Nayland College

Nayland College - Mathematics

Home . Year 9 . Year 10 . Level 1 . Level 2 . L3 Statistics . L3 Maths . L3 Calculus . About . Links

NZAMT NZQA NZ Grapher NZ Maths Census at School Study It

3.10 Inference HOME | Achievement Objectives | Overview | Statistical Cycle | Introduction & Research Question | Discussing Samples | Sample Variability | Sampling Methods | Informal Confidence Interval | Bootstrapping Confidence Interval | Comparing two populations | Using iNZight | Writing a report | Assessment Practice

Bootstrap Confidence Intervals

7



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)

Video Chris Wilds overview of sample variation etc, (view from 7:20 for bootstrapping)

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)

Starter 8

Class notes, Class notes
Class site

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
Download and run iNZight ( iNZight free download and videos on how to get started )

iNZite Bootstrap confidence intervals

Import data

Add a Variable

Analyse

Mean or median

Record your choices

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.

Now discuss these results
What does the bootstrap confidence interval mean?

 

 

 

 

back to top