stackexchange.com/questions/210515/confidence-intervals-for-group-means-r | <p>Here are some sample data in R:</p>
<pre><code>set.seed(42)
df <- data.frame(g = factor(rep(1:2, each= 50)), y = rnorm(100)+rep(0:1, each=50))
</code></pre>
<p>One can easily get group means using e.g. <code>with(df, tapply(y,g,mean))</code> but there is no such easy way to get the confidence intervals for grou... | <p>The answer to your "naive question" contains the solution to your problem.</p>
<p>In the linear model on all the data, the residual variance is estimated from all 100 data points, based on the difference of each value from its associated group mean. Thus you will note that the difference between the top and bottom ... | 689 |
confidence intervals | Frequentist confidence intervals = constant trapping probability? | https://stats.stackexchange.com/questions/44018/frequentist-confidence-intervals-constant-trapping-probability | <p>In the case of estimating an unknown mean of a normal distribution with known variance, if I'm not mistaken, the confidence interval contains $\theta$ with probability $1 - \alpha$, regardless of the actual value of $\theta$. In other cases (e.g. when the variance is not necessarily constant), is it still the case t... | <p>It depends on how strictly <em>you</em> want to define it, most I believe would accept that for all parameter values, if the interval has at least 1 - alpha coverage - it can be taken as a confidence interval (no matter how you came up with it). There is an interesting post on this right now at <a href="http://norma... | 690 |
confidence intervals | Confidence intervals of bounded variable | https://stats.stackexchange.com/questions/249115/confidence-intervals-of-bounded-variable | <p>Given 1000 observations that come from a distribution that is bounded between 0 and 1. How do you calculate correct 95% Confidence intervals when dealing with a bounded distribution?</p>
<pre><code>set.seed(10)
data = runif(1000, min=0, max=1)
mean(data)
mean(data) + 1.96*sd(data)/sqrt(length(data)) # usual CIs
mea... | <p>This is a later answer but perhaps may be useful to someone. I have an R package on github (<a href="https://github.com/mattelisi/mlisi" rel="nofollow noreferrer"><code>mlisi</code></a>) with a set of convenient functions, including one that calculate boostrapped confidence intervals using the bias-corrected and acc... | 691 |
confidence intervals | Interpreting 95% confidence intervals for relative risk (known true RR, 100 samples) | https://stats.stackexchange.com/questions/306149/interpreting-95-confidence-intervals-for-relative-risk-known-true-rr-100-samp | <p>Let's assume that we are investigating how tobacco smoking is associated with incident lung cancer in a population. In the full population, the true relative risk of lung cancer associated with tobacco smoking is 2.</p>
<p>Next, we collect 100 random samples from the population. For each sample, we calculate 95% co... | <p>The answer is A2. Confidence intervals are agnostic to the "null value" of a parameter. They may freely include it or not. There may be some confusion stemming from the idea that a 95% CI will cause you to incorrectly reject H0 5% of the time; but this is only true if the true RR is the null RR (i.e., 1). This is no... | 692 |
confidence intervals | Calculate Confidence Intervals for Lognormal Distribution | https://stats.stackexchange.com/questions/299135/calculate-confidence-intervals-for-lognormal-distribution | <p>Surprisingly, I can't find a discussion on calculating confidence intervals for the mean $EY=e^{\mu+\sigma^2/2}$ of the lognormal distribution. My question goes beyond what is covered in the link below, and is specific to the package <code>EnvStats</code>.</p>
<p><a href="https://stackoverflow.com/questions/2184374... | 693 | |
confidence intervals | Confidence intervals for derivatives from GAM predictions | https://stats.stackexchange.com/questions/503819/confidence-intervals-for-derivatives-from-gam-predictions | <p>I have built the following GAM model in <code>mgcv</code></p>
<pre><code>wt9 <- gam(weight_t ~
tagged +
sex_t0 +
s(age.x, by = tagged, k = 5) +
s(age.x, by = sex_t0, k = 5) +
s(scale_id, bs = "re") +
s(age.x, scale_id, bs ... | <p>You can do posterior simulation to draw a large set of samples from the posterior distribution of the model, and then for each sample (which is one set of curves if you are predicting for all your groups over a grid of values in <code>age.x</code>) compute the derivatives and store the values.</p>
