hierarchical designs

“nested in treatment”

subjects are clustered into distinct groups which cannot be ignored nor disturbed (ex. family, class, school, therapy group)

true experiment

when groups are formed by the experimenter

quasi-experiment

when groups already exist

what is the weakness of quasi-experiments?

they can cause bias to spread in a group

hierarchical designs look like factorial designs, only with XXXs on missing cells

column is usually nested, row is treatment

What are the sources of variation in a hierarchical design?

main effect of treatment, main effect of nested factor + interaction of nested factor/treatment is lumped together (confounded)

What is SS_B(A)

B: main effect of B (distinct groups, the nested part)
A: the interaction of A and B

When nested effect (Factor B) is random and treatment (Factor A) is fixed, what do we use as the error term for Factor A?

We use MS_B(A) because it contains the interaction

When nested effect (Factor B) is fixed and treatment (Factor A) is fixed, what do we use as the error term for Factor A?

We use MS_within

What are the consequences of treating nested effect as random?

We lose power in the fixed main effect of Factor A (treatment)

What are the assumptions of the hierarchical design model when Factor B is fixed?

1. Scores on the dependent measure are independent

2. The dependent measure is normally distributed in the population

3. The population variance corresponding to a given cell is equal for each cell

What are the assumptions of the hierarchical design model when Factor B is random?

1. Scores on the dependent measure are independent

2. The dependent measure is normally distributed in the population

3. The population variance corresponding to a given cell is equal for each cell

4. The b_jk effects are independent from each other

5. The b_jk effects are normally distributed in the population of possible levels of the random factor with a mean of 0

6. The population variance of the b_jk effects is constant o²_B(A)

What measures of association do you use when Factor B is fixed?

n² or w²

What measures of association do you use when Factor B is random?

w² for A and p_B(A) for B

COMPLETE: MCPs when Factor B is fixed

MCPs when Factor B is random