12. Comparison of Several Means 1 Flashcards
What do you use with 2 samples?
t-test
What is ANOVA?
analysis of variance
Why use an ANOVA instead of multiple t-tests?
when you run multiple t-tests, get an inflated familywise (type I error) rate
What does an ANOVA do?
tests whether 3+ means are the same or not
What type of test is an ANOVA?
omnibus test
What is an omnibus test?
- tests for overall experimental effect
- doesn’t provide info regarding which groups were affected
f-stat equation
f-stat = model/error
What does the f-stat tell us?
- only that the experimental manipulation had some effect
- doesn’t tell specifically what it was
ANOVA partitions variance into two categories
- systematic
- unsystematic
SS_T
- total sum of squares
- total amount of variation within a data set
SS_M
- model sum of squares
- amount of systematic variation (explained by the model)
SS_R
- residual sum of squares
- amount of unsystematic variation (not explained by the model)
MS_M
- mean squares model
- SS_M ÷ df_M
MS_R
- mean squares residual
- SS_R ÷ df_R
f-stat equation
MS_M ÷ MS_R
df_M
one less than the number of groups
k-1
df_R
total degrees of freedom - df_M
N-K (total sample size - number of groups)
What do you do once you calculate the f-stat?
compare to critical value with the same df in the appendix
If the f-stat is more than the critical value:
- difference between means due to more than chance
- significant difference
If the f-stat is less than the critical value:
- difference between means due to only chance
- not a significant value
types of ANOVAs
- one-way independent
- factorial ANOVA
- ANCOVA
IVs for a one-way ANOVA
1 IV with between group differences
IVs for a factorial ANOVA
2+ IVs
What is an ANCOVA?
ANOVA with an addition of a covariate