<p>This gives you ... | 694 |
confidence intervals | Confidence intervals with penalized likelihood | https://stats.stackexchange.com/questions/314677/confidence-intervals-with-penalized-likelihood | <p>I am trying to perform parameter estimation using something like a maximum likelihood ratio method, however I need to add a penalty term to constrain nuisance parameters which describe certain systematic uncertainties in the measurement process. So I have been digging around in the literature to try and better under... | <p>I don't think it's possible to provide meaningful confidence intervals in that case in a natural way.</p>
<p>Call $\theta$ the parameter and $\hat\theta$ the penalized likelihood estimator. Confidence intervals at 95% say that $P(|\theta-\hat\theta|\leq d|\theta)\geq0.95$ <strong>for all $\theta$</strong>. If you r... | 695 |
confidence intervals | Question about calculating confidence intervals | https://stats.stackexchange.com/questions/457649/question-about-calculating-confidence-intervals | <p>I am reading about confidence intervals and got stuck with this example from L. Wasserman's book titled "All of Statistics". Could anybody explain why P<sub>Q</sub>(θ ∈ C) = 3/4 in this example? Below is the paragraph from the book:</p>
<blockquote>
<p>Let θ be a fixed, known real number and let X<sub>1</sub>,
... | <p>You can dissociate cases : </p>
<ul>
<li><p>if <span class="math-container">$X_1 \neq X_2$</span>, which happens with probability <span class="math-container">$\frac{1}{2}$</span>, then <span class="math-container">$X_1 = -X_2$</span> (since <span class="math-container">$X$</span> can only be <span class="math-cont... | 696 |
confidence intervals | Distance between Vectors with Confidence Intervals | https://stats.stackexchange.com/questions/159820/distance-between-vectors-with-confidence-intervals | <p>I have a machine learning application where I extract numerical features $a_{i1}, a_{i2}, \dots, a_{ik}$ for each object $a_i$ to study. Objects are then compared using standard euclidean distance. </p>
<p>The problem is that the features entail uncertainty. The good message is that I have confidence intervals, mea... | <p>Bayesian machine learning relies on probability distribution to represent uncertainty. In the present case, using multivariate normal distributions instead of finite boxes may lead to simpler calculations. </p>
<p>Currently, you assme that the interval <span class="math-container">$a_{ij}−c_{ij} \leq a_{ij} \leq a_... | 697 |
confidence intervals | Confidence intervals for frequency tables | https://stats.stackexchange.com/questions/298398/confidence-intervals-for-frequency-tables | <p>I am analyzing the results of a survey on R. The questionnaire is a series of questions that participants answer using a Likert scale (<a href="https://en.wikipedia.org/wiki/Likert_scale" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Likert_scale</a>). </p>
<p>I have obtained frequency tables for each que... | <p>There are different methods for calculating confidence intervals for proportions without using bootstrapping.</p>
<p>For a multinomial proportion, you might try the methods in the <code>DescTools</code> package.</p>
<pre><code>### Adapted from http://rcompanion.org/handbook/H_02.html
if(!require(DescTools)){insta... | 698 |
confidence intervals | Significant difference from regression confidence intervals | https://stats.stackexchange.com/questions/55687/significant-difference-from-regression-confidence-intervals | <p>I have a question about statistical significance in relation to confidence intervals from linear regression. I'm obviously far from a stats expert, and I've been searching for the answer to this, probably simple, question for a while now without any luck.</p>
<p>I've made an example to clarify my question:
I'm inte... | <p>You don't compare the individual points to conclude a treatment effect. You see whether the lines for the treatment and control are different.</p>
<p>In some circumstances, the fitted lines might be parallel, and just the difference in intercept is of interest. In others, both the intercept and slope might differ, ... | 699 |
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