Statistics
ANOVA
November 11, 2008
Outline
1. Situation: a categorical variable with I levels and a quantitative variable
(a) Simple random samples from each of I populations
(b) Simple random sample from one population divided into I groups based on a categorical variable
(c) Randomized comparative experiment with I treatments
2. Research question: is there a difference in the population means?
H0 : µ1 = µ2 = · · · = µI
Ha : not all of the µi are equal
3. Assumptions for ANOVA: Ideal
(a) Each population (treatment) has a normal distribution
(b) Each population has the same standard deviation
4. 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
5. Statistic; F – the bigger F is, the greater the evidence against H0 .
6. What does F measure?
F =
variation among means
variation within samples
Statistics
ANOVA
November 11, 2008
Reading Quiz: Pallets
A local Grand Rapids company repairs wooden pallets. It has four workers. Over a 10 day
period, the number of pallets repaired by each worker is recorded. The results are here:
1. There are two variables in this story. Name them and their type.
2. The company is interested in whether the workers repair pallets at different rates. What
are reasonable parameters measuring the rate of pallet repair?
3. What is the most reasonable null hypothesis to test in this situation?
4. What is the conclusion concerning this null hypothesis?