module 6 Flashcards
when and why to use between subjects factorial ANOVA
- when: between subjects experiments have more than 1 independent variable
- why: modest gain in efficiency, and tests the joint effects of the IV
one way vs two way between subjects ANOVA
- one way: test one effect (effect of the IV)
- two way: test three effects (main effect of IV1, main effect of IV2, and interaction effect of IV1+IV2
interactions
- indicates that effect of one IV is not the same across levels of another IV (they effect differently)
- tests difference of differences
what are the three null hypotheses used in 2 way anovas
- H0: μa1=μa2
- H0= μb1=μb2
- H0= no interaction present (effect of each factor is independent)
t or f: 2 way anovas with more than 2 levels each (ex 2x3) still only have 3 null hypotheses
true, they just have more means within the hypotheses
f test formula for null hypotheses for a between subjects two way anova simple
f = variance between treatments/variance within treatments
f test formula for null hypotheses for a between subjects two way anova with factors in numerator and denominator specified
f = treatment effect of (A/B/AxB) + individual difference + experimental error/individual difference+ experimental error
what factors make up between variance in an f test for between subjects factorial anova
- factor a between variance (MSa)
- factor b between variance (MSb)
- factor a x factor b between treatment variance (MSaxb)
f value near 1 indicates that that the given treatment effect is ____ and an f value way greater than 1 indicates that the given treatment effect is ____
non-existant/0, existant
in a two way between subjects anova computation, what do the values G and N represent
G: grand total of all scores in experiment
N: total number of score in entire experiment
in a two way between subjects anova computation, what do the values p, q, and n represent
p: # of levels in factor A
q: # of levels in factor B
n; # of scores in each treatment condition (each cell of the AxB matrix)
AB total (two way between subjects anova)
sum totals of all scores in specific cell of AxB matrix (ex A1+B1, A1+B2, A2+B2, A2+B1)
A and B totals (two way between subjects anova)
- total of all scores in a level of each factor (A1, A2, B1, B2)
total sums of squares for two way between subjects anova
- SStotal= SSwithin+SSbetween
- or = ∑X^2 - G^2/N
within treatment variability for two way between subjects anova
SS within = ∑ SS w/in each treatment cell
general between treatment variability for two way between subjects anova
SS between = ∑ AB^2/n - G^2/N
how does a two way anova shoe variability for A, B, and AxB
- A: SSa= ∑ A^2/qn - G^2/N
- B: SSb=∑ B^2/pn - G^2/N
- AxB: SSaxb= SSbetween - SSa-SSb
t or f: each SS has the same df value in a two way between subjects anova
false, theyre all different
df total= ___, and df within= ____
N-1, ∑ (n-1) or N-pq
df for between subjects anova
- df between = pq-1
- dfA= p-1
- dfB= q-1
- dfAxB= df between-dfA-dfB
means squared for two way between subjects anova
- general MS= SS/df
- MSa=SSa/dfA
- MSb=SSb/dfB
- MS within= SSwithin/dfwithin
- MSAxB=SSaxb/dfaxb
f ratio formula for between subjects two way anova
f=MSa/Mswithin
or = MSb/MSwithin
or = MSaxb/MS within
why are follow up tests required for 2 (and 3) way anovas
doesnt show nature of change in effect of one IV across the other
follow up tests for between subjects ANOVA
- general: posteriori (post hoc) or priori (planned)
- main effect follow ups: none for main effects w/ 2 levels or planned contrasts if basis exists or post hoc if no expectation exists
simple effect
- effect of one IV at a specific level of the other IV)
- if the simple effect is significant, a difference exists somewhere
abelson’s types of claims
- ticks: clearly stated findings, detailed statements of distinct research results
- buts: statements that qualify/constrain ticks
- blobs: cluster of undifferentiated research results (shows difference but not where)
examples of ticks and buts in 2x2 anova
- main effect of IV1
- main effect of IV2
- interaction of IV1xIV2
simple effect analysis
- looks at the difference between MS across levels of one IV at a single level of the other IV (ex single column/row of AB design)
setting alpha and beta in a two way between subjects factorial anova
- alpha: 0.05=norm for omnibus tests in factorial anova
- beta: compute power for each test since there are multi, establish the min acceptable power and use it for all so its all strong
standard effect size calculation for 2 way between subjects anova
- partial eta squared: ηp^2= SS effect/ SSeffect + SSwithin
- cohen’s f:
f= √SSeffect/SSerror
guide for cohen’s f and partial eta squared
- cohen’s f: .10=small, .25=med, .40=large
- partial eta squared: .01=small, .06=med, .14=large
