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Knox Academy Geography Department
Advanced Higher
Inferential Statistics 1:
Basic Concepts
Ollie Bray – Knox Academy, East Lothian
Sampling

There are three standard sampling
techniques:
 Random
 Systematic
 Stratified
Random Sampling

This is where each item from a population has
an equal chance of being selected.

To select from this population each member is
assigned a number using computer generated
random number tables.

Once a number has been chosen it can be
related to a grid reference, an angular
direction, a distance or whatever else we are
sampling.
Systematic Sampling

This is where samples are selected in
a regular manner. For example:
 taking
a vegetation sample every 10 metres
(linear sample),
 taking a sample at a series of points located
at the intersection of a 10 metre grid
(point sampling),
 selecting every tenth customer at the
supermarket
 etc…
©LT Scotland. From Geographical
Measurements and Techniques: Statistical
Awareness. June 2000.
Stratified Sampling

This takes into account the relative proportion of
different groups within the sample.

For example in a sand dune investigation two
thirds of the dune may be managed and the rest
unmanaged.

Stratified sampling will select a representative
sample from each of the two areas.

If nine transects are to be selected then the
correct balance is six managed and three
unmanaged.
Sample Size and Bias

Many investigations fail because the
size of the sample is too small and this
leads to unreliable results.

When collecting a sample the main
concern is to remove bias (eg: obtain a
representative sample)
Your turn

Read page 37 – 38 in the ‘Geographical
Measurements and Techniques: Statistical
Awareness’ from LT Scotland. Answer Task 1
(pg 38) and Task 2 (pg 39).
Hypothesis

A hypothesis is a statement or a hunch.

To test a hypothesis the first thing we
do is write down a statement – called
the null hypothesis (written NH).

The null hypothesis is the opposite of
what the researcher is trying to prove.
Example

We are interested in finding out if there is
any difference between the average number
of Highers passed by S5 & S6 pupils in Knox
Academy and Dunbar Grammar School.

There will almost certainly be a difference.
But how big does are difference have to be
before we can say that it is a ‘real’ or
‘significant’ difference?
Test Statistics

To answer this we calculate a figure known as
a test statistic, which is based in data from
our samples.

Different types of problems require
different test statistics these have all been
put into statistical tables.

All we need to do is to calculate our value and
compare it with the value in the table to get
our answer.
Null Hypothesis

‘There is no difference between the average
number of Highers passed at Knox Academy
and Dunbar Grammar School. ‘
If you are proved correct then you reject the
null hypothesis and accept the alternative
hypothesis (AH) which would be:

‘There is a difference between the average
number of Highers passed at Knox Academy
and Dunbar Grammar School. ‘
Significance (1)

Before carrying out the test we have to
decide on a significance level which lets
us determine at what point to reject
the null hypothesis and accept the
alternative hypothesis.
Significance (2)

Significance is based on the probability
of chance.
Difference between the average number of
Higher’s passed by S5 & S6 pupils in Knox
Academy and Dunbar Grammar School.
Probability of chance

Statisticians have calculated the
probability of ‘chance’ events occurring
that may affect our results.

They have come to the conclusion that,
if the probability that an event could
occur by chance is less than 1 in 20,
they say the result is significant. ie: the
result is not just a chance event.
Look at page 62 – 65 at the
back of the blue book.

The significance levels at the back of
the blue book are 0.05 and 0.01 which
means there is only a 1 in 20 (0.05), or a
1 in 100 (0.01), probability of the event
occurring by chance.

The values in the tables are called
critical values.
Critical Values In Use

From your calculations and the
significance tables you will find that if
the value of the test statistic you have
calculated is greater than the value in
the table (the critical value), you can
reject the null hypothesis and accept
the alternative hypothesis.