One-Way RM ANOVA Flashcards
RM
Repeated Measures
Ss
Subjects
One-Way RM ANOVA
Analysis of variance when you have one nominal IV, one interval/ratio DV, and the levels of the IV are related. You use the same subjects/participants at each level.
One-Way RM ANOVA example
Recruit athletes and have them attempt to score as many goals as possible while being watched by 0 people, 5 people, and 100 people.
Source table labels
Sources: Between, IV, Ss, Within, and Total.
Calculating F-ratio
- Calculate SS:
a. Calculate SS(b/w). You will be provided SS(IV) and SS(Ss)
b. Calculate SS(Total)
c. Calculate SS(w/in) - Calculate dfs (5):
a. Calculate df(IV)
b. Calculate df(Ss)
c. Calculate df(b/w)
d. Calculate df(Total)
e. Calculate df(w/in) - Calculate MS (2):
a. Calculate MS(IV)
b. Calculate MS(w/in) - Calculate F-ratio (1)
One-Way RM ANOVA hypothesis testing steps
- Compute F ratio
- Set criteria for decision: using df(IV), df(w/in), and α level
- Make a decision: if F > F[crit], results are sig and you can conclude that the IV has an effect on the DV; if F < F[crit], results are nonsig (IV does not have an effect on DV)!!
- Compute comparisons: Run a Tukey test if needed (only for sig results)
SS(b/w) formula
SS(IV) + SS(Ss)
SS(IV) definition
Group’s difference from GM
SS(Ss) definition
Ss’s difference from GM
SS(w/in) formula
SS(total) – SS(b/w)
SS(total) formula
SS(b/w) + SS(w/in)
df(b/w) formula
df(IV) + df(Ss)
df(IV) formula
k - 1
df(Ss) formula
N - 1
df(w/in) formula
df(total) - df(b/w)
df(total) formula
(N * k) - 1
MS(IV) formula
SS(IV)/df(IV)
MS(w/in) formula
SS(w/in)/df(w/in)
F-ratio formula
MS(b/w)/MS(w/in)
F[crit] components
df(IV) as numerator df, df(w/in) as denominator df, α (alpha level)
Post-hoc tests
Compare all means after conducting ANOVA
Tukey test formula
q(x,y) = [M(x) - M(y)]/√(MS(within)/n). Use critical q-table to locate q(crit) after computing formula for each pairing of your IV levels.
Tukey test steps
- Calculate denominator term
- Calculate q(x,y) - Tukey test formula
- Locate q(crit): use k, df(w/in), and α (alpha level)
- ID significant differences between means (interpret meaning in context of problem)
Eta squared (η2)
Percentage of variance in the DV that can be attributed to the IV.
η2 formula
η2 = SS(IV)/SS(total)
