Higherarchial anova Flashcards
What is a factorial anova DESIGN
one thing they all share - all levels of one independent variable appear at all levels of the other independent variables; applies to both fixed and random effects ANOVA
what we refer to when factors are crossed.
what is a hierachrial/nested ANOVA design
A design where each level of one of your factor/variable appears only at a single level of another; factors are nested
- A design in which factors are hierarchically built up.
- or one factor that’s nested within another.
provide an example of a nested factorial design
One method implemented in 3 schools. means the factor school is nested within the factor method.
goog critique for paper?
maybe you read it and think oh this should have been analyzed as a nested design but it was analysed as nested?
the problem of this is that if you treat is as a factorial design people will get interaction effects which is meaningless. and secondly, it doesn’t take into account this confound of everything not being combined with everything else. get a bias ANOVA results.
anova might tell. yout heres something significant even though there might not be
how many levels down max should you go with a nested ANOA desgin
2 levels should be the limit
what is the logic of ANOVA?
that we are comparing variability(means squared) due to some experimental manipulation with variability(means squared) due to error
this is the basis of the f ratio
why is the f ratio adjusted in random factor ANOVA designs?
to account for the added variability we get from having random factors
(using interaction terms as error terms)
nested anova and f ratio - what 2 issues do we now have to consider?
- each of the nested factors is only combined with certain levels of other factors - don’t have a total combination of everything with everything.
* means we do not have interactions, doesn’t make sense to assess the significance of interaction terms - in nested designs the difference between the two kings at the top of each level is confounded with the difference between king one’s assistant factors on one hand and the difference between king two’s assistant factors on the other.
We have to consider both of these while doing the analysis
factor ___ is nested within factor ___
story number is nested within story type
story example. Remember the first problem to consider with nested designs:
- each of the nested factors is only combined with certain levels of other factors - don’t have a total combination of everything with everything. Mean’s we do not have interactions doesn’t make sense to assess the significance of interaction terms
how do we analyse the data, taking this problem into account?
- We compute the main effects for each story type
- compute the effect of story number nested within story type
(2) Not to be confused with an interaction effect. It simply tells us whether there is a difference across exotic stories, and separately, if there is a difference across familiar stories
story number example. Remember one of the issues we need to consider with nested designs
- in this example, the effect of story type is confounded by differences among stories 1-3 and stories 3-6.
For stories 1-3 the third story’s mean is higher than the first two. we need to now if this is because the story is exotic or one story (regardless of exotic or not) just more memorable than the others
how can we tease this apart in analysis?
we can consider this confound in our statistical analysis by TREATING NESTED FACTORS (the story numbers) AS RANDOM FACTORS
takes care of the counfound between the top level variable and second level variable (in this example)
so in nested ANOVA we treat the nested factors as random. what about the top level factors? what about for this specific example?
Need to decide whether to treat them as fixed or random
- based on experimental design and your goal in terms of how you want. to interpret the results/generalise
for story example
- If the levels of story type – chosen randomly
- And goal is to draw general conclusions about familiarity – then story type should be considered random
OR
- If levels for story type are chosen purposely
- And all you are interested in is familiar vs exotic
- Then treat it as fixed
In this example story type is considered random
when should you check for homogeneity of variance?
always! whether you have fixed effects or random effects you always have to check!
what does the levene test tell us and do we want it to be significant?
- insignificant result tells us the variance or error variance is homogeneous or equivalent across all conditions.
- If however, the levene term is significant it tells us the variance or error variance in at least one of or conditions differ significantly with at least one of the other condition.
- This would be a problem.
output of the nested ANOVA table - how could you interpret the last source results conceptually?
the results of story number nested within story type
And for this example both of these effects are significant. Based on this we would reject the null hypothesis. Shows there is significant difference across the conditions.
The ANOVA told us there was a significant difference across conditions. Using this and the plot explain what was gwarning?
- exotic stories are recalled significantly better than familiar stories
- there is significant differences in recall WITHIN stories 1-3 and WITHIN 4-6. this is a significant effect of story number nested within story type
Written report of hierarchial/nested ANOVA. What do we include?
