Bootstrap Confidence Intervals Using Percentiles - Montgomery College
Section 3.4 Bootstrap Confidence Intervals using Percentiles Statistics: Unlocking the Power of Data Lock5
Outline Confidence intervals based on bootstrap percentiles Different levels of confidence Impact of sample size and level of confidence on interval width Cautions for bootstrap intervals Statistics: Unlocking the Power of Data Lock5
Body Temperature What is the average body temperature of humans? www.lock5stat.com/statkey 98.26 2 0.105 98.26 0.21 ( 98.05,98.47 ) We are 95% sure that the average body temperature for humans is between 98.05 and 98.47 98.6 ? Shoemaker (1996). “What's Normal: Temperature, Gender and Heartrate”, Journal of Statistics Education, 4(2). Statistics: Unlocking the Power of Data Lock5
Other Levels of Confidence What if we want to be more than 95% confident? How might you produce a 99% confidence interval for the average body temperature? Statistics: Unlocking the Power of Data Lock5
Percentile Method If the bootstrap distribution is approximately symmetric, we can construct a confidence interval by finding the percentiles in the bootstrap distribution so that the proportion of bootstrap statistics between the percentiles matches the desired confidence level. Statistics: Unlocking the Power of Data Lock5
Bootstrap Distribution For a P% confidence interval: P% Lower Bound 2 3 Observed Statistic 4 5 Upper Bound 6 7 8 Statistic Statistics: Unlocking the Power of Data Lock5
Percentile Method For a P% confidence interval, keep the middle P% of bootstrap statistics For a 99% confidence interval, keep the middle 99%, leaving 0.5% in each tail. The 99% confidence interval would be (0.5th percentile, 99.5th percentile) where the percentiles refer to the bootstrap distribution. Statistics: Unlocking the Power of Data Lock5
Body Temperature www.lock5stat.com/statkey Middle 99% of bootstrap statistics We are 99% sure that the average body temperature is between 98.00 and 98.58 . Statistics: Unlocking the Power of Data Lock5
Level of Confidence Which is wider, a 90% confidence interval or a 95% confidence interval? A 95% CI contains the middle 95%, which is more than the middle 90% Statistics: Unlocking the Power of Data Lock5
Mercury and pH in Lakes For Florida lakes, what is the correlation between average mercury level (ppm) in fish taken from a lake and acidity (pH) of the lake? 𝑟𝑟 0.575 Give a 90% CI for ρ Lange, Royals, and Connor, Transactions of the American Fisheries Society (1993) Statistics: Unlocking the Power of Data Lock5
Mercury and pH in Lakes www.lock5stat.com/statkey We are 90% confident that the true correlation between average mercury level and pH of Florida lakes is between -0.702 and -0.433. Statistics: Unlocking the Power of Data Lock5
Sample Size Remember the effect of sample size? The larger the sample size the (a) wider (b) narrower the confidence interval. The larger the sample size the smaller the variability in the bootstrap distribution, which will make the interval narrower. The larger the sample size, the more precise the estimate. Statistics: Unlocking the Power of Data Lock5
Bootstrap CI Option 1: Estimate the standard error of the statistic by computing the standard deviation of the bootstrap distribution, and then generate a 95% confidence interval by statistic 2 SE Option 2: Generate a P% confidence interval as the range for the middle P% of bootstrap statistics Statistics: Unlocking the Power of Data Lock5
Two Methods for 95% statistic 2 SE : Percentile Method : 98.26 2 0.105 ( 98.05,98.47 ) ( 98.05,98.47 ) Statistics: Unlocking the Power of Data Lock5
Two Methods Either the standard error method or the percentile method will give similar 95% confidence intervals If a level of confidence other than 95% is desired, use the percentile method Statistics: Unlocking the Power of Data Lock5
Bootstrap Cautions These methods for creating a confidence interval only work if the bootstrap distribution is smooth and symmetric ALWAYS look at a plot of the bootstrap distribution! If the bootstrap distribution is highly skewed or looks “spiky” with gaps, you will need to go beyond intro stat to create a confidence interval Statistics: Unlocking the Power of Data Lock5
Bootstrap Cautions Statistics: Unlocking the Power of Data Lock5
Number of Bootstrap Samples When using bootstrapping, you may get a slightly different confidence interval each time. This is fine! The more bootstrap samples you use, the more precise your answer will be. For the purposes of this class, 1000 bootstrap samples is fine. In real life, you probably want to take 10,000 or even 100,000 bootstrap samples Statistics: Unlocking the Power of Data Lock5
Summary 95% confidence intervals can be created using the standard error or the percentiles of a bootstrap distribution For any other desired level of confidence, the percentile method may be used A confidence interval from bootstrap percentiles can be created for any parameter, as long as the bootstrap distribution is approximately smooth and symmetric Statistics: Unlocking the Power of Data Lock5
Bootstrap Cautions These methods for creating a confidence interval only work if the bootstrap distribution is smooth and symmetric ALWAYS look at a plot of the bootstrap distribution! If the bootstrap distribution is highly skewed or looks "spiky" with gaps, you will need to go beyond intro stat to create a confidence interval
Aug 16, 2018 · Biometrics & Biostatistics International Journal Research Article Open Access. Bootstrap confidence intervals for dissolution similarity factor f 2 398 Copy 2018 Citation: Islam MM, Begum M. Bootstrap confidence intervals for dissolution similarity factor f 2. Biom Biostat Int J. 2018;7(5):397‒403.
bootstrap confidence interval, but it will be noisy, because it is based on a (small) subsample. But we can proceed as in subsampling, repeating the procedure multiple times with randomly chosen subsamples. We obtain a set of bootstrap confidence intervals, which we combine (e.g., by averaging) to yield the overall bootstrap confidence interval.
know how to create bootstrap weights in Stata and R know how to choose parameters of the bootstrap. Survey bootstrap Stas Kolenikov Bootstrap for i.i.d. data Variance estimation for complex surveys Survey bootstraps Software im-plementation Conclusions References Outline
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Bootstrap adalah metode berbasis komputer yang dikembangkan untuk mengestimasi berbagai kuantitas statistik, metode bootstrap tidak memerlukan asumsi apapun. Bootstrap merupakan salah satu metode alternatif dalam SEM untuk memecahkan masalah non-normal multivariat. Metode bootstrap pertama kali dikenalkan oleh Elfron (1979 dan 1982)
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