1. Come up with a research question that could be addressed by a 2X2 factorial A

ID: 3152737 • Letter: 1

Question

1. Come up with a research question that could be addressed by a 2X2 factorial ANOVA. You can make up the scales needed to measure the DV if you want. Feel free to be as creative as you need to be. 2. Explain the advantage(s) of using the factorial ANOVA over the one?way ANOVA. 3. Conceptually explain main effect and interaction tests. 4. Pretend that you did an experiment to answer your research question from #1. Let’s assume that the scale of the DV (it is ok if you make up the DV) is measured on a 5?point Likert?scale from 1?5 (strongly disagree to strongly agree), with 3 being considered neutral. Use the ANOVA table below to report the results of your “experiment”.

a. How many people were in your study?

b. What are the three null hypotheses?

c. What are the results of your null hypothesis significance tests for the three ANOVA tests (i.e., retain or reject)? i. What do you conclude about your research questions (there should be three conclusions)?

df MS p-value Source Between Groups Main effect1 Main effect2 Interaction Within Groups Total 28.4 5 16.2 7.2 16.4 44.8 4.88 5 16.2 7.2 1.03 0.04 15.81 0.001 0.02 7.02 16 19 marginal means table Factor 2 level1 level2 2.9 3.9 Factor1 level1 level2 1.4 3.6 2.5 4.2 4.3

Explanation / Answer

(IV) Room Temperature

(IV) Test Difficulty

(Level) 30 degrees

(Level) 50degrees

(Level) Hard Test

Hard Test in 30 degrees

Hard Test in 50 degrees

(Level) Easy Test

Easy Test in 30 degrees

Easy Test in 50 degree

Let this experiment is conducted in two different groups of student to study the effect of these two factor on the performance of student. We can frame the research question as:

Room temperature or difficulty level of test affects the performance of student more.

2. Advantages of factorial ANOVA over one way ANOVA

a)More precision on each and factor as compared to one way ANOVA (Which is due to hidden replications in factorial ANOVA)

b)Factorial ANOVA helps in broadening the scope of experiment by consider the effect of more than one variable of different levels

c)The interaction effect of various factors can be estimated

d)Factorial ANOVA suits the conditions of exploratory analysis where one wish to find out the domination factor or optimal level of factor or combination of level of different factors

Let us take the example 2X2 ANOVA with two variables A and B there three basic types of effects that are tested:

We will consider main effects first. A main effect for a given independent variable means that there is a significant difference between the levels of this independent variable across levels of the other independent variable. Another way of thinking of this is that there is an effect for one independent variable regardless of the level of the other. In similar way in the interaction test, we find the effect of combination of two, for example the effect of A and B combine.