Download File

Inference
AS 91582
Every time you over-indulge, your life
shortens – expert
• 11:40 AM Wednesday Dec 19, 2012
• http://www.nzherald.co.nz/lifestyle/news/arti
cle.cfm?c_id=6&objectid=10855064
Every time you over-indulge, your life
shortens - expert
• It's the season for eating, drinking and being
merry, but experts warn that every time you
over-indulge you could be cutting hours off
your life.
• A new report, published in the British Medical
Journal, claims activities like having a couple
of drinks, smoking, eating red meat and sitting
in front of the TV can cut at least 30 minutes
off a person's life for every day that do it.
• On the flip side, sticking to one alcoholic
beverage, eating plenty of fruit and vegetables
and working up a sweat can add a couple of
hours on to your life, Medical Daily reports.
• Professor David Spiegelhalter, a statistician
from the University of Cambridge, figured out
the impact of different activities on a person's
lifespan by using a concept of accelerated or
decelerated ageing.
• Prof Spiegelhalter hopes expressing activities
in microlives like this will help people make
better lifestyle decisions.
• "Each day of smoking 20 cigarettes is as if you
are rushing towards your death," he said.
"Of course, evaluation studies would be needed
to quantify any effect on behaviour, but one
does not need a study to conclude that people
do not generally like the idea of getting older
faster.”
Maximise your chance of living to 100 – Tails you
win: the science of chance
www.magsmaths.com
Meet the Doozers
• www.magsmaths.com
Height distribution of Doozers at
Fraggle Rock
• The mean height of Doozers at Fraggle Rock is
150mm with a standard deviation of 5mm
Height distribution of Doozers at
Fraggle Rock
• The mean height of Doozers at Fraggle Rock is
150mm with a standard deviation of 5mm
• Sketch a possible height distribution of
Doozers at Fraggle Rock. Remember to give an
indication of scale.
Height distribution of the population
of Doozers at Fraggle Rock
Problem
I would like to get an estimate of the mean
height of Doozers in Fraggle Rock.
Bootstrapping
Outline of the method:
• Re-sample with replacement from our original
sample.
• Create a re-sample that is the same size as our
original random sample
• Calculate the mean (or statistic of interest) for
the re-sample
INZight
Bootstrapping using iNZight
iNZight
• Start iNZight and select the Sampling Variation
VIT module (or select FILE and VIT modules).
• Import the Doozer height population file.
• Drag “Height” down to the variable 1 box, and
then click the Analyse tab.
• The default quantity is mean. Do NOT change
this. Change Sample Size to 10, then click on
Record my choices.
• Play. Check you know what each selection does,
and how it relates to sampling from the
population.
1000 samples of size 10 from the
entire population.
We can see that samples of size 10 form a Normal Distribution as
the population was Normally Distributed.
Bootstrap Intervals
• Using iNZight to create a bootstrap confidence interval
• Start iNZight and select the Bootstrap Confidence Interval
Construction VIT module.
• Import the Doozer sample session 1 file.
• Drag Height down to the variable 1 box, and then click the
Analyse tab.
• The default quantity is “mean”. Do NOT change this, just
click on “Record my choices”
• Play, and replicate what you have just done by hand. Check
you know what each selection does.
• To finish, copy and paste the Bootstrap distribution of resample means into a word document.
Distribution from the sample
iNZight
• Start iNZight and select the Confidence interval
coverage VIT module (or select FILE and VIT modules).
• Import the Doozer height population file.
• Drag “Height” down to the variable 1 box, and then
click the Analyse tab.
• The default quantity is mean. Do NOT change this.
Change the CI Method to bootstrap: percentile and the
Sample Size to 10, then click on Record my choices.
• Play. Check you know what each selection does, and
how it relates to the bootstrap confidence intervals.
How well does the method work
We can use iNZight to check how well the
Bootstrap method works, by repeating the
process many times taking different random
samples from a known population.
Key Points
The distribution of re-sample means (the
bootstrap distribution) is similar to the
distribution of means from repeated random
sampling.
Therefore we can use the bootstrap distribution
to model the sampling variability in our data,
and base our confidence interval on this
bootstrap distribution.
NOTE
The method doesn’t rely on having a Normal
distribution and it works for small numbers.
Confidence Interval coverage
• Increasing the sample size – what’s the impact
on our confidence intervals?
• We will use the Doozer height data to
investigate this. Each file contains 10 different
random samples from the population of
Doozers at Fraggle Rock.
• What seems to happen to the widths of the
bootstrap confidence intervals when you
increase the sample size?
Consider the following:
• How much does the width change?
• How could you describe the change?
• Can you describe how the width is related to
the number of Doozers in the samples?