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## Factorial designs: Main effects and interactions

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**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 < .001; while no effect of colour was observed; F(1, 9) < 1, p > .5. No interaction between rate of presentation and colour was found; F(1, 9) < 1, p > .7. ”**Slow-red Slow-blue Fast-red Fast-blue**Sub1 87.000 82.000 56.000 54.000 Sub2 82.000 79.000 57.000 59.000 Sub3 76.000 78.000 38.000 28.000 Sub4 75.000 76.000 45.000 46.000 Sub5 74.000 73.000 32.000 39.000 Sub6 72.000 77.000 42.000 50.000 Sub7 69.000 80.000 41.000 39.000 Sub8 75.000 73.000 38.000 25.000 Sub9 58.000 57.000 29.000 28.000 Sub10 76.000 65.000 59.000 57.000 xSR= 74.4 xFR= 43.7 xSB= 74.0 xFB= 42.5**xR* = ( xRS + xRF ) / 2**xB* = ( xBS + xBF ) / 2 xR* = (74.4+43.7) / 2 = 59.05 xB* = (74+42.5) / 2 = 58.25 Performance levels in colour conditions, regardless of rate of presentation, are similar**xF* = ( xFR + xFB ) / 2**xF* = (43.7 + 42.5) / 2 = 43.1 xS* = ( xSR + xSB ) / 2 xS* = (74.4 + 74) / 2 = 74.2 Performance levels in rate of presentation conditions, regardless of colour, are different**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...**Interaction**Task(explicit/implicit) Memoryperformance Group ofparticipants(Ctrls/amnesics)**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.**A & B & interaction**B A A & 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?**1**2 1 2 2 x 3 design Main effect of B 1 <2 Effect of B is not linear**2 x 3 design**Main effect of A & B**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**Small**Large The relationship between colour and rate is not different for the small and large conditions: No 3-way interaction**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 3-way Interaction A B C**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