two and three way anova Flashcards
partitioning of variance
anova divides the variance observed in data into different parts resulting from different sources and assesses the relative magnitude of the different parts of variance
then examines whether a particular part of the variance is greater than expectation under the null hypothesis
in one way anova variance is partitioned into SSM and SSR
partitioning of variation in two way ANOVA
SSM is further partitioned into:
SSA: (variation between means for Factor A)
- look at marginal row means
SSB: (variation between means for Factor B)
- look at marginal column means
SSAxB: (variation between cell means)
how do we establish whether an interaction is present
on a graph: if lines cross, or look like they would if the graph was extended
omega squared for the main effect of factor A:
wA^2=o^^2A/o^^2 total
omega squared for the main effect of factor B
w^2B=o^^2B/o^^2 total
omega squared for the interaction effect (w^2AxB)
w^2AxB= o^^2 AxB/o^^2 total
o^^2A
((a-1)(MSA-MSR))÷Ngab
O^^2B
((b-1)(MSB-MSR))÷Ngab
O^^2AxB
((a-1)(b-1)(MSAxB-MSR))÷Ngab
O^^2 total
o^^2A+O^^2B+o^^2AxB+MSR
Ng
number of people per condition
when is a two/three way ANOVA appropriate for a research question
when you have more than two means and two or more factors
