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Objectives
After studying this chapter you should
appreciate the need for analysing data from more than two
samples;
understand the underlying models to analysis of variance;
understand when, and be able, to carry out a one way
analysis of variance;
understand when, and be able, to carry out a two way
analysis of variance.
7.0
Introduction
What is the common characteristic of all tests described in
Chapter 4?
Consider the following two investigations.
(a) A car magazine wishes to compare the average petrol
consumption of THREE similar models of car and has
available six vehicles of each model.
(b) A teacher is interested in a comparison of the average
percentage marks attained in the examinations of FIVE
different subjects and has available the marks of eight
students who all completed each examination.
In both these investigations, interest is centred on a comparison
of more than two populations; THREE models of car, FIVE
examinations.
In (a), six vehicles of each of the three models are available so
there are three independent samples, each of size six. This
example requires an extension of the test considered in Section
4.3, which was for two normal population means using
independent samples and a pooled estimate of variance.
In (b) however, there is the additional feature that the same eight
students each completed the five examinations, so there are five
dependent samples each of size eight. This example requires
an extension of the test considered in Section 4.4, which was for
two normal population means using dependent (paired) samples.
This chapter will show that an appropriate method for
investigation (a) is a one way anova to test for differences
between the three models of car. For (b), an appropriate method
is a two way anova to test for differences between the five
subjects and, if required, for differences between the eight
students.
7.1
Ideas for data collection
Undertake at least one of Activities 1 and 2 AND at least one of
Activities 3 and 4. You will require your data for subsequent
analysis later in this chapter.
Activity 1
Estimating length
Draw a straight line of between 20 cm and 25 cm on a sheet of
plain white card. (Only you should know its exact length.)
Collect 6 to 10 volunteers from each of school years 7, 10 and
13. Ask each volunteer to estimate independently the length of
the line.
Do differences in year means appear to outweigh differences
within years?
Activity 2
Apples
Obtain random samples of each of at least three varieties of
apple. The samples should be of at least 5 apples but need not
be of the same size.
Weigh, as accurately as you are able, each apple.
Compare variation within varieties with variability between
varieties.