Chapter 12 Two-Way Between-Group ANOVA

Assumptions for all types of ANOVA are the same (3) 1. The sample should be selected ____ 2. The population should be distributed ____ 3. Population variances should be ____

1. Randomly 2. Normally 3. Equal - In reality, most of these do not occur (?)

For a two-way between-groups ANOVA, the within-groups degrees of freedom is calculated by...

Adding all of the degrees of freedom in each of the cells - In the current example, there are three participants in each cell (in each level) so the within groups DOF is 3-1=2 for each cell, and there are 4 levels and thus there are 8 DOF

Two-way ANOVA allows us to compare levels from ____ different ____

Allows us to compare levels from two different independent variables - Also, allows us to study the joint effects of those two variables

The F statistic for each of the two independent variables describes the ____ effect

F stat for each of the two independent variables describes the MAIN EFFECT

Any ANOVA with at least two IV can be called a ____ ANOVA

Factorial ANOVA - Factor is another word to describe an independent variable in a study with more than one IV

A main effect occurs in a factorial design when one of the independent variables has an...

Has an influence on the dependent variable

If line plots in a graph are not parallel then there is evidence of an ____

Interaction - Because each line plot tells the same story, the relative effects of the three genres do NOT seem depend on release time

DOF from above study When we find DOF for each main effect on its own, then we find the between-groups DOF for the interaction by...

Multiplying the DOF for the two main effects

An interaction in which the effect of one independent variable is strengthened or weakened at one or more levels of the other independent variable, but the direction of the initial effect does not change

Quantitative

We can check our work by calculating the total degrees of freedom by...

Subtracting 1 from the total number of participants There are 12 participants so, DF_total = Ntotal - 1 = 12 - 1 = 11 - Then, we can add up the three between-groups DOF and the within-groups DOF to see if they add up to the total DOF

Study that has two IV (age and # of repetitions) What would the null and alternative hypothesis be?

There would be three null hypothesis and three alternative - There is one for each main effect and one for the interaction Hypotheses for the main effect of first IV, age, are as follow... Ho: On average, compared with older adults, younger adults have the same proportion of responses that are wrong when remembering which claims are myths Ha: On average, compared with older adults, younger adults have a different proportion of responses that are wrong when remembering which claims are myths - Do same thing for the second IV of number of repetitions Interaction: - Null: effect of number of repetitions is not dependent on the levels of age - AlternativE: effect of number of repetitions depends on the levels of age

Two-way ANOVAs produce ____ F statistics

Three F statistics - One for the first independent variable - One for the second independent variable - One for the interaction between the two independent variables

Two way ANOVA is a hypothesis test that includes ____ ____ independent variables, regardless of their number of ____, and a ____ dependent variables

Two way ANOVA is a hypothesis test that includes 2 nominal IV (number of levels in the nominal IV does NOT matter) - Also, includes a scale DV

We evaluate whether there is a main effect by disregarding the influence of any other ____ ____ in the study

We disregard influence of any other independent variables in the study - We temporarily pretend the other variable does not exist

With a 2 way ANOVA we get ____ distinct findings by conducting just one study

We get 3 distinct findings by conducting just one study