Ch. 14, factorial ANOVA

When to use factorial ANOVA

• you have more than 1 factor (IV)

2 factors: known as “two-way”

3 factor: known as “three way”

what study design can we use for factorial ANOVA

• all between subjects

• all within subjects

• a mix of both designs

why choose a factorial

• we can answer more complex research questions

• we can take into consideration the interaction of factors

• helps to guide human behaviour & interventions from research

hypothesis 1

1. testing the main effect: the effect of factor A

   EX: how does gender (male vs. female) affect aggression)

hypothesis 2

2. main effect of condition: effect of factor B

   EX: how does condition (violent vs. non-v) affect aggression

hypothesis 3

3. interaction between factors

   EX: does the effect of condition on aggression depend on one’s gender?

parallel line graphs =

no interaction

different slopes =

interaction

a steeper slope means

a larger interaction

opposite patterns/directions =

interaction

how do we calculate effect size?

we do not calculate effect size (η) for this test, instead we run a simple main effect to find which variables are correlated

calculating simple main effects

run a t test on one factor (either A or B),

define power

the probability that your hypothesis will identify a treatment (rejected the null hypothesis) if an effect really exists

it is a probability value that proves an effect

calculating type 2

calculated by knowing our power

power of your test = 1 - β

as probability increases …

the probability of making a type 2 error decreases

we generally want what lvl of power?

a power of at least .80 (meaning we generally accept a type 2 error rate of .20 (20%)

you will have greater power with …

• larger effects sizes

• larger sample sizes

• larger alpha lvl

• one tailed tests

how do we know how many people to test?

you use a power analysis

what do you need to know to conduct a power analysis

1. your desired level of power (at least .80)

2. the size of the effect you expect to find

3. your alpha lvl

4. if you will be running a 1 vs 2 tailed test

smaller effect need…

more poeple to get sufficient power to detect them (because small effects are harder to find)

large effects need

fewer people to get sufficient power to detect it

how do you know what effect size to predict

• past literature

• similar studies that have published results/effect sizes

• pilot data (a mini study)

• theoretical predictions

correlation values

pearson r value is what is calculated - from (-1) to (1)

-negative value = negative correlation

positive value = positive correlation

linear regression

Examining how one or more variables predict one continuous variable

EX: does one’s time spent on social media and one’s age predict depression levels?

if you want to do a linear regression but have more than 1 predictor variables, what would we use?

use a multiple linear regression, or Hierarchical linear regression

Chi square

Testing the likelihood of being in a certain outcome/ testing if one group membership predicts the likelihood of being in another group membership

EX: does age group (younger vs. older adult) predict the likelihood of voting in the election? (voting = did vote; didn’t vote)

chi square examines only ….

2 CATEGORICAL VARIABLES, and the outcome can only be 2 levels

binary logistic

Tests the likelihood of being in a certain outcome

does condition (peer vs. alone) and age predict the likelihood of telling a lie? (lie = yes or no)