Lecture 4 Flashcards
why not use multiple unpaired t tests when a factor has 3 (or more) levels?
> testing all differences pairwise is cumbersome
> chance capitalization for repeated tests on the same data
ANOVA: whats in numerator? whats in denominator?
ANOVA:
numerator: variance between groups
denominator: variance within groups
how to calculate the SStotal?
SStotal
> sum of deviation of all observations from the overall mean
how to calculate SSeffect?
SS effect
> sum of the deviations of the group means from the overall mean
how to calculate SSerror?
SS error
> sum of the deviations within a group from the group mean
3 types degrees of freedom in one way ANOVA
(between subjects design)
> how to calculate
total: df = N-1
effect: df = number of levels - 1
error: df = (n -1) x number of levels
total = effect + error
ANOVA:
> what F value to expect when there is null effect
> why?
ANOVA:
> typical null effect has an F value around 1
> if F = 0, the conditions are identical
> but MSeffect also contains error, so F = 0 is unlikely
how does F test relate to t test?
F- test is a generalization of the t test
> F with df = (1,x) equals t² with df = x
4 types degrees of freedom in ANOVA
(within subject design)
> how to calculate
- total = ( a x n ) -1
- effect = a - 1
- subject = n-1
- error = (n-1)(a-1)
why does a within anova (assuming the same data) have more power than between?
withing subjects anova partitions the error variance into within subject variance and pure error variance
> MS effect = SS effect / SS error
> SSeffect is the same, but SS error is smaller
what are post hoc tests?
why are they important?
post hoc: anova tells you that there is a difference between two or more of the groups you tested
> does not tell you which groups, and if more than one
post hoc tests:
> determine which groups differ, and take chance capitalization into account
what are 2 common post hoc tests?
post hoc tests
- bonferroni
> divide alpha by number of tests (conservative!)
- tuckey HSD
> less conservative
what are two non parametric alternatives for one way ANOVA?
> when use which?
distribution free alternatives
- kruskal wallis test
> use for between subject design
- friedman test
> use for within subject design
>>> both provide chi square values
