sadc course in statistics revision on tests for means using cast (session 17)

SADC Course in Statistics

Revision on tests for means using CAST

(Session 17)

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Learning Objectives

By the end of this session, you will be able to

• discuss the different approaches used in dealing with independent and paired samples for comparing means

• explain how you will decide when to use a one-sided test and when to use a two-sided test

• appreciate how the evidence against the null hypothesis becomes stronger as the difference between the two means increases


Using CAST for SADC: Higher Level

• Further insight into the concepts introduced in sessions 12 and 13 can be obtained by working through some of the pages of CAST in Sections 7.4 and 7.5

• 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


CAST – Section 7.4

Consider CAST Section 7.4: Hypothesis test for difference

This section has 3 sub-sections as follows:

• Testing a hypothesis

• One-tailed tests

• Exercises about tests

We briefly outline below what each section contains. This is aimed at reminding you of the key ideas involved.


CAST – Section 7.4 – Page 1

This sections is aimed at showing

• the development of a test for testing whether 2 group means are equal.

• There is a choice of 4 data sets you might use for this purpose.

• There is also a simulation exercise designed to emphasise that even when H0 is true, it is

still possible to get a significant result 5% of the time when testing at a 5% level of significance.



This sections is aimed at

• distinguishing between a 1-tailed and 2-tailed test.

• This choice is important and you will be given examples that help you to understand the difference.

• Again a simulation exercise is included to illustrate the ideas involved.



This section gives some exercises.

It gives you practice in doing 1-tailed and 2-tailed tests for testing the difference between two population means.


CAST – Section 7.5

Consider CAST Section 7.5: Paired Data

This section has 4 sub-sections as follows:

• Paired data

• Analysis of differences

• Paired t-test

• Pairing and experimental design

We look at each in turn and also remind youof the key ideas involved.


CAST – Section 7.5 – Pages 1 and 2

These sections are aimed at

• explaining what pairing is

• providing a range of different examples to illustrate the ideas

• emphasising the need to compute and analyse differences between paired values

Can you remember why pairing is done?

What is the benefit of pairing?


CAST – Section 7.5 – Pages 3 and 4

These sections are aimed at

• explaining the testing approach with paired samples

• demonstrating how the evidence against the null hypothesis increases as the difference between the means of the two populations increases

• using a simulation exercise to help distinguish between independent and paired samples.


Practical work on CAST follows…

sadc course in statistics revision on tests for means using cast (session 17)

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