Analysis of variance (ANOVA) - comparing several means at once

Question 1

what is this about?

Answer 1

is there a difference among many sub-groups (eg. different treatment groups or level of the explanatory) in the mean for a response variable x

Question 2

numerator in the standardised score

Answer 2

a measure of the difference in the group means between groups (called treatment sum of squares)

Question 3

denomenator in the standardised score

Answer 3

a measure of the variability of the date (within groups) (called error sum of squares)

Question 4

preforming an ANOVA test

Answer 4

there are treatment groups with N observations in all

H0: means of groups are the same
H1: means of groups are not the same

calculate test statistic

Question 5

what assumptions does ANOVA make?

Answer 5

variability within groups is the same, populations have the same SD, all normally distributed