Statistics
ANOVA
April 17, 2009
1. Situation: a categorical variable with I levels and a quantitative variable
2. Research question: is there a difference in the population means between the I different
groups?
H0 : µ1 = µ2 = · · · = µI
Ha : not all of the µi are equal
3. Possible solution: do all two-sample t tests.
(a) multiple comparisons
(b) post hoc analysis
4. Assumptions for ANOVA: Ideal
(a) Each population (treatment) has a normal distribution
(b) Each population has the same standard deviation
5. Assumptions for ANOVA: Practical
(a) It is safe to dispense with the normality assumption for large sample sizes and even
for quite small sample sizes if the distributions are not heavily skewed and there are
no outliers
(b) It is safe to dispense with the equal standard deviation assumption if the largest sample standard deviation is no more than twice the smaller sample standard deviation
or if the sample sizes are relatively large and of approximately the same size
6. Statistic; F – the bigger F is, the greater the evidence against H0 .
7. What does F measure?
F =
variation among means
variation within samples