2x2 ANOVA

Levels in example

(Rows and Columns) 2 levels of roles (lead or supporting) 2 levels of gender (male and female)

Number of numbers

(ex. 2 x 3 x 4= 3 numbers) How many factors (IVs)

If there is a potential interaction, than what?

ANOVA tells is interaction is significant (with a chance of 5% chance of being wrong

Research Question 2: Main effect for GENDER

Are male Oscar winners older than female Oscar winners? -Sum data across the each column and obtain a mean for each column. Gender difference= 7.7

Levels

Elements that make up the factor (IV)

3 X 3 ANOVA

Have to do a post-hoc test

Two- Way ANOVA (If you have 2 IVs in the same study....)

If you have 2 IVs in the same study, you can examine them independently and in conjunction with each other: 1) Does IV1 influence DV? (main effect) 2) Does IV2 influence DV? (main effect) 3) Do the effects of IV1 and IV2 combined differentially affect DV? (Interaction)

What is an interaction?

When the effects of one independent variable differ according to the levels of another independent variable Ex. We are testing two IV's, Gender (male and female) and Age (young, medium, and old) and their effect on performance If males performance differed as a function of age, i.e. males performed better or worse with age, but females performance was the same across ages, we would say that Age and Gender interact, or that we have an Age x Gender interaction

Another possible interaction

•Are supporting actors older than leading actors only when they are men or only when they are women? -If so, we can conclude that role and gender interact. •This interaction is different than the main effect question: Are supporting actors always older than leading actors?

One possible interaction

•Interaction question: Are men older than woman only when they are leading actors or only when they are supporting actors ? -If so, we can conclude that role and gender interact. •This Interaction is different than the main effect question which was: Are men always older than woman? - Find difference across row

Main Effect for Role Results= -3.9

•Is the difference of 3.9 years in our sample enough to infer that the population of all leading and supporting Oscar winners are different? •The ANOVA will tell us if this main effect is significant (with a 5% chance of being wrong)

Where do main effects occur?

In rows and columns Rows= ROLES Columns= GENDER

Research Question 3: Interaction

Is there an interaction? •Do differences between levels of one factor (e.g., gender) change from level to level on the second factor (e.g., role)?

What does number in ANOVA refer to

Refers to the number of levels

In our example, what are the factors?

Role and gender Can "manipulate" them by selecting them

Rows

Role of oscars (lead or supporting)

What is a main effect

The effect of an IV independent of any other IVs (When one IV influences the DV)

The number themselves

The number of levels in each IV

Primary purpose of 2 x 2 anova

Understand if there is an interaction between the two IVs on the DV. DV is continuous (interval or ratio)

Research Question 1: Main Effect for ROLE

Are leading actor Oscar winners older or younger than supporting actor Oscar winners? -Sum data across each row and obtain a mean for each row. Role difference= -3.9

Columns

Gender of actors

Main Effect for Gender results= 7.7

•Is the difference of 7.7 years in our sample enough to infer that the population of all male and female Oscar winners are different? •The ANOVA will tell us if this main effect is significant (with a 5% chance of being wrong)

Post-hoc test: interactions

•When interactions are significant, researchers will refrain from interpreting main effects -Because one interaction (e.g., one cell) can cause main effect differences. In such case it would not be appropriate to conclude there were larger main effects.

Difference between One-way ANOVA and Two-way ANOVA

1) One Way ANOVA= one factor= one independent variable with 2 or more levels/conditions 2) Two-way ANOVA= two factors= two independent variables; each IV has 2 or more levels/conditions

What are main effects

Analyses of factors

How many factors

How many "ways" (One factor= one way) (Two factor= two ways)

What are the factors?

Independent variables