Analysis of Variance - MA772

Location Term Level Credits (ECTS) Current Convenor 2018-19 2019-20
Canterbury Autumn
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6 15 (7.5) PROF MS Ridout


Probability and Inference (MA629), Regression Models (MA632); Linear Algebra (MA553) is strongly recommended.





Analysis of variance is a fundamentally important method for the statistical analysis of data. It is used widely in biological, medical, psychological, sociological and industrial research when we wish to compare more than two treatments at once. In analysing experimental data, the appropriate form of analysis of variance is determined by the design of the experiment, and we shall therefore discuss some aspects of experimental design in this module. Lectures are supplemented by computing classes which explore the analysis of variance facilities of the statistical package R. Syllabus: One-way ANOVA (fixed effects model); alternative models; least squares estimation; expectations of mean squares; distributional results; ANOVA table; follow-up analysis; multiple comparisons; least significant difference; confidence intervals; contrasts; orthogonal polynomials; checking assumptions; residual plots; Bartlett's test; transformations; one-way ANOVA (random effects model); types of experiment; experimental and observational units; treatment structure; randomisation; replication; blocking; the size of an experiment; two-way ANOVA; the randomised complete block design; two-way layout with interaction; the general linear model; matrix formulation; models of full rank; constraints; motivations for using least squares; properties of estimators; model partitions; extra sum of squares principle; orthogonality; multiple regression; polynomial regression; comparison of regression lines; analysis of covariance; balanced incomplete block designs; Latin square designs; Youden rectangles; factorial experiments; main effects and interactions.


This module appears in:

Contact hours

48, 36 lectures and 12 computer classes

Method of assessment

80% Examination, 20% Coursework

Preliminary reading

NR Draper and H Smith Applied Regression Analysis, Wiley, 3rd ed., 1998 (R)
AM Dean and D Voss Design and Analysis of Experiments, Springer, 1999 (B)
GM Clarke and RE Kempson Introduction to the Design and Analysis of Experiments, Arnold, 1997 (R)

See the library reading list for this module (Canterbury)

See the library reading list for this module (Medway)

Learning outcomes

The Intended Subject Specific Learning Outcomes. On successful completion of the module students will have:
a. a reasonable knowledge of analysis of variance and its application to a
variety of different models.
b. a reasonable knowledge of the basic principles of experimental design.
c. a reasonable ability to do analysis of variance calculations with a computer, and to interpret the resulting output.
d. a reasonable understanding of the inter-relationship between the design of a study and its subsequent analysis.
e. some appreciation of the relevance experimental design and analysis to real world problems.

The Intended Generic Learning Outcomes. On successful completion of this module, students will have
a. developed their understanding of probability and statistics
b. applied a range of mathematical techniques to solve statistical problems.
c. developed their ability to abstract the essentials of problems and to formulate them mathematically.
d. improved their key skills in numeracy, written communication and problem solving
e. enhanced their study skills and ability to work with relatively little supervision.

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