Factorial Design Flashcards
(13 cards)
Ronald Fisher and Factorial Design
one of the main developers of many statistical methods used in scientific research
- cited more than any other scientist
spent life developing statistic methods but also used method to understand the heritability of traits
- used this to value eugenics, clearly an abhorrent idea
- it shows that on occasion people can be mathematically smart but can be silly in other ways
The Design of Experiments (1935)
one difference between conditions varying at a time
- “usually have no knowledge that any one factor will exert its effects independent of all others that can be varied, or if its effects are related to variations in other factors”
- not just one thing that is driving the impact of the samples
Factorial
when we have more than one thing we want to manipulate
2x2 Factorial Design
———- b1 b2
a1 a1b1 a1b2
a2 a2b1 a2b2
Interpreting Factorial Designs (the main effect)
report the main effects of interactions
- main effects: effects of factor, averaged over levels of other factor
difference between averages
42 + 60 / 2 = 51
50 + 55 / 2 = 52.5
ME: 1.5
- vice versa for vertical columns
we have 2 factors and therefore 2 main effects
the results of our averages are called marginal means
Draw, plot and interpret the different instances of main effects on a graph.
main effects will never intersect on a graph, symmetrical
lines are closer if there is no effect on a
if both have an effect then they will move as a constant
if there is an effect on b and not on a the lines will be horizontal
Interactions
size of effect due to one factor depends on the state of the other factor
- what if coffee influences the affect of stress?
Draw, plot and interpret the different instances of interactions on a graph.
when a1 is low, b has larger effect on scores than when a2 is high (intersecting lines)
lines in different directions - a has opposite effect on test performance when b is increased
Principles of ME’s and Interactions
ME will never cross each other
- for interactions, slopes are not parallel
- parallel slopes means two main effects do not interact, effects of each are independent of each other
- the presence of an interaction does not alter the literal interpretation of the main effect, i.e. effect of a factor averaged over levels of the other factor
- however, interaction says something more complex in the data, adding info about second factor tells more about ways first factor can influence test scores
- “stress impairs performance, but only under high caffeine levels”
Factorial designs in independent groups samples
increasing the number of factors rapidly increases sample size
- find number of cells by taking product of factor cells
Factorial designs in repeated-measures samples
- counterbalance
- can have completely within-subject
- participants tested for all possible combinations
Factorial Mixed Designs
- between + within subject factor
- e.g. Factor A: group (piano vs crossword), Factor B: time of performance (before vs after practice interventions)
Higher Order Interactions
3 factor design has:
- 3 main effects
- A(group), B(time of performance), C(task)
- 3 ‘regular’ interactions (AB,AC,BC)
- 1 triple interaction (ABC), practice x time x task
triple interaction: interaction between B and C differ across the other factor, A
