Lecture 19 Introduction to ANOVA - Purdue University

33 Pages·2011·0.25 MB·English

Lecture 19
Introduction to ANOVA

STAT 512
Spring 2011

Background Reading
KNNL: 15.1-15.3, 16.1-16.2
19-1
Topic Overview

•
Categorical Variables
•
Analysis of Variance
•
Lots of Terminology
•
An ANOVA example

19-2
Categorical Variables

•
To this point, with the exception of the last
lecture, all explanatory variables have been
quantitative; e.g. comparing X = 3 to X = 5
makes sense numerically

•
For categorical or qualitative variables there
is no ‘numerical’ labeling; or if there is, it
isn’t meaningful.

19-3
Example

•
Five medical treatments – ten subjects on
each treatment.

•
Goal: Compare the treatments in terms of
their effectiveness
(cid:1)
If there were two treatments, what would
we use?

19-4
ANOVA

•
ANOVA = Analysis of Variance

•
Compare means among treatment groups,
without assuming any parametric
relationships (regression does assume such
a relationship).

•
Example: Price vs. Sales Volume

19-5
Regression Model

19-6
ANOVA Model

KEY DIFFERENCE: No assumption is made
about the manner in which Price and Sales
Volume are related.
19-7
Similarities to Regression

•
Assumptions on errors identical as to
regression

•
We assume each population is normal and
the variances are identical. We also
assume independence.

•
Can get “predicted values” for each group,
as well as CI’s.
19-8
Differences

•
No specific relationship is assumed.

•
Goal becomes: look for differences among
the groups.

19-9
Terminology
•
We may refer to any qualitative predictor
variable as a factor.
•
Each factor has a certain number of levels.
•
Experimental factors are “set” or
“assigned” to the experimental units;
observational factors are characteristics of
the experimental units that cannot be
assigned.
19-10