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STAT1008
Section 1
Variables, Data and
Statistics – Basic
Concepts
What is “Statistics”?
“a way to get information from data”
A framework for dealing with variability
A way to make decisions under uncertainty
Statistical inference:
the problem of
determining the behaviour of a large
population by studying a small sample from
that population
What is a population? What is a sample?
Population:
a collection of the whole of
something – e.g. all female students of ANU;
all people who live in Tuggeranong; all
all people who live in Tuggeranong; all
people who play the flute.
Sample:
a set of individuals drawn from a
population e.g. the female students in
STAT1008 are a sample of all female
students at ANU.

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If we have a population….
We can get parameters
– true values for
things like the centre and spread of the
population
We know the answers – what proportion are
this tall? We look at the population and get
the answer.
If we have a sample…
We can get statistics
– these are values that
estimate the parameters e.g. sample centre
and sample spread used to estimate
and sample spread used to estimate
population centre and population spread
We have to use
inference
to do this
estimation – what proportion are this tall?
Based on our sample, we would expect….
So, statistical inference…
The process of making an estimate, prediction or
decision about a population, based on a sample.
Note: populations are generally hard to study – large
Note: populations are generally hard to study – large,
awkward! So using samples is much more common
Decisions made using samples will not always be
correct: need a measure of
reliability
–
Confidence level:
proportion of times that an estimating
procedure will be correct
–
Significance level:
measures how many times the conclusion
will be wrong