Factorial designs: Main effects and interactions Psy 245 Research Methods

Objectives: By the end of this session, you should be able to: - define the concept of interaction - determine the relationship between variables from the results of statistical analyses - differentiate main effects and interactions

Imaginary study: - Looking at the effect of rate of presentation and colour of stimuli on memory for a sequence of consonants “… Performance was weaker for the fast presentation rate than for the slow; F(1,9)=110.12, p.5. No interaction between rate of presentation and colour was found; F(1, 9).7. ”

Slow-redSlow-blueFast-red Fast-blue Sub Sub Sub Sub Sub Sub Sub Sub Sub Sub x SR = 74.4 x SB = 74.0 x FR = 43.7 x FB = 42.5

x R * = ( x RS + x RF ) / 2 x B* = ( x BS + x BF ) / 2 x R* = ( ) / 2 = x B* = ( ) / 2 = Performance levels in colour conditions, regardless of rate of presentation, are similar

x S* = ( x SR + x SB ) / 2 x F* = ( x FR + x FB ) / 2 Performance levels in rate of presentation conditions, regardless of colour, are different x F* = ( ) / 2 = 43.1 x S* = ( ) / 2 = 74.2

Main effect of rate of presentation

No main effect of A No main effect of B

Main effect of A No main effect of B

No main effect of A Main effect of B

Main effect of A Main effect of B

?

Interaction Presence of an interaction: conclusions based on main effects alone do not fully describe the outcome of the factorial experiment Interaction: The effect of one independent variable on the dependent variable changes at the different levels of the second independent variable e.g.: Do control participants show better long-term memory than amnesic patients? For explicit memory tasks? For implicit memory tasks?

Does the group of participants predict memory performance ? Yes, to a certain extent… but it also depends on the task...

Memory performance Group of participants (Ctrls/amnesics) Task (explicit/implicit) Interaction

Independent variables influence the dependent variables and not one another. Mathematically: Interaction is present when the differences between means representing the effect of a factor A at one level of B do not equal the corresponding differences at another level of factor B. An interaction is present when one of the independent variables does not have a constant effect at all levels of the other independent variable.

Interaction & No main effect

Main effect of A & interaction

Interaction & main effect of B

Main effect of A & B & interaction

Practice

A & B & interaction B AA & B

Main effect of A, interaction Same data; changed factor illustrated on X-axis. Plotting the data in different ways can help interpretation

2 x 2 design so far… What about 2x3? 3x3? 2x2x2? 2x2x2x2?

2 x 3 design Main effect of B 11 22  1 <  2 Effect of B is not linear 22 11

2 x 3 design Main effect of A & B

Main effect of A & B & interaction

3-way design: 2 x 2 x 2 E.g.: Looking at the effect of rate of presentation, colour and font size of the stimuli on memory for a sequence of consonants Rate of presentation: Fast versus Slow Colour: Red versus Blue Size: small versus large

Main effect of size No main effect of colour Main effect of rate

Size x Colour: No Rate x Colour: No Size x Rate: No

SmallLarge The relationship between colour and rate is not different for the small and large conditions: No 3-way interaction

C1C2 2 x 2 x 2 : For you to practice at home

3-way interaction 3 factors interact when the interaction of two of the factors is not the same at all the levels of the third variable Y A 3-way Interaction B C

Why the stats?

Same data !!! Always look at the Y-axis values! What really tells you what effects are present is the statistic analysis

Statistical tests take variations of the DV into account Only the statistical test can evaluate whether differences in your samples can be relatively safely generalised to the population