Question 1

Which of the following best describes the main effect in a two-way ANOVA?

Accepted Answer

The effect of one factor averaged over the levels of the other factor.

Question 2

In a two-way ANOVA, what does a significant interaction effect indicate?

Accepted Answer

The effect of one factor depends on the level of the other factor.

Question 3

Given the model $$y_{ijk} = \mu + \alpha_i + \beta_j + (\alpha\beta)_{ij} + \epsilon_{ijk}$$, what does $$(\alpha\beta)_{ij}$$ represent?

Accepted Answer

The interaction effect between factor A at level $$i$$ and factor B at level $$j.$$

Question 4

Which hypothesis is tested for the main effect of factor A in a two-way ANOVA?

Accepted Answer

$$H_0$$: \$$alpha_1$$ = \$$alpha_2$$ = \cdots = \alpha_a = 0$$

Question 5

In a randomized block design, what is the primary purpose of including the block factor?

Accepted Answer

To reduce variability due to nuisance factors.

Question 6

Suppose you have three drugs and three age groups in a two-way ANOVA. If the lines connecting mean ratings for each drug across age groups are not parallel, what does this suggest?

Accepted Answer

There is an interaction between drug and age group.

Question 7

Which sum of squares in two-way ANOVA captures the variability due to the interaction between two factors?

Accepted Answer

$$SS_{AB}$$

Question 8

What is the assumption of sphericity in repeated measures ANOVA?

Accepted Answer

The variances of the differences between all pairs of conditions are equal.

Question 9

Why can't repeated measurements on the same subject be treated as independent observations in repeated measures ANOVA?

Accepted Answer

They are correlated and share subject-specific variability.

Question 10

In the context of repeated measures ANOVA, what is the main advantage over a completely randomized design?

Accepted Answer

It increases statistical power by removing between-subject variability.

Question 11

If the F statistic for the interaction term in a two-way ANOVA is significant, what should you do next?

Accepted Answer

Interpret the simple effects or conduct post-hoc comparisons.

Question 12

Which formula correctly represents the partitioning of total sum of squares in a balanced two-way ANOVA?

Accepted Answer

$$SS_{Total} = SS_A + SS_B + SS_{AB} + SS_{Error}$$

Question 13

A researcher uses a randomized block design to test the effect of four fertilizers on crop yield, blocking by field. What is the block factor in this experiment?

Accepted Answer

Field

Question 14

Which of the following is a correct null hypothesis for testing the interaction effect in a two-way ANOVA?

Accepted Answer

$$H_0$$: (\alpha\beta)_{ij} = 0$$ 	ext{ for all } i, j$

Question 15

In repeated measures ANOVA, what adjustment is commonly used if the sphericity assumption is violated?

Accepted Answer

Apply a Greenhouse-Geisser correction.

Question 16

Which of the following best describes a randomized block design?

Accepted Answer

A two-way ANOVA where one factor is used to control for nuisance variability.

Question 17

In the two-way ANOVA example with antidepressants and age, what would parallel lines in the interaction plot indicate?

Accepted Answer

No interaction between drug and age group.

Question 18

Which of the following is NOT an assumption of repeated measures ANOVA?

Accepted Answer

The means of all groups are equal.

Two-Way ANOVA, Randomized Block Designs, and Repeated Measures ANOVA

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