Anova

Why use anova?

running separate tests multiple times inflates type one error

type one error

rejecting the null hypothesis even if it is true

ANOVA

tests to see if there are differences between 2 or more groups simultaneously

f-statistic

(variation between groups)/(variation within groups)

x double bar

the mean of all values, ignoring which group they're in (grand mean)

Total variation (SS total)

=variation between groups + variation within groups

variation between groups

is the variation caused by which group you are in

variation within groups

variation within each group/between humans

k

number of groups

n

total number of participants in all groups

MS (mean square)

SS/df

large F statistic

there is a large difference between at least two of the groups

eta squared

(Between groups SS)/(Total SS)

analyzing eta squared

-less than or equal to .09, small effect
-between .09 and .25, medium effect
-greater than or equal to .25, large effect

Same Variance assumption

Variance should not be 4 times larger in one group than another, so standard deviations should not be more than two times larger in one group

null hypothesis

all group means are equal

alternative hypothesis

at least one group mean is not equal to another

post hoc test

only done following a reject the null conclusion.
uses independent t tests of groups to find which groups are different from one another

number of comparisons used for post hoc

k(k-1)/2

Bonferroni correction

adjusts the alpha level for each of the post-hoc tests to be equal to .05/(number of comparisons)