Calculate Standard Error Bootstrap
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Standard Error Bootstrap R
Individual Differences in Pain Perception Pain-Free and Hating It: Peripheral Neuropathy Neurotransmitters That Reduce or Block Pain Load more EducationScienceBiologyThe Bootstrap Method for how to calculate standard error in excel Standard Errors and Confidence Intervals The Bootstrap Method for Standard Errors and Confidence Intervals Related Book Biostatistics For Dummies By John Pezzullo You can calculate the standard error (SE) and confidence interval (CI) of the more
How To Calculate Standard Error Without Standard Deviation
common sample statistics (means, proportions, event counts and rates, and regression coefficients). But an SE and CI exist (theoretically, at least) for any number you could possibly wring from your data -- medians, centiles, correlation coefficients, and other quantities that might involve complicated calculations, like the area under a concentration-versus-time curve (AUC) or the estimated five-year survival probability derived from a survival analysis. Formulas for the SE and CI around these numbers might not calculate standard error regression be available or might be hopelessly difficult to evaluate. Also, the formulas that do exist might apply only to normally distributed numbers, and you might not be sure what kind of distribution your data follows. Consider a very simple problem. Suppose you've measured the IQ of 20 subjects and have gotten the following results: 61, 88, 89, 89, 90, 92, 93, 94, 98, 98, 101, 102, 105, 108, 109, 113, 114, 115, 120, and 138. These numbers have a mean of 100.85 and a median of 99.5. Because you're a good scientist, you know that whenever you report some number you've calculated from your data (like a mean or median), you'll also want to indicate the precision of that value in the form of an SE and CI. For the mean, and if you can assume that the IQ values are approximately normally distributed, things are pretty simple. You can calculate the SE of the mean as 3.54 and the 95% CI around the mean as 93.4 to 108.3. But what about the SE and CI for the median, for which there are no simple formulas? And what if you can't be sure those IQ values come from a normal distribution? Then the simple formulas might not be reliable. Fortunately, there is a very general method for estimating SEs an
standard deviation and the median absolute deviation (both measures of dispersion) distributions. In statistics, bootstrapping can refer to any test or
Calculate Standard Error Of Estimate
metric that relies on random sampling with replacement. Bootstrapping allows
Calculate Standard Error Confidence Interval
assigning measures of accuracy (defined in terms of bias, variance, confidence intervals, prediction error or calculate standard error of measurement some other such measure) to sample estimates.[1][2] This technique allows estimation of the sampling distribution of almost any statistic using random sampling methods.[3][4] Generally, it http://www.dummies.com/education/science/biology/the-bootstrap-method-for-standard-errors-and-confidence-intervals/ falls in the broader class of resampling methods. Bootstrapping is the practice of estimating properties of an estimator (such as its variance) by measuring those properties when sampling from an approximating distribution. One standard choice for an approximating distribution is the empirical distribution function of the observed data. In the https://en.wikipedia.org/wiki/Bootstrapping_(statistics) case where a set of observations can be assumed to be from an independent and identically distributed population, this can be implemented by constructing a number of resamples with replacement, of the observed dataset (and of equal size to the observed dataset). It may also be used for constructing hypothesis tests. It is often used as an alternative to statistical inference based on the assumption of a parametric model when that assumption is in doubt, or where parametric inference is impossible or requires complicated formulas for the calculation of standard errors. Contents 1 History 2 Approach 3 Discussion 3.1 Advantages 3.2 Disadvantages 3.3 Recommendations 4 Types of bootstrap scheme 4.1 Case resampling 4.1.1 Estimating the distribution of sample mean 4.1.2 Regression 4.2 Bayesian bootstrap 4.3 Smooth bootstrap 4.4 Parametric bootstrap 4.5 Resampling residuals 4.6 Gaussian process regression bootstrap 4.7 Wild bootstrap 4.8 Block bootstrap 4.8.1 Time series: Simple
Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company http://stats.stackexchange.com/questions/141583/bootstrap-regression-standard-errors-and-re-calculate-t-statistic Business Learn more about hiring developers or posting ads with us Cross Validated Questions Tags http://www.ats.ucla.edu/stat/r/library/bootstrap.htm Users Badges Unanswered Ask Question _ Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top Bootstrap standard error regression standard errors and re-calculate t-statistic? up vote 1 down vote favorite I am working on a few (both simple and multivariable) regression analyses, and I have cases where the residuals are non-normal, to varying degrees. As I've understood, the Gauss-Markov theorem states that normality of residuals is not necessary for the coefficient point estimates to be correct, i.e., I can trust that the regression summary tells me the BLUE coefficient estimates. However, the standard calculate standard error errors may be biased, and thus, the corresponding t- and p-values may not be correct. A previous question (How to obtain p-values of coefficients from bootstrap regression?) asked if it was possible to calculate p-values from bootstrapped coefficients and their CIs. However, if I bootstrap the coefficients and use the bootstrapped mean and the bootstrapped SE to re-calculate t- and p-values, would that be a sound approach? Here is the code I use, in R: # create linear model mod <- lm(Y~X,data=dataset); summary(mod) # create function to return coefficient mod.bootstrap <- function(data, indices) { d <- data[indices, ] mod <- lm(Y~X, data=d) return(coef(mod)) } # set seed set.seed(1234) # begin bootstrap using the boot package mod.boot <- boot(data=dataset, statistic=mod.bootstrap, R=2000) # now here is how I re-calculate t- and p-values bootmean <- mean(mod.boot$t[,2]) booter <- sd(boot.t[,2]) tval <- bootmean/booter p <- 2*pt(-abs(tval),df=mod$df.residual) The new t- and p-values come out fairly close to the LM summary, albeit a bit more conservative, as expected. Is this something I could report? I am very new at this, so I can't really tell if my logic is valid or not. Edit: Clarified a bit. r regression bootstrap share|improve this question edited Mar 16 '15 at 9:33 asked Mar 13 '15 at 10:31 The Mind's I 62 add a comment| active oldest votes Know someone who can answer? Share a
programs The R program (as a text file) for the code on this page. In order to see more than just the results from the computations of the functions (i.e. if you want to see the functions echoed back in console as they are processed) use the echo=T option in the source function when running the program. source("d:/stat/bootstrap.txt", echo=T) Introduction Bootstrapping can be a very useful tool in statistics and it is very easily implemented in R. Bootstrapping comes in handy when there is doubt that the usual distributional assumptions and asymptotic results are valid and accurate. Bootstrapping is a nonparametric method which lets us compute estimated standard errors, confidence intervals and hypothesis testing. Generally bootstrapping follows the same basic steps: 1. Resample a given data set a specified number of times 2. Calculate a specific statistic from each sample 3. Find the standard deviation of the distribution of that statistic The sample function A major component of bootstrapping is being able to resample a given data set and in R the function which does this is the sample function.
sample(x, size, replace, prob) The first argument is a vector containing the data set to be resampled or the indices of the data to be resampled. The size option specifies the sample size with the default being the size of the population being resampled. The replace option determines if the sample will be drawn with or without replacement where the default value is FALSE, i.e. without replacement. The prob option takes a vector of length equal to the data set given in the first argument containing the probability of selection for each element of x. The default value is for a random sample where each element has equal probability of being sampled. In a typical bootstrapping situation we would want to obtain bootstrapping samples of the same size as the