The tiny taste of Stats708
As at Saturday, 6 February 2016
Part of Stats708 required the keeping of a journal. My journal was over 12,000
words, reduced here to just over 1000 words. Hence this document captures
some key points and highlights but is not comprehensive. Another part of
Stats708 was to write an essay on a topic of my choice, and to present some of
the key ideas from the essay to my cl assmates. The PowerPoint presented today
is from that assignment.
Stats708: Topics in Statistical Education
https://www.stat.auckland.ac.nz/courses/postgrad/2013/STATS_708
Why take stats708?
Take stats708 to gain knowledge about how to best teach statistics, and to
gain a deeper understanding of why teaching statistics is important.
Priscilla Allan
Table of Contents

Overview ......................................................................................................................................... 1

Planning........................................................................................................................................... 1
o
Teaching through a context rather than teaching concepts....................................................... 1
o
Hands on activities (first) ............................................................................................................ 1
o
Real world connections. .............................................................................................................. 2
o
Probabilistic modelling links the real world. ............................................................................... 2
o
Pachinkogram ............................................................................................................................. 2
o
Equally likely outcome bias ......................................................................................................... 2
o
Strategic use of Pip Arnold resources. ........................................................................................ 2
o
Follow Anna-Marie Martins blog about teaching. ...................................................................... 2
o
Passion found through deeper understanding. .......................................................................... 2

Probability and statistics concepts are real world and tricky. ........................................................ 3
o
Real world ignorance .................................................................................................................. 3
o
Regression to the mean .............................................................................................................. 3
o
Framing questions....................................................................................................................... 3
o
A misleading real world .............................................................................................................. 3
o
Natural frequencies easier than conditional probabilities. ........................................................ 4

3 types of Randomisation ............................................................................................................... 5
o
Simulations for stochastic modelling .......................................................................................... 5
o
Bootstrapping for sampling ........................................................................................................ 5
o
Random re-grouping for experiments ........................................................................................ 5
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 Overview
We have a pretty good idea now of what we are teaching. But what is the best way
to teach it? The next step is to refine our pedagogical practises and trial different
ways of introducing content.
 Planning
Get the census at school resources embedded into planning at the department level.
Probability concepts take years to learn, not months, so long term, school wide
planning is required. We planned by course, but I wonder about the progression
from the student perspective over the years. The careful progression of lessons
builds concepts through activities. I was expecting too much from my students.
When students look at graphs they are not seeing what I see in spite of my best
efforts; hands on tasks are required in order for students to comprehend what the
computer is doing, and to understand the concepts.
o Teaching through a context rather than teaching concepts
In mathematics we often teach a concept and then we apply the concept. In
statistics concepts cannot be taught without a context, they must be taught through
a context.
o Hands on activities (first)
Tinkerplots scaffolds the students, so they can connect the real world with digital
simulation. Simulations are meaningless if they are not connected to the real world.
Students invent their own data, which helps them think of data as a whole.
Growing samples allows students to see stable features of variable processes.
Predicting shapes can encourage a global view and the concept of signal and noise.
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o Real world connections.
Go beyond coins, dice and spinners and connect to the real world. This generation
do not play board games as much, as they have technology at their fingertips. Build
probability models through computer applications.
o Probabilistic modelling links the real world.
The SWAMTU model is the PPDAC equivalent for probability modelling. Coming soon
and comes from the “real world”.
o Pachinkogram
The Pachinkogram (M. Pfannkuch, 2014) is on Census at School (CensusAtSchool,
2015a). Frequencies being easier to understand than probabilities; visualizations aid
understanding.
o Equally likely outcome bias
Perhaps the preference for equal probability has everything to do with their
exposure to dice, coins and regular spinners. Investigate “pass the pigs” as there is
no obvious theoretical model hence frequencies must be used.
o Strategic use of Pip Arnold resources.
I better understand their purpose to deal with shape and the story behind the data.
Building understanding through doing creates a deeper understanding than telling
students about concepts which gives superficial understanding.
o Follow Anna-Marie Martins blog about teaching.
http://teaching.statistics-is-awesome.org/probability-teaching-ideas-usingsimulation-part-1/ now that we have moved beyond survival we need to start
thinking about pedagogy.
o Passion found through deeper understanding.
I have gained lots of stories to share, about doctors, lawyers and risk. Linking
statistical literacy and financial literacy could also help student’s motivation.
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 Probability and statistics concepts are real world and tricky.
o Real world ignorance
Doctors and lawyers do not have a strong grasp on statistical and probability
concepts. The way information is presented can make a huge difference to the way
people interpret it. The media knows little. People must be taught how to simply
problems to enable intuitive understanding.
o Regression to the mean
Regression to the mean: any outcome with an element of chance involved will
naturally vary, and after a particularly good or bad event, a more normal one will
tend to follow. Humans tend to look for cause and effect when looking at two
sequential data values. Whilst a system change may impact on the mean, the
difference between two sequential events is random.
o Framing questions
Framing questions can cause rational people to give opposite answers as we tend to
take risk to avoid loss. I can be tempted to risk in order to avoid loss, but will always
take the bird in the hand. This explains why people often keep going down the
wrong path, rather than admit they have made a mistake and cut their losses.
o A misleading real world
Relative risk can be reported in a truthful and simultaneously misleading manner
which can have significant negative health implications. We teach the mathematics
of certainty, but not as much of the mathematics of uncertainty.
Lead-time bias and over diagnosis are not well understood by Doctors, leaving
doctors as easy targets for manipulation through misleading statistics.
Deception by confusing survival with mortality paints untrue improvements. Early
detection of cancer through screening may result in unnecessary treatments which
leave the patient with lifelong issues, without increasing the patients’ survival rate.
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We need to prepare the next generation to understand five year survival rates rather
than p-values.
Teach students to convert to natural frequencies so they can get a feel for complex
conditional probability questions. A chilling piece of evidence was that guilty verdicts
in court happen more often when probabilities are used, that are not understood.
Only around 15% of lawyers actually understand probabilities.
The overall message is to report facts honestly and transparently so that people can
make up their own minds.
o Natural frequencies easier than conditional probabilities.
Natural frequencies are easier to understand than conditional probabilities. Mortality
rates are more truthful than 5-year-survival rates. 5 year survival rates are
dependent on when screening happens, so do not report anything meaningful in
terms of health. Absolute risks are honest, whereas relative risks are meaningless
without the absolute risk being transparently reported.
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 3 types of Randomisation
o Simulations for stochastic modelling
Americans are talking about the curriculum being based on randomisation they are
referring to simulations.
o Bootstrapping for sampling
Bootstrapping is used for sample to population inference. I felt the signal was the
population parameter, and the noise was sampling error, when considering
inference.
o Random re-grouping for experiments
Random re-grouping is used to check for causality in experimental data. I felt the
signal was the effect of the treatment in an experiment, and the noise was chance.
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