Topic 4: ANOVA & ANCOVA Flashcards
single-factor design
involves a single IV with multiple levels
factorial design
involves more than one IV iwht multiple levels
between-subjects design
subjects receive only one of the different treatment condition
within-subjects design
each subject receives all treatment conditions
purpose of one-way ANOVA
to test whether the means of K ≥ 2 populations significantly differ
stating hypotheses for one-way ANOVA
- H0: μ1 = μ2 · · · = μK
- H1: Not all μs are the same (at least one of the means is different)
assumption of one-way ANOVA
normality, homogeneity of variance, independence of observation
two sources of variance in one-way ANOVA
between-group and within-group variance
between-group variance
the variance due to different treatments/levels of a factor across gorups
within-group variance
the random fluctuations of subjects within each group
the F distribuiton
a right-skewed distribution that varies in shape according to df(B) and df(W)
effect size
a quantity that measures the size of an effect as it exists in the population
3 ways to calculate effect size in one-way ANOVA
cohen’s d, eta squared, and omega squared
cohen’s d
standardized mean difference
eta squared
the ratio of variance explained in the DV by one or more IVs, making it analogous to R2
omega squared
a bias-corrected version of eta squared
interpreting omega squared
w2 = 0.01 (small)
w2 = 0.06 (medium)
w2 = 0.14 (large)
post-hoc test
determine which pairs of means are significantly different
tukey’s HSD
the simplest and post accurate post-hoc test
ANOVA vs. linear regression
ANOVA can be viewed as a special case of linear regression with nominal IVs with multiple categories/levels
dummy coding
involves the assignment of binary variables (0 or 1) to represent membership in each level of a nominal variable
steps of dummy coding
- create k-1 variables as dummy variables, where k = # of levels
- choose one group as a baseline
- assign the baseline a value of 0
- for the kth dummy variable, assign the value 1 to the kth group. Assign all other groups 0 for this variable
extraneous variables
individual characteristics of subjects that are also likely to affect the DV
ANCOVA
- a more precise test of the differences among group means
- controls for the effects of covariates on the DV
- includes both nominal (dummy-coded) an continuous variables as IVs
partitioning variance in ANCOVA
same as linear regression (ss regression & error)
stating hypotheses for ANCOVA
H0: µ1A = µ2A = … = µK A
H1: At least one adjusted mean is different.
assumptions of ANCOVA
same as ANOVA & linear regression + homogeneity of regression slopes
homogeneity of regression slopes
- the regression slopes need to be parallel
- there is no interaction between a factor and a covariate
stating hypotheses for homogeneity of regression slopes assumption
H0: Bz1 = Bz2 = … = B2k
H1: not all Bz’s are the same
