Revision on tests for
proportions using CAST
(Session 18)
SADC Course in Statistics
Learning Objectives
By the end of this session, you will be able to
• discuss how two proportions may be
compared using an z-test or several
proportions compared using a chi-squared
test
• set up hypotheses to test for independence
between two categorical variables
• have a greater understanding of testing
procedures and underlying assumptions
when dealing with categorical variables
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Using CAST for SADC: Higher Level
• Further insight into the concepts
introduced in sessions 14 and 15 can be
obtained by working through some of the
pages of CAST in Sections 8 and 9
• Practical work using CAST will therefore
form the main activity in this session
• Here we will just highlight a few of the
features that the above pages in CAST aim
to demonstrate
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CAST – Section 8.2
Consider CAST
Section 8.2: Hypothesis test for difference
This section has 2 sub-sections as follows:
• Testing for differences between probabilities
• Exercises about testing hypotheses
Both these pages give a good illustration of
the testing procedure for comparing two
proportions. Evaluation and interpretation
of p-values is re-enforced.
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CAST – Section 9.3
Consider CAST
Section 9.3: Testing for independence
This section has 6 sub-sections as follows:
• Independence from samples
• Testing for independence
• Chi-squared test statistic
• P-value for ch-squared test
• Examples
• Comparing groups
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CAST – Section 9.3 – Page 1
This section is aimed at showing clearly
• the meaning of independence using
numerical examples
• the calculations of expected values under
the hypothesis of independence are clarified
The illustrations are clear and easy to follow.
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CAST – Section 9.3 – Page 2
This section is aimed at showing
• the need to compare observed and
expected frequencies in order to judge
whether two categorical variables are
independent
• difficulties caused if the comparison is made
by only looking at the deviation sums of
squares between observed and expected
values, e.g. due to its dependence on the
sample size
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CAST – Section 9.3 – Page 3
This section illustrates quite a few points:
• The justification for the formula used in
computing thechi-squared test statistic
• A simulation exercise to demonstrate that
the 2 is little affected by changes in sample
size
• Graphical demonstration to show
– how the shape of the 2 changes to a more
symmetric shape as its d.f. increases
– That the mean of the 2 equals its d.f.
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CAST – Section 9.3 – Page 4
This section is aimed at:
• showing how the chi-squared test for
independence is carried out
• graphically illustrating exactly what the pvalue is and how it may be interpreted
• recognising that the chi-squared test is an
approximate test and highlighting
conditions under which it yields a reliable pvalue
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CAST – Section 9.3 – Pages 5 & 6
These sections show:
• further illustrative examples
• how the test of independence can be
extended to situations where interest lies in
comparing several groups
– e.g. comparing two proportions is equivalent
to performing a chi-square test on a 2x2
table of frequency counts.
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Practical work on CAST follows…
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