test 4 Flashcards
When do you use one-way between subjects ANOVA?
- 2 variables
- independent groups design
- IV has more than 2 variables
- DV is interval level
Why not do pairwise tests?
- would increase probability of making Type I error
- ANOVA f- ratio provides a single omnibus (overall) test of null hypothesis
One-way between-subjects ANOVA hypotheses
Ho: σ2μj= 0
H1: σ2μj > 0
One-way between-subjects ANOVA assumptions
- normative
- homogeneity of variance
F ratio for one-way between-subjects ANOVA - conceptual
F = variance between groups / variance within groups
One-way between-subjects ANOVA partition of sums of squares
SS total = SS between + SS within
One-way between-subjects ANOVA degrees of freedom
df (BG) = k - 1
df (E) = N - k
df (total) = N - 1
One-way between-subjects ANOVA critical value
Look up in table C.3
Numerator: df (BG)
Denominator: df (E)
F ratio
F = MS (between) / MS (within)
Tukeys HSD Test
in one-way between-subjects ANOVA
- tells us which pairwise comparisons are significantly different from one another
1. calculate differences between all the pairs of means
2. use Tukey’s CD
3. q is in table C. 4
Any difference in pairwise comparisons of means that meets or exceeds the CD (in abs val) is significant
When is one-way repeated measures ANOVA used?
- 2 variables
- IV has more than 2 levels
- DV is interval level
one-way repeated measures ANOVA key assumptions
- normality
- sphericity (equal variances for all treatments and each participants’ scores are related across treatments
one-way repeated measures ANOVA hypotheses
Ho: σ2μj = 0
H1: σ2μj > 0
F- ratio one-way repeated measures ANOVA- conceptual
F = variance between treatment means/ error variance
one-way repeated measures ANOVA partitioning 2 sources of error
SS (BP): overall individual differences on the DV (controlled by design)
SS (E): individual differences in the way that IV influences scores on DV
one-way repeated measures ANOVA partitioning of SS
SS (T) = SS (BG) + SS (BP) = SS (E)
one-way repeated measures ANOVA degrees of freedom
df (BG) = k - 1 df (BP)= n - 1 df (E) = (k - 1) (n - 1) df (T) = kn - 1 Check that df (BG) + df (BP) + df (E) = df (T)
one-way repeated measures ANOVA critical value of F
numerator: df (BG)
denominator: df (E)
Post hoc: Bonferroni procedure
one-way repeated measures ANOVA
a way of controlling experiment-wise error rate
testwise alpha = experimentwise alpha / # of pairwise comparisons
find df for all pairwise related-samples t tests
When do we use the two-way between subjects ANOVA?
- 3 variables (2 IV, 1 DV)
- independent groups design
- DV is interval level
two-way between subjects ANOVA key assumptions
- normality
- homogeneity of variance
main effects
overall effect of an IV, ignoring the effect of the other IV(s)
- compare relevant marginal means
interaction
conceptual- occurs when the effect of one IV changes over levels of another IV
mathematical- indicated when variability among cells means cannot be accounted for by main effects
two-way between subjects ANOVA partition of sums of squares
SS (T) = SS (A) + SS (B) + SS (A x B) + SS (E)
two-way between subjects ANOVA degrees of freedom
df (A) = p - 1
df (B) = q - 1
df (A x B) = (p - 1) (q - 1)
df (E) = pq (n - 1)
simple effects analyses
two-way between subjects ANOVA
- pinpoint the nature of a significant interaction
- significant interaction indicates a significant effect of an IV at one level of the second IV but NOT at another level of that second IV
- use a one-way between subjects ANOVA to compare levels of one factor for each level of the second factor separately
- look at notes for procedure
