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# Bootstrap Confidence Intervals

 Bootstrap Confidence Intervals Repeated sampling from a population may be impractical, expensive or not possible (sample items destroyed during sampling) If we cannot resample from the population, (the true sampling distribution is unavailable) then we resample from the best approximation of the population we have - which is the sample itself (producing a bootstrap distribution) Use the original sample to represent the population. Take repeated re-samples from the ordinal sample. Use these re-samples to calculate an estimate for the population statistic (mean or median) This is called Bootstrapping The re-sampling produces a distribution of means (or medians) which form a distribution The bootstrap confidence interval provides an estimate for the population mean Review maui/hectors dolphin data sets Assuming our sample was representative of the population then the bootstrapped confidence interval can be used as an estimate of the true population mean (or median) Teaching bootstrapping (link to census at school Class notes) Bootstrapping animations page (Link to stat.auckland) Stats Learning Workbook Ex D p95, 96 with explanation on pg 93 - read it and weep tears of joy. IAS 3.10 pg 53-55 iNZight simulation popn --> sample distribution iNZight simulation popn --> sample --> bootstrap distribution What do you notice
###### Using iNZight

iNZite Bootstrap confidence intervals

Import data

Analyse

Mean or median

Resample and animation

From this sample select a single item, record it, with replacement, repeat selection process 'n' times then calculate the median (or mean)

Top box plot is of the sample

Bottom box plot is of the resample and the median of the resample (Bootstrap)

Include Bootstrap Distribution

Repeat 100 times and...

Show the CI to see the Bootstrap confidence interval.

This is the interval within which we can be reasonably sure the population median lies.