### Statistical Inference

```Statistical Inference
L3, Bootstrap, L2, L1 progression
Formal and informal
Continuing implementation of new NCEA standards
Team Solutions
Steel • Hogan • Cathcart • McNaughton • Barks • Johnson
What may happen in this session.
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Data
Questions and PPDAC
Bootstrap idea
Bootstrap confidence interval
(CLT, normal and CI )
Contextual information
Census at School resources
Level 2, level 1, Year 9 and 10.
What are we learning?
• The bootstrap idea and how it is used to make
an inference (now called formal inference).
• The importance of contextual information for
this standard 3.10
• A possible lesson sequence
• How to justify √n
• Where there are a lot of resources
Data
• The big idea of this standard
is to make a useful inference
population.
The Population
• The only definite thing we know about the
population is we never know anything definite
• And there would be no need for statistics
• But, if we did, we could check to see if our
statistical ways work. Let’s do that!
The Vineyard
Problem
Before the harvest I want to estimate the total
harvest weight reasonably accurately to plan
processing.
The population is 10,000
bunches of grapes. There
are 500 vines and each
vine is managed to have
10 shoots and each shoot
grows two bunches of
grapes.
The Plan
The plan is to pick a random sample of bunches
and weigh each bunch. There are 13 rows 50m
long so 6 random numbers between 1 and 650
were chosen.
The bunches of grapes in
a metre long section
were picked from the
vines at these places and
weighed.
The Sample Data
I have the weights of
212 bunches of grapes.
Analysis
The median weight is 87.5
grams.
The IQR is 109 – 70.5 =38.5
So the Y12 median estimate for
the vineyard is
87.5 ± 1.5 x 38.5/√212
=[83.5, 91.5]
I am pretty sure confident that
this interval will contain the
median.
Conclusion
Population
parameter median is
very likely to be
contained in this
interval;[83.5, 91.5].
I am pretty sure the vineyard harvest will be
between 835kg and 915kg. I have stainless vats
for 800kg so there will be a small surplus which
I can ferment in a 200L plastic drum.
Bootstrap for a better estimate
I have the weights of
212 bunches of grapes.
Bootstrap
• The idea behind a bootstrap is to mimic the
sample many times.
• This is best simulated.
• A computer is needed.
• The distributions of means/medians of all the
mimic samples reflect the population.
The distribution
of 200 resamples of size 212.
Bootstrap, likely to
be between 860kg
to 945kg with 95%
confidence.
What controls the spread of the
means?
• From the left, sample sizes 3, 5, 8, 12 and 40.
• Here I am varying the sample size.
√n
width
80
70
60
y = 125.41x-0.512
R² = 0.96453
50
40
30
20
10
0
0
5
10
15
20
25
Sample size
30
35
40
45
Key Ideas
• List all the ideas of statistics Years 9 to 13
• Order the development of these
Resources!
• http://3rs.ccac.ca/en/research/reduction/experimentaldesign.html
•
• http://www.corwin.com/upmdata/29173_Millsap___Chapter_2.pdf
• http://curiouscat.com/bill/101doe.cfm
• http://stattrek.com/experiments/what-is-an-experiment.aspx
• http://en.wikipedia.org/wiki/Design_of_experiments
• http://webspace.ship.edu/cgboer/experiments.html
• http://www.stat.auckland.ac.nz/~iase/publications/icots8/ICOTS8_
4B2_ENGEL..pdf
• http://www.stat.rutgers.edu/home/mxie/rcpapers/bootstrap.pdf
Resources!
And …
http://mediasite.temanuaute.org.nz/mediasite
/Catalog/pages/catalog.aspx?catalogId=22dcec
d5-8520-4ab7-b6c3-d96115a5dacf
This is not the end, it is not even the
beginning of the end, it is only the end
of the beginning!
Puzzle time
Who on Earth said
that and when?
```