Wk 5: Multi-Factor Between-participants designs: ANOVA

multi factor vs one way

example music type

one way:

  • no music, classical, lo-fi

  • each participant is assigned to one of the 3 groups

  • do the three groups differ in concentration scores?

multi factor:

  • music type x time of day

  • factor A music type: no music, classicl lo-fi

  • factor B time of day: morning afternoon

  • partiipants are assigned to one cell only of the table

music type

morning

arvo

none

group 1

4

classical

2

5

lo-fi

3

6

  • 3×2/2×3 design

  • does music type matter overall?

  • are people more focused in the morning vs afternoon

  • does effect of music depend on the time of day? etc

multifactor between participant

  • more than one IV is being manipulated

  • factorial design: if factor A and factor B is crossed. you must include all cells in the grid

  • factor = IV category, levels = split

    • e.g. factor = therapy type, level = CBT, control, DBT

main effect: does factor A matter on average, across all levels of factor B

  • e.g. CBT overall produces higher improvement than DBT

interaction: does the effect of factor A change depending on factor B?

  • e.g. CBT works better at 60 minutes, but SBT works better at 30 minutes

  • effect of therapy depends on session length

  • main effects and interactions

  • interactions refer to the difference in differences

  • when interactions are present it can be difficult to see the main effects clearly

    • hence important to plot means of A, averaged across B and vice versa

sub-dividing the between-groups sum of squares

how do we estimate each of the main effects and the interaction?

  • start with partition variance

  • SS_T, SS_B, SS_W

  • SS_B is further sub-divided

between-group SS

n = multiplied participants in that condition