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ECON1320  Lecture 3
Analysis of Variance (ANOVA)
Chapter 11.1 – 11.5
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Topics
1. Introduction to the concept of experimental
2. Completely randomised design & oneway
ANOVA
3. Multiple comparison tests
4. Randomised block design & twoway
ANOVA without replication
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Topic 1: Experimental design
• is a plan or a structure to test hypotheses in which
the researcher controls one or more variables
• It is made up of
independent
and
dependent
variables
•
dependent
variable (or
response
variable) is the
response to different
levels
of the independent
variable
• An independent variable (or
factor
) may be either a
treatment
variable or a
classification
variable.
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Treatment or classification variables?
• The treatment variable is under the control of the
analyst.
– Examples: amount of light, temperature
• The classification variable is an existing
characteristic of the experimental subjects which is
outside the control of the analyst. Classification
variables are present prior to experiment,
– Examples: work shift, gender, type of machine
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Treatment or classification variables?
• Each variable has two or more levels or
classifications/subcategories used by researcher
• Levels can be
categorical
or
numerical
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Example 1: Experimental design
• ABC Airlines flies three different versions of the
Boeing 737: the 737838, the 737476 and the 737
376. ABC Airlines wants to conduct a study to
determine if there is a significant difference in the
average annual maintenance costs for the three
Boeing types used. What are
– A dependent variable?
– Possible independent variables?
– Levels of independent variables?
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Example 1: Solutions
• A dependent variable: average annual maintenance
cost
– Levels of Type of 737
: Type I (737–838), Type II (737–
476), Type III (737–376)
– Levels of Age of plane
: 0–2 years, 3–5 years, 6–10 years,
over 10 years
– Levels of Number of flights
per week: 0–5, 6–10, over 10
– Levels of City
: Sydney, Melbourne, Brisbane, Perth
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ANOVA
• ANOVA is a statistical analysis technique
• In the experiment, individual items/people
being studied are not all the same.
• There is existence of variation and ANOVA
explores possible reasons for variation.
• ANOVA breaks down total variation into
possible causes.
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ANOVA methodology
• k samples are analysed and ANOVA is used
to test the following hypotheses
– H
0
: all population means are equal
– H
1
: At least one of the means is different from the
others
• In this case, there are k treatment levels
(groups)
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ANOVA methodology
• ANOVA partitions the total variance of the data into
two variances
– among (between)group variation attributable to treatment
effects
– withingroup variation = experimental error which is
unexplained by the treatment
• Given that the variances of populations are equal, a
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