PSYC3010 – Factorial Between-Participants ANOVA I: Omnibus Tests

Flashcards cover key terminology, hypotheses, variance partitioning, F-tests, structural models, assumptions, omnibus tests, and applied example from Week 2 lecture on factorial between-participants ANOVA.

In ANOVA, what two sources is total variance partitioned into?

Between-groups variance (systematic/treatment) and within-groups variance (random/error).

What does the F-ratio compare in a one-way ANOVA?

Mean square between groups (treatment) to mean square within groups (error).

If the F value is close to 1, what does this suggest about the IV’s effect?

Between-groups variance is not larger than error; likely no treatment effect (fail to reject H0).

State the null hypothesis for a one-way ANOVA with three groups.

μ1 = μ2 = μ3 (no difference between any group means).

Why can’t the alternative hypothesis for 3+ groups list all means as unequal (μ1 ≠ μ2 ≠ μ3)?

Because the alternative only claims at least one mean differs; it does not specify all are different.

What are ‘cell means’ in a factorial design?

Means of the DV for each unique combination of factor levels (each cell of the design).

Define a ‘crossed’ factorial design.

A design in which every level of Factor A occurs with every level of Factor B (e.g., A × B).

In the structural model Xij = μ. + τj + εij, what does τj represent?

The treatment effect for group j (how far that group mean is from the grand mean).

Give the research question for a main effect of Factor A in a two-way ANOVA.

Is there a significant difference between the means of the levels of Factor A on the DV, averaging over Factor B?

What three omnibus tests are provided by a 2 × 2 factorial ANOVA?

Main effect of Factor A, main effect of Factor B, and the A × B interaction.

How is the interaction null hypothesis framed in a 2 × 2 design?

The simple differences for Factor A are equal across the levels of Factor B (or vice-versa).

For equal n designs, how is total N calculated?

N = a × b × n (levels of A × levels of B × participants per cell).

What assumption relates to group variances in ANOVA?

Homogeneity of variance (populations have the same variance).

Is ANOVA robust to moderate violations of normality and homogeneity?

Yes, usually robust, especially with equal group sizes.

What is ‘within-groups variance’ unable to reflect in a between-participants design?

Treatment effects, because every participant in a group receives the same treatment.

What graphical feature often signals an interaction in a line graph?

Non-parallel (crossing or diverging) lines for the factors.

What does a significant main effect but non-significant interaction suggest?

Factor influences the DV consistently across levels of the other factor.

Name the four components of the 2-way structural model Xijk = μ.. + αj + βk + αβjk + εijk.

Grand mean, main effect of A, main effect of B, interaction effect, and individual error.

What is an omnibus test?

An initial test that detects if any group differences exist without specifying where.

Which follow-up analyses are needed after a significant interaction?

Simple effects (examining one factor at each level of the other) and possibly pairwise comparisons.

What does MSerror (MSe) serve as in factorial ANOVA?

The pooled within-cell variance used as the denominator for all F-ratios.

How are degrees of freedom for Factor A calculated?

dfA = a – 1 (where a = number of levels of Factor A).

How are interaction degrees of freedom obtained?

dfAB = (a – 1)(b – 1).

What practical skill is assessed in Practical Test 1 of PSYC3010?

Interpreting line graphs for 2 × 2 designs (identifying main and interaction effects).

Define ‘grand mean’.

The average of all observations across all groups and cells.

When is follow-up testing unnecessary for a main effect?

When the factor has only two levels—direction is evident from the two means.

What is the purpose of a Summary Table in SPSS ANOVA output?

To condense SS, df, MS, F, and p for each effect into an interpretable format.

Write the formula for F in a two-way ANOVA main effect of A.

FA = MSA / MS_error.

How does error variance influence the F-ratio?

Larger error variance lowers F, making significance harder to achieve.

What design was used in the creativity example (beer × distraction)?

3 × 2 between-participants factorial design (Alcohol Consumption × Distraction).

List the factors and their levels in the creativity study.

Alcohol: 0, 2, 4 pints; Distraction: Distracted, Control.

What outcome did the creativity example find for distraction?

No significant main effect of distraction.

State one assumption about the sample for between-participants ANOVA.

Independence of observations (scores from different participants are independent).

What key question does partitioning variance help answer in ANOVA?

How much of total variability can be explained by systematic treatment effects versus error.

Why are tutorial attendance and practical tests emphasized in PSYC3010?

They teach hands-on data analysis skills required for assignments and exams.

What do marginal means represent in factorial ANOVA?

Means for each level of a factor averaged over the levels of the other factor.

Why might follow-up tests be required after a significant main effect with >2 levels?

To determine which specific means differ (post-hoc or planned comparisons).

How is ‘variance’ defined in the lecture?

A measure of the dispersion of scores around the mean.

What does a significant interaction indicate about the effect of one factor?

Its effect on the DV changes depending on the level of the other factor.

In SPSS output, which column tells you the significance of an effect?

The Sig. (p-value) column in the Tests of Between-Subjects Effects table.

If MSbetween ≈ MSwithin, what would you expect for F and the null hypothesis?

F ≈ 1; fail to reject the null hypothesis.

What is the role of ‘error’ in the structural model?

Captures individual variability not explained by the factors or their interaction.

What upcoming topic follows omnibus tests according to the lecture schedule?

Follow-up tests and effect sizes.

Which book chapter was suggested for mathematical details of ANOVA?

Andy Field, "Discovering Statistics Using IBM SPSS Statistics" – chapter on comparing several independent means.