Factorial ANOVA

2-Way Factorial ANOVA

Factorial Design

• Research Study

- Involves MORE THAN ONE FACTOR(IV)

Factorial Design Notation

• Each Number REPRESENTS a Factor → 2 × 3 × 6 × 7 → 4 Factors

• Value of Each Number PROVIDES the Level for each factor

EXAMPLE) 2 × 3

2(Humidity) = Low, High x 3(Temperature) = 50*, 70*, 90*

NOTE) Dependent Variable(DV) would be Learning Performance

Advantages of Factorial ANOVA

• Greater Generalizability of the RESULTS

• Interaction of Variables

- is the Effect of One Variable(Factor) DEPENDENT … on the Level of Another Variable(Factor)

- is the Effect of Room Temperature on Learning Performance Dependent on ____ Humidity

• Requires FEWER Participants

Factoial ANOVA Research Questions

• Mean Level DIFFERENCES of Learning Performance AS Temperature CHANGES Throughout it’s own Level

• Mean Level Differences of Learning Performance AS Humidity CHANGES Throughout it’s own Level

• Specific Combination of ALL Factors (Included in study) Effecting Learning Performance

Interactions

• Means Difference BETWEEN Individual Treatment Conditions(Cells) Different From Predicted OVERALL Mean Effects

• Compare Cell Means to Marginal Means

Interaction Hypotheses

• Interactions: Room Temperature by Humidity

NULL HYPOTHESES:

- No Interaction BETWEEN Factor A & Factor B

ALTERNATIVE HYPOTHESES:

- Yes Interaction … Effect of Factor A On Learning Performance is PARTLY DEPENDABLE On Factor B

Interaction Graphs Characteristics

1) Do LINES INTERCEPT

YES → INTERACTION

• Lines Cross … DISORDINAL

• NOT Touching BUT NOT Parallel … ORDINAL

• EFFECT of ONE Factor DEPENDS on the Other Factor

NO → NO Interaction

• Lines DO NOT Cross

• NOT Touching & Are PARALLEL

• Factors Act INDPENDENTLY

2) Are Lines VERTICALLY STRETCHED

YES → MAIN EFFECT OF A

• Either A1 or A2 has HIGHER SCORES Overall

• Vertical GAP BETWEEN Lines

NO → NO Main Effect of A

• Lines Cross

• Lines SIT ON-TOP of Each Other

3) Are HEIGHTS of B1 & B2 DIFFERENT

YES; BOTH Lines go UP or DOWN → MAIN EFFECT OF B

• B1 ≠ B2

NO; BOTH Lines are FLAT → NO Main Effect of B

• B1 = B2

• One Line going (+) & One Line going (-)