4 Three Way Factorial Anova

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Three-Way Factorial ANOVA

(2 2 2 Factorial)

Example

A researcher is interested in determining the

effects of the two types of learning strategies

(A and B) on the memorization of easy-vs.-

difficult list as well as in determining the

effects of high vs. low intensity shock on

learning. The researcher records the totalnumber of errors made by each subject.


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The three-way factorial combination of the three

independent variables yields the following eight

experimental groups, with six subjects per group

Enter data using the following:


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6. To plot the three-way STRATEGY*LIST*SHOCKinteraction, some data transformation must

be carried out. Suppose the researcherdecides to plot the variables of STRATEGYand LIST (i.e., STRATEGY*LIST interaction)against the variable of SHOCK. The first stepis to create a new grouping variable calledGROUP that contains the four levelsgenerated by the STRATEGY*LIST interaction(Strategy AEasy List, Strategy AHard List,

Strategy B

Easy List, and Strategy B

HardList).


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SPSS OUTPUT


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Results and Interpretation


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Main Effects The main effect of STRATEGY is significant, F(1,40) = 95.16,

p < .001. From the estimated marginal means, subjectsmade significantly more errors under strategy B (M =25.71) than under strategy A (M = 14.00) (collapsing acrossthe LIST and SHOCK factors).

The main effect of LIST is significant, F(1,40) = 121.10,p .05. The difference in the number of errors made under

the low-shock condition (M = 19.21) is not significantlydifferent from the number of errors made under the high-shock condition (M = 20.50) (collapsing across the LIST andSTRATEGY factors).

Two-Way Interactions


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Strategy*List Interaction

The STRATEGY*LIST interaction is significant,F(1,40) = 14.32,p < .01.

The significant interaction effect indicates thatthe effect of learning strategy on the numberof errors made is dependent on the difficultyof the list learned. Although the number oferrors made increased from Strategy A toStrategy B when learning either hard or easylist, the increase is more pronounced when

learning the hard list than the easy list.


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Post Hoc Comparisons


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Results and Interpretation

Post Hoc Comparisons

Results from the post hoc comparisons indicatethat the significant STRATEGY*LIST interaction isdue primarily to subjects making significantlyless errors in the Strategy AEasy List conditionthan in the other three experimental conditions(AHard, BEasy, and BHard), and to subjects

making significantly more errors in the StrategyBHard List condition than in the other threeexperimental conditions (BEasy, AEasy, and AHard).


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STRATEGY*SHOCK Interaction

STRATEGY*SHOCK Interaction

The STRATEGY*SHOCK interaction is notsignificant, F(1,40) = 3.13,p > .05.

As the interaction is not significant, the result canbe interpreted in terms of the significant maineffect for STRATEGY. That is, the effect ofSTRATEGY on the number of errors made is not

dependent on the levels of SHOCK, such thatregardless of SHOCK level, subjects madesignificantly more errors under Strategy B (M =25.71) than under Strategy A (M = 14.00).


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LIST*SHOCK Interaction


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LIST*SHOCK Interaction

The LIST*SHOCK interaction is not significant,

F(1,40) = 1.47,p > .05.

The effect of LIST on the number of errors

made is not dependent on the levels of

SHOCK, such that regardless of SHOCK level,

subjects made more errors on the hard list (M

= 26.45) than on the easy list (M = 13.25).


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Three-Way Interaction

STRATEGY*LIST*SHOCK Interaction

The three-way interaction between STRATEGY,LIST, and SHOCK is not significant, F(1,40) = 0.27,

p > .05.

As the three-way interaction is not significant, it islegitimate to interpret the significant main effectsof LIST and STRATEGY. For example, the results

indicate that more errors were made on the hardlist (M = 26.45) than on the easy list (M = 13.25),and under Strategy B (M = 25.71) than underStrategy A (M = 14.00), regardless of shock level.


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4 Three Way Factorial Anova