1. Why would you expect an F ratio of about 1, and departures from this only due to chance, if there was no significant difference among treatments analysed by a single-factor ANOVA?
2. The following simple set of data is for three 'treatments' each of which contains four replicates: Treatment A: 1, 2, 3, 4; Treatment B: 2, 3, 4, 5; Treatment C: 3, 4, 5, 6. The means of the three samples are similar and there is some within group (error) variance around each treatment mean. Use a statistical package to run a single-factor ANOVA on these data.
(a) Is there a significant difference among treatments?
(b) What are the within group (error) sum of squares and mean square? Change the values for Treatment C to 21, 22, 23 and 24, and run the analysis again.
(c) Is there a significant difference among groups?
(d) Have the within group (error) sum of squares and mean square changed from the analysis in (a)? Can you explain why?