Statistical Methods
for Economists
Lecture (7 & 8)a
One-Way Analysis of Variance
(ANOVA)
•David Bartl
•Statistical Methods for Economists
•INM/BASTE

Outline of the lecture
•One-Way ANOVA:  Introduction and Motivation
•One-Way ANOVA:  Summary, Assumptions, and the Goal of the analysis
•One-Way ANOVA as a model of Multiple Linear Regression
•One-Way ANOVA:  the F-test

ANOVA:  Introduction



ANOVA:  Introduction



One-factor ANOVA:  Motivation:  Example 1



One-factor ANOVA:  Motivation:  Example 1



One-factor ANOVA:  Motivation:  Example 1



One-factor ANOVA:  Motivation:  Example 1



One-factor ANOVA:  Motivation:  Example 2



One-Way ANOVA
•Summary
•Assumptions
•The classical assumptions
•The purpose of the Analysis of Variance
•

One-way ANOVA:  Summary



One-way ANOVA:  Summary



One-way ANOVA:  Summary



One-way ANOVA:  Summary



One-way ANOVA:  Assumptions



One-way ANOVA:  Assumptions



One-way ANOVA:  Assumptions



One-way ANOVA:  Assumptions



One-way ANOVA:  The Classical Assumptions



One-way ANOVA:  The Classical Assumptions



One-way ANOVA:  The Classical Assumptions
homoscedasticity, i.e. the variance
is the same

One-way ANOVA:  The purpose of the analysis



One-way ANOVA:  Solution



One-way ANOVA:  Solution



One-Way ANOVA
as a model
of Multiple Linear Regression
•
•

One-way ANOVA:  Model of Multiple Linear Regression



One-way ANOVA:  Model of Multiple Linear Regression



One-way ANOVA:  Model of Multiple Linear Regression



One-way ANOVA:  Model of Multiple Linear Regression



One-way ANOVA:  Model of Multiple Linear Regression



The Coefficient of Determination  (R2):  Th. 8:  Corollary
0
(the orthogonal
complement =
= the space of
the residuals)
subspace
of dimension
the line is a subspace
of dimension
By Theorem 8:
Let:

The Coefficient of Determination  (R2):  Th. 8:  Corollary
0
(the orthogonal
complement =
= the space of
the residuals)
subspace
of dimension
the line is a subspace
of dimension
The Coefficient of Determination:
Let:

The Coefficient of Determination (R2):  TSS=RSS+RegSS
0
(the orthogonal
complement =
= the space of
the residuals)
subspace
of dimension
the line is a subspace
of dimension
By the Pythagoras Theorem:
Let:

The Coefficient of Determination  (R2)



The Coefficient of Determination  (R2):  Th. 8:  Corollary



One-way ANOVA:  Model of Multiple Linear Regression



One-way ANOVA:  Model of Multiple Linear Regression



One-way ANOVA:  Model of Multiple Linear Regression



One-way ANOVA:  Model of Multiple Linear Regression



One-way ANOVA:  Model of Multiple Linear Regression



One-way ANOVA:  Model of Multiple Linear Regression



One-way ANOVA:  Model of Multiple Linear Regression



One-way ANOVA:  Remarks:  Sample variances



One-Way ANOVA:  The F-test
•The F-test
•

One-Way ANOVA:  the F-test



One-Way ANOVA:  the F-test