PSYC 3010 EXAM QUESTIONS WITH
CORRECT ANSWERS
1. Factorial Design - ANSWER - Has at least two factors (IVs), each with at least two
levels
- Two IVs can be examined simultaneously
1. Advantages of Factorial Design - ANSWER - More economical in terms of participants
- Allows us to examine the interaction of independent variables (assess generalisability)
1. Interactions in Factorial Designs - ANSWER - One IV interacts with another when the
effects of one are different depending on the level of the other
- And when it changes (moderates or qualifies) the impact of a second IV on the DV
2. Variance - ANSWER - "Dispersion or spread of scores around a point of central
tendency, e.g. mean"
- Error Variance: cannot be explained; should go up with more observations
- Treatment Variance: systematic differences due to our IV
2. Three Questions of Two-Way ANOVA - ANSWER 1. Variance due to factor A? (df a-1)
2. Variance due to factor B? (df b-1)
3. Variance due to AxB interaction? (df(a-1)(b-1))
2. Structural Model of 2-way ANOVA - ANSWER Xijk = mew. + aj + Bk + aBjk + eijk
- X (Specific DV) e.g. height, age, gender
- mew. -> the grand mean (e.g. 1.5m) for IV
- aj -> the effect of the j-th treatment of factor A (e.g. effect of being male or female)
- Bk -> the effect of the k-th treatment of factor B (e.g. effect of age)
- aBjk -> effect of differences in factor A treatments at different levels of factor B
treatments (interaction between age and gender)
- eijk = error for i person in the j-th and k-th treatments (anything left over after main
effects are removed which is not error is due to the interaction)
2. Variance and Significance - ANSWER The more variability attributable to the effects,
,the more significant they are
2. Assumptions of ANOVA - ANSWER - Population: normally distributed (normality) and
have the same variance (homogeneity of variance)
- Samples: Independent; obtained by random sampling; at least two observations and
equal n
- Data (DV Scores): measured on continuous scale for mathematical operations (mean,
SD, variance)
3. Effect Sizes - ANSWER Been proposed as an accompaniment, if not replacement, for
significance testing, as it relays implications of findings (ANOVA is binary)
- Offers another way of assessing reliability of results in terms of variance
- Can compare size of effects within a factorial design: Cohen's d (0.2, 0.5, 0.8)
3. Eta-Squared (n) - ANSWER Describes the proportion of variance in the SAMPLE'S DV
scores that is accounted for by the effect
- Considered biased
3. Omega Squared (w) - ANSWER Describes the proportion of variance in the
POPULATION'S DV scores that is accounted for by the effect
- Less biased
- Larger difference between n and w with smaller sample
3. Partial Eta-Squared - ANSWER Proportion of residual variance accounted for by the
effect (variance left over to be explained)
- usually more inflated
- can add up to >100%
- Hard to make meaningful comparisons
3. Following-Up Main Effects - ANSWER Use linear contrasts (protected t test) to
determine if a set of groups is different from another set using weights (aj)
3. Following-Up Interactions - ANSWER Test of simple effects:
- simple effects test the effects of one factor at each level of the other factor
3. Variance Partitioning of Omnibus Tests - ANSWER Variance partitioned into four
parts:
- Effect due to first factor
- Effect due to second factor
, - Effect due to interaction
- Error/Residual/Within-group variance
3. Partitioning of Simple Effects - ANSWER - Simple effects re-partition the main effect
and interaction variance
- The simple effects of factor 2 should be equal to the combination of the main effect and
the interaction
3. Simple Comparisons - ANSWER Follow up simple effects of interactions, comparing
cell means rather than marginal.
