(M)AN(C)OVA Flashcards
Process AN(C)OVA
Identify IV & DV –> decompose total variation –> measure effects –> test sig –> interpret results
T-test/Hotelling’s t-test
- Exactly 2 groups (IVs) and 1 DV: t-test
- Exactly 2 groups (IVs) and _>2 DVs: Hotelling’s t-test
ANOVA =
- Min size per group = > # DV or _> 20 observations
- IV: at least 1 categorical, DV: metrically scaled
- H0 means no differences (all population means are equal) so you want to reject H0
Types of ANOVA
- One-way: 1 categorical IV + 1 DV (compare means across 2+ groups)
- N-way: 2+ categorical IVs + 1 DV (tests main & interaction effects)
- Repeated measures: 1 categorical IV (within subjects) + 1 DV (measure same participant multiple times under diff conditions)
- ANCOVA: 1+ categorical IVs & 1 covariate + 1 DV
- MANOVA: 1+ categorical IVs + 2+ DVs (tests effects on multiple outcomes at once)
ANOVA in general: 1+ categorical IVs + 1 DV
Understand logic behind ANOVA
(1) check variation within group, (2) between groups, (3) calculate F-ratio
F-ratio:
- Larger = more likely groups have diff means
- If big enough -> sig
- You want to reject F (H0)
F = …, which determines critical value of F at alpha level of .5
Should be above “…” to be sig.
F statistics for main & interaction effects should be sig (<.05) for there to be an effect
One-way ANOVA
- SSx = how much of total variation is explained by IV
- SSerror = variation within group (“leftover unexplained stuff”)
- SSy = total variation
- F statistic = compares SSx with SSerror
- Eta2 = how much of total variation is explained by 1 factor
> Small = .01
> Medium = .06
> Large + .14+
N-way ANOVA
- Main effects = indiv impact of 1 IV on DV
- Interaction effects = when the effect of 1 IV depends on the level of another IV
Sig is tested by F test
ANCOVA
Used to include control var that are measured and not manipulated in an experiment (eg knowledge)
Two main purposes:
- In quasi-experimental (observational) studies: control for extra var that might mess with results
- Experimental studies: measure factors that can’t be randomized
–> Reduce error term with ANCOVA + include statistical error
Diff N-way and ANCOVA
- Both use _>2 IVs
- N-way considers only categorical IVs, ANCOVA considers (at least 1) categorical IV + metric IVs
Repeated measures ANOVA
Within subjects.
- Change over time (before, during, after)
- Similar to paired samples t-test, but for more complex situations
Assumptions
- Sampling is distributed normally (skewness and kurtosis -3 to 3) (no issue if N>30 because of limit theory)
- Errors should be independent of eachother (no systemic biases, normal distirbution + uncorrelated error terms)
- Independent scores (NOT for repeated measures ANOVA)
- N_>30 for each group
- (Test for) Homogeneity of variance (equality)
Interpretation issues
- Of ANOVA: diff interactions can arise, depending on relative important of factors
> Experimental designs should be balanced = equal N for each factor
> No, ordinal, or disordinal ((non)crossover) interaction (see summary) - Between subjects model:
> Only partial Eta2 is calculated -> Omega2 should also be calculated
> Normally, Eta2 & Omega2 are only interpreted for sig effects - Multiple comparisons to examine diff among means (contrasts). 2 types;
(1) A priori: simple = compare 2 specific groups, deviation = compare each group to grand mean
(2) Post hoc (when you didn’t plan comparisons in advance): LSD, Tukey, Scheffé, Duncan, Hochberg, Games-Howell (depending on group size and Levene’s test) > see summary
Testing homogeneity of variance (equality)
- Important because it strongly affects F test (sig)
- Levene’s test or Box’s M test: assumption is equality (H0), so you want H0 to be accepted, so you want Levene’s test to be nonsig (p>.05). If Levene’s test is sig: ok if groups have equal sizes, or use Welch test (i.o. regular F test)
- Multicollinearity (test with Bartlett’s test of sphericity)
Key overview [MANOVA]
Compare groups on 2 or more DVs at the same time.
- Cofounder = var affecting both IV and DV, making it difficult to know what exactly causes the effect.
Sample size recommendation: 20 observations per group.
