Understanding Factorial Designs :Designing, Running, and Analyzing Experiments(Interaction Design Specialization) Answers 2026

Question 1

Interaction effects explore which of the following?

❌ How the response changes as factors change
❌ How the response is affected by levels of a factor
✅ How the response is differentially affected by levels of one factor based on levels of another factor
❌ How the response is differentially affected by levels of one factor depending on the different levels the factor can take on
❌ None of the above

Explanation:
An interaction effect occurs when the effect of one factor on the response depends on the level of another factor.

Question 2

Which of the following is a description of a 3 × 2 factorial design? (Mark all that apply.)

✅ Comparison of task completion times using each of three drawing tools while at a standing desk and a sitting desk
❌ Comparison of task completion times while working at one of three desk types with one of two drawing tools
❌ Comparison of task completion times using a drawing tool at a desk
❌ Comparison of task completion times using a drawing tool at a standing or sitting desk three times
❌ Comparison of task completion times using a drawing tool at a standing or sitting desk

Explanation:
A 3 × 2 factorial design means:

• Two factors

• One with 3 levels

• One with 2 levels

Question 3

Parallel lines on an interaction plot often indicate the presence of a statistically significant interaction effect.

❌ False
✅ True

Explanation:
Parallel lines indicate no interaction.
Interaction effects are suggested by non-parallel or crossing lines.

Question 4

(Based on the given interaction plot — assuming small variances)

✅ A significant main effect of Numbers
❌ A significant main effect of Letters
❌ A significant Numbers × Letters interaction

Explanation:
A consistent vertical separation across Letters indicates a main effect of Numbers only.

Question 5

(Based on the given interaction plot — assuming small variances)

❌ A significant main effect of Numbers
✅ A significant main effect of Letters
❌ A significant Numbers × Letters interaction

Explanation:
Differences across Letters that remain consistent across Numbers indicate a main effect of Letters.

Question 6

(Based on the given interaction plot — assuming small variances)

❌ A significant main effect of Numbers
❌ A significant main effect of Letters
✅ A significant Numbers × Letters interaction

Explanation:
Crossing or diverging lines indicate an interaction effect, even if main effects are weak or absent.

Question 7

(Based on the given interaction plot — assuming small variances)

✅ A significant main effect of Numbers
✅ A significant main effect of Letters
❌ A significant Numbers × Letters interaction

Explanation:
Both factors shift the response independently, but lines remain parallel → no interaction.

Question 8

(Based on the given interaction plot — assuming small variances)

❌ A significant main effect of Numbers
❌ A significant main effect of Letters
❌ A significant Numbers × Letters interaction

Explanation:
Minimal differences and overlapping means suggest no significant effects.

Question 9

(Based on the given interaction plot — assuming small variances)

✅ A significant main effect of Numbers
❌ A significant main effect of Letters
✅ A significant Numbers × Letters interaction

Explanation:
Both a shift in Numbers and non-parallel lines indicate a main effect and an interaction.

Question 10

The aligned rank transform (ART) generally refers to which procedure?

❌ For each main and interaction effect, align the data and conduct an ANOVA.
❌ For each main and interaction effect, rank the data and conduct an ANOVA.
✅ For each main and interaction effect, align the data, rank it, and conduct an ANOVA.
❌ For each main and interaction effect, rank the data, align it, and conduct an ANOVA.
❌ None of the above.

Explanation:
ART is a nonparametric factorial analysis technique:

1. Align data for each effect

2. Rank the aligned data

3. Run a standard ANOVA

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