Topic 4: ANOVA & ANCOVA

Question 1

single-factor design

Answer 1

involves a single IV with multiple levels

Question 2

factorial design

Answer 2

involves more than one IV iwht multiple levels

Question 3

between-subjects design

Answer 3

subjects receive only one of the different treatment condition

Question 4

within-subjects design

Answer 4

each subject receives all treatment conditions

Question 5

purpose of one-way ANOVA

Answer 5

to test whether the means of K ≥ 2 populations significantly differ

Question 6

stating hypotheses for one-way ANOVA

Answer 6

• H0: μ1 = μ2 · · · = μK
• H1: Not all μs are the same (at least one of the means is different)

Question 7

assumption of one-way ANOVA

Answer 7

normality, homogeneity of variance, independence of observation

Question 8

two sources of variance in one-way ANOVA

Answer 8

between-group and within-group variance

Question 9

between-group variance

Answer 9

the variance due to different treatments/levels of a factor across gorups

Question 10

within-group variance

Answer 10

the random fluctuations of subjects within each group

Question 11

the F distribuiton

Answer 11

a right-skewed distribution that varies in shape according to df(B) and df(W)

Question 12

effect size

Answer 12

a quantity that measures the size of an effect as it exists in the population

Question 13

3 ways to calculate effect size in one-way ANOVA

Answer 13

cohen’s d, eta squared, and omega squared

Question 14

cohen’s d

Answer 14

standardized mean difference

Question 15

eta squared

Answer 15

the ratio of variance explained in the DV by one or more IVs, making it analogous to R2

Question 16

omega squared

Answer 16

a bias-corrected version of eta squared

Question 17

interpreting omega squared

Answer 17

w2 = 0.01 (small)
w2 = 0.06 (medium)
w2 = 0.14 (large)

Question 18

post-hoc test

Answer 18

determine which pairs of means are significantly different

Question 19

tukey’s HSD

Answer 19

the simplest and post accurate post-hoc test

Question 20

ANOVA vs. linear regression

Answer 20

ANOVA can be viewed as a special case of linear regression with nominal IVs with multiple categories/levels

Question 21

dummy coding

Answer 21

involves the assignment of binary variables (0 or 1) to represent membership in each level of a nominal variable

Question 22

steps of dummy coding

Answer 22

1. create k-1 variables as dummy variables, where k = # of levels
2. choose one group as a baseline
3. assign the baseline a value of 0
4. for the kth dummy variable, assign the value 1 to the kth group. Assign all other groups 0 for this variable

Question 23

extraneous variables

Answer 23

individual characteristics of subjects that are also likely to affect the DV

Question 24

ANCOVA

Answer 24

• 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

Question 25

partitioning variance in ANCOVA

Answer 25

same as linear regression (ss regression & error)

Question 26

stating hypotheses for ANCOVA

Answer 26

H0: µ1A = µ2A = … = µK A
H1: At least one adjusted mean is different.

Question 27

assumptions of ANCOVA

Answer 27

same as ANOVA & linear regression + homogeneity of regression slopes

Question 28

homogeneity of regression slopes

Answer 28

• the regression slopes need to be parallel
• there is no interaction between a factor and a covariate

Question 29

stating hypotheses for homogeneity of regression slopes assumption

Answer 29

H0: Bz1 = Bz2 = … = B2k
H1: not all Bz’s are the same