Shavelson Chapter 14

Shavelson Chapter 14S14-1. Know the purpose of a two-way factorial

design and what type of information it will supply (e.g. main effects and interaction effects) (418-419)

General purpose of two-way factorial design:• Used when you have 4 or more groups, in a

factorial design• Provides information on main effects (the effect

each IV might have on the DV)• Provides information on interaction effects (the

effect one IV has on the other - i.e. the effect both conditions have together)

Shavelson Chapter 14S14-1 continued

Shavelson Chapter 14S14-2. What are the three reasons why factorial

designs might be used over one-way research studies? (419)

Reasons to use a factorial design:

1. Economical, time and money wise!

2. Provides more information (main and interaction effects)

3. Can get a better estimate of error variance (within variance) in factorial design (can add suspected Extraneous Variable as a factor)

Shavelson Chapter 14S14-3. Be able to create a graph of the interactions in a study

and know the difference between a disordinal interaction and an ordinal interaction. (420) and figure 14-3). Given a graph of an interaction, you should be able to explain what they mean in terms of an interaction. (as is done on the top of 420, 2)


3, 4, 5 = 4

2, 1, 3 = 2

1, 5, 6 = 4

8, 6, 4 = 6

- -

- -

No exer. B1 Exer. B2

Vit. AA1

Vit. BA2

Exercise

A

10

DV

0

3

5

4 4 A1 A2Vit. A Vit. B

DV = Performance on a test

(2)

(6)

(4) (4)

B2 Exercise

B1 No exercise

Shavelson Chapter 14

S14-3 continued


Disordinal Ordinal

Ordinal No Interaction

S14-3 continued

S14-4. Know in general terms how to calculate the F for the main and interaction effects in a factorial design (321-322). To aid in this, you should be familiar with the breakdown of the total variability as illustrated in formula 14-1 on page 425. Given a partially completed table, (e.g. 14-2, p 422) be able to complete it. I will not ask you to calculate or to know how to calculate the sum of squares, but you should be able to calculate the degrees of freedom, the mean squares and

the Fobserved.

Calculating the Fs for factorial designs:

For main effects:MSa

MSwithinF =

variance of factor A variance within

Variance within + Trtmnt EffectsVariance within=

MSb

MSwithin Variance within + Trtmnt EffectsVariance within

=variance of factor B variance within

F =

For interaction effects:

MSaB(interaction)

MSwithinF =

variance of AxB variance within

= (Variance AB) - (Var A) - (Var B) + (Variance WithinVariance within

S14-5. For the Two-way ANOVA you should know:A. The design requirements and assumptions (423-424).B. Be able to recognize or generate hypotheses (423-424).C. Know the decision rules for rejecting the null hypothesis and be able to interpret the results

of a two-way ANOVA. In interpreting you need to look at the interaction effects first. Note the points on page 431 regarding interpreting the main effects.

S14-5(a)2 Way ANOVA Design Requirements:

A. 2 IV’s each with 2 or more levels (completely crossed)B. Levels can differ Qualitatively or QuantitativelyC. Participant only appears in one cell of design, and is randomly selected

from the population


S14-5(a) continued

Assumptions of the 2 way ANOVA

A. All scores are independent of each other

B. The population from which each group was drawn should be normally distributed

(but not usually a problem)

C. Homogeneity of variance (that is, each group’s population should have equal variances)

But if group sizes are equal, no problem)


S14-5(b)Hypotheses for the 2 way ANOVA

Null Hypotheses used:(For each factor)

Ho: 1 = 2 = 3…

(All means are equal)

(For each Factor)

H1: i ≠ i'

(At least one of the pairs of means differ from one another)

Interaction:

Ho: interaction effect = 0

H1: interaction effect ≠ 0

1. Examine the interaction first. If null is rejected, then main effects of A & B are not straightforward. Should plot interaction and examine.

2. If no interaction effect exists, main effects can be interpreted in straightforward manner.


S14-6. Given a value for the omega statistic (and for what it was calculated), be able to explain what that number means (I.e. given and omega value of .64 for interaction, what does this mean?) (436-437)

Omega-SquaredProvides information on the strength of the association between

each factor (e.g. factor A & B), as well as the interaction (AB) and the DV.

e.g.Omega (A) = .08 (accounts for 8 % of DV variability)Omega (B) = .21 (accounts for 21% of DV variability)Omega (AB) = .64 (accounts for 64% of DV variability)


14-7. ANOVA Source Table – be able to complete it and interpret it!

Source SS DF Ms F obs

Verbal

Ability

8.34 1 8.34 16.68

Question Type 20.67 2 10.34 20.67

AxB 60.66 2 30.33 60.66

Within Group

(error or residual)

3 6 .5

Total 92.67 11

Tukey posthocs for the factorial ANOVA (2-way)

Shavelson Chapter 14

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