Statistics
Lecture 11
ANOVA:
Analysis of Variance
(for a single factor)
•David Bartl
•Statistics
•INM/BASTA

Outline of the lecture
•Analysis of Variance  (ANOVA)  for a single factor
•Bartlett’s test

Two-sample t-test for the diff. of the pop. means // σX=σY



Two-sample t-test for the diff. of the pop. means // σX=σY
and


Two-sample t-test for the diff. of the pop. means // σX=σY



One-Way  ANOVA
•
•

One-way  ANOVA



One-way  ANOVA



One-way  ANOVA



One-way  ANOVA



One-way  ANOVA



One-way  ANOVA



One-way  ANOVA



One-way  ANOVA



One-way  ANOVA



One-way  ANOVA
sum of squares (between)
degrees of freedom (between)
mean squares (between)

One-way  ANOVA



One-way  ANOVA



One-way  ANOVA
sum of squares (within)
degrees of freedom (within)
mean squares (within)

One-way  ANOVA



One-way  ANOVA



One-way  ANOVA



One-way  ANOVA:   the test



One-way  ANOVA:   the test



One-way  ANOVA:   the test



One-way  ANOVA:   total variation
sum of squares (total)
degrees of freedom (total)
mean squares (total)

One-way  ANOVA:   total variation



One-way  ANOVA:   total variation



One-way  ANOVA:   total variation



One-way  ANOVA:   total variation



One-way  ANOVA:   total variation



Bartlett’s test
•
•

Bartlett’s test



Bartlett’s test



Bartlett’s test



Bartlett’s test



Bartlett’s test