- somewhat redundant, explaining the same thing more than once
- Increases family-wise error rate (use Bonferroni or conduct test a priori to avoid)
4. Higher-Order Factorial Designs - ANSWER - More than two independent factors
- Allow for designs with higher external validity
4. Effects in HO Designs - ANSWER Main Effects:
- Differences between marginal means of one factor averaging over levels of another
(e.g. Driving ability; car size/age/experience/gender)
Two-Way Interactions:
- The effect of one factor changes depending on the level of another (e.g. age is
beneficial but gender is not)
Three-Way Interactions:
- the two-way interaction between two factors changes depending on the level of a third
(when graphed, if lines do not form same pattern, there is interaction)
4. Partitioning the Variance in Three-Way ANOVA (2x2x2) --> 7 Omnibus tests - ANSWER
- Main effects
• Variance due to a, b, and y
- 2-Way interactions
• Variance due to ab, by, ay
- Error/residual
• Variance due to e
- 3-way interaction
• Variance due to aby
CORRECT ANSWERS
1. Factorial Design - ANSWER - Has at least two factors (IVs), each with at least two
levels
- Two IVs can be examined simultaneously
1. Advantages of Factorial Design - ANSWER - More economical in terms of participants
- Allows us to examine the interaction of independent variables (assess generalisability)
1. Interactions in Factorial Designs - ANSWER - One IV interacts with another when the
effects of one are different depending on the level of the other
- And when it changes (moderates or qualifies) the impact of a second IV on the DV
2. Variance - ANSWER - "Dispersion or spread of scores around a point of central
tendency, e.g. mean"
- Error Variance: cannot be explained; should go up with more observations
- Treatment Variance: systematic differences due to our IV
2. Three Questions of Two-Way ANOVA - ANSWER 1. Variance due to factor A? (df a-1)
2. Variance due to factor B? (df b-1)
3. Variance due to AxB interaction? (df(a-1)(b-1))
2. Structural Model of 2-way ANOVA - ANSWER Xijk = mew. + aj + Bk + aBjk + eijk
- X (Specific DV) e.g. height, age, gender
- mew. -> the grand mean (e.g. 1.5m) for IV
- aj -> the effect of the j-th treatment of factor A (e.g. effect of being male or female)
- Bk -> the effect of the k-th treatment of factor B (e.g. effect of age)
- aBjk -> effect of differences in factor A treatments at different levels of factor B
treatments (interaction between age and gender)
- eijk = error for i person in the j-th and k-th treatments (anything left over after main
effects are removed which is not error is due to the interaction)
2. Variance and Significance - ANSWER The more variability attributable to the effects,
,the more significant they are
2. Assumptions of ANOVA - ANSWER - Population: normally distributed (normality) and
have the same variance (homogeneity of variance)
- Samples: Independent; obtained by random sampling; at least two observations and
equal n
- Data (DV Scores): measured on continuous scale for mathematical operations (mean,
SD, variance)
3. Effect Sizes - ANSWER Been proposed as an accompaniment, if not replacement, for
significance testing, as it relays implications of findings (ANOVA is binary)
- Offers another way of assessing reliability of results in terms of variance
- Can compare size of effects within a factorial design: Cohen's d (0.2, 0.5, 0.8)
3. Eta-Squared (n) - ANSWER Describes the proportion of variance in the SAMPLE'S DV
scores that is accounted for by the effect
- Considered biased
3. Omega Squared (w) - ANSWER Describes the proportion of variance in the
POPULATION'S DV scores that is accounted for by the effect
- Less biased
- Larger difference between n and w with smaller sample
3. Partial Eta-Squared - ANSWER Proportion of residual variance accounted for by the
effect (variance left over to be explained)
- usually more inflated
- can add up to >100%
- Hard to make meaningful comparisons
3. Following-Up Main Effects - ANSWER Use linear contrasts (protected t test) to
determine if a set of groups is different from another set using weights (aj)
3. Following-Up Interactions - ANSWER Test of simple effects:
- simple effects test the effects of one factor at each level of the other factor
3. Variance Partitioning of Omnibus Tests - ANSWER Variance partitioned into four
parts:
- Effect due to first factor
- Effect due to second factor
, - Effect due to interaction
- Error/Residual/Within-group variance
3. Partitioning of Simple Effects - ANSWER - Simple effects re-partition the main effect
and interaction variance
- The simple effects of factor 2 should be equal to the combination of the main effect and
the interaction
3. Simple Comparisons - ANSWER Follow up simple effects of interactions, comparing
cell means rather than marginal.
- somewhat redundant, explaining the same thing more than once
- Increases family-wise error rate (use Bonferroni or conduct test a priori to avoid)
4. Higher-Order Factorial Designs - ANSWER - More than two independent factors
- Allow for designs with higher external validity
4. Effects in HO Designs - ANSWER Main Effects:
- Differences between marginal means of one factor averaging over levels of another
(e.g. Driving ability; car size/age/experience/gender)
Two-Way Interactions:
- The effect of one factor changes depending on the level of another (e.g. age is
beneficial but gender is not)
Three-Way Interactions:
- the two-way interaction between two factors changes depending on the level of a third
(when graphed, if lines do not form same pattern, there is interaction)
4. Partitioning the Variance in Three-Way ANOVA (2x2x2) --> 7 Omnibus tests - ANSWER
- Main effects
• Variance due to a, b, and y
- 2-Way interactions
• Variance due to ab, by, ay
- Error/residual
• Variance due to e
- 3-way interaction
• Variance due to aby
