TWO WAY FACTORIAL ANOVA

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Last updated 5:33 AM on 6/11/26
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10 Terms

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FACTORIAL DESIGN

  • Has at least two factors (IV's), each with at least two levels 

  • Then the two factors can be examined simultaneously 

  • *Factor = IV in the context of ANOVA.  

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MAIN EFFECTS

Main effect of Factor A 

  • Is there an effect of factor A on the DV? 

  • On average, is there a difference between the levels of factor A on the DV? 

Main effect of Factor B 

  • Is there an effect of factor B on the DV? 

  • On average, is there a difference between the levels of factor B on the DV? 

Factor A x Factor B Interaction 

  • Does the effect of factor A on the DV change at each level of factor B? 

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SIMPLE EFFECT

The effect of one factor at one level of the other factor  

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MARGINAL MEAN

The mean of factor A or B's levels 

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CELL MEAN

  • The mean of factor A at each level of factor B 

  • Vice versa  

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ADVANTAGES OF FACTORIAL ANOVA

  • Allows us to examine both the individual effect of each factor and interactions between factors 

  • Interactions indicate whether the effect of one factor on a DV is 'moderated/qualified' by another factor 

  • Interactions tell us whether the effect of one factor changes at different levels of another factor 

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NOTATION

TYPE OF DESIGN

  • between subjects

  • within subjects

  • mixed model

NUMBER OF FACTORS

  • two-way / three-way, etc.

NUMBER OF FACTOR LEVELS

  • 2×2 / 3×3 / 4×4

COMBINED

A 2×2 between-subjects factorial design.

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PLOTTING GRAPHS

  • Y-axis for DV 

  • X-axis for the factor with the most levels or the factor which is most theoretically important 

    • Other factor is represented by separate lines on the graph 

  • All cell means in the design must be represented on the graph 

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LINES AND INTERACTIONS

  • Parallel lines indicate that there is no interaction (rough guide) 

  • Non-parallel lines indicate an interaction 

    • Disordinal interaction (lines cross) = effect reverses 

    • Ordinal interaction (lines do not cross) = effect changes in size, not direction 

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READING MAIN EFFECTS FROM GRAPH

Visible as the differences in the average height of points for each factor.