Statistics
ANOVA - Further Topics
November 12, 2008
Outline
Research question: is there a difference in the population means of I populations (or treatments)?
H0 : µ1 = µ2 = · · · = µI
Ha : not all of the µi are equal
1. Why is it called ANOVA?
2. What is the relationship between ANOVA and the two-sample t?
3. What do we do if we find strong evidence against the null hypothesis? Example: the
chicks again.
4. Where does the F statistic come from?
F =
variation among means
variation within samples
(a) Measuring variations among the means
SStreatments =
X
(x̄i − x̄)2
(b) Measuring variation withing the samples:
X
SSerror =
(x − x̄i )2
(c) Measuring total variation:
SStotal =
X
(x − x̄)2
Statistics
ANOVA - Further Topics
November 12, 2008
Reading Quiz - Chicks again
Six groups of 12 chicks are each fed a different diet. The weight of each chick is measured
after a fixed time period. The results of an ANOVA on this data are in the following Crunchit
output.
1. What are the parameters in this story?
2. What is the null hypothesis tested by this analysis?
3. What conclusion do you draw about the six diets? Write a sentence that expresses this
conclusion.