# Thread: SPSS: regression analysis for 3x2 experiment. How to test for interaction

1. ## SPSS: regression analysis for 3x2 experiment. How to test for interaction

Dear all,

For my research I have the following facts:
- I have two categorical IVs:
- treatment condition called competition, which has three conditions ("low", "medium" and "high")
- Another factor that is given to half of the group, called accountability (two options: "non-accountability" and "accountability")
- Hence, I have a 3x2 experiment with 20 participants in each group.
- My DV is a scale variable
- I also have a set of control variables (both scale and categorical)

Then:
- Hypothesis one is that if you go from low to medium to high, the DV will increase
- Hypothesis two is that if you introduce accountability, the differences between the low, medium and high group decrease.

The problem I encounter is that I have three groups for the competition condition (which are coded 0, 1 and 2). If I multiply it with accountability, they become 0, 2 and 4, which is a problem according to my supervisor. Therefore, a factorial ANOVA seems to be a suboptimal solution.

He recommended a regression analysis with dummy variables of the three competition scenarios. But then still I have no idea on how to test for the interaction effect between competition and accountability.

2. ## Re: SPSS: regression analysis for 3x2 experiment. How to test for interaction

Originally Posted by Ricovermeulen
Dear all,

For my research I have the following facts:
- I have two categorical IVs:
- treatment condition called competition, which has three conditions ("low", "medium" and "high")
- Another factor that is given to half of the group, called accountability (two options: "non-accountability" and "accountability")
Just to be clear, are you saying that half of the total sample size is in the accountability group and the other half is in the non-accountability group (and within each of those, they are split into one of the three categories for competition?)?

Originally Posted by Ricovermeulen
- Hence, I have a 3x2 experiment with 20 participants in each group.
- My DV is a scale variable
- I also have a set of control variables (both scale and categorical)
Would you clarify what you mean by a scale variable (I think I'm unfamiliar with that particular term).

Originally Posted by Ricovermeulen
Then:
- Hypothesis one is that if you go from low to medium to high, the DV will increase
- Hypothesis two is that if you introduce accountability, the differences between the low, medium and high group decrease.

The problem I encounter is that I have three groups for the competition condition (which are coded 0, 1 and 2). If I multiply it with accountability, they become 0, 2 and 4, which is a problem according to my supervisor. Therefore, a factorial ANOVA seems to be a suboptimal solution.

He recommended a regression analysis with dummy variables of the three competition scenarios. But then still I have no idea on how to test for the interaction effect between competition and accountability.
Assuming that the dependent variable is appropriate for an ANOVA/Regression, I agree with your supervisor that it would be better to fit a regression with the appropriate dummy variables.

First, you will need to determine the baseline/reference group. I recommend setting low competition and non-accountability as your baselines. In other words, for competition, you have three groups, so you will need 2 dummy variables (number of groups minus 1, and fit the intercept in the model). Create X1: 1 if medium competition, 0 if not; Create X2: 1 if high competition, 0 if not; this implicitly codes low as the reference level (0,0), so if your hypothesis #1 is true, you would see positive coefficients for X1 and X2 since they represent the difference of the group relative to low.
Create X3 for accountability: 1 if accountability, 0 if non-accountable

To test for interaction, include terms: X1*X3, X2*X3

You will have 5 coefficients aside from an intercept.

Conduct a global f-test and proceed if significant (also make sure assumptions are reasonably satisfied).
I would then do a nested f-test to test the 2 coefficients for interaction.
If you've followed up until this point, feel free to post some output with the full model and interaction subset test. If you're a little confused, feel free to ask some more questions!

3. ## Re: SPSS: regression analysis for 3x2 experiment. How to test for interaction

Thanks a lot for the helpful response! My DV is continuous, and indeed half of the group got the accountability treatment.

If I run this regression analysis, can I include my control variables without converting them to dummy variables too? There are quite a few of them and almost half of them is categorical.

For now I have done a factorial ANCOVA with competition and accountability as factors and all control variables as covariates. Could you explain to me why that is a worse approach than a multiple regression. I literally have no idea haha..

4. ## Re: SPSS: regression analysis for 3x2 experiment. How to test for interaction

Originally Posted by Ricovermeulen
Thanks a lot for the helpful response! My DV is continuous, and indeed half of the group got the accountability treatment.

If I run this regression analysis, can I include my control variables without converting them to dummy variables too? There are quite a few of them and almost half of them is categorical.

For now I have done a factorial ANCOVA with competition and accountability as factors and all control variables as covariates. Could you explain to me why that is a worse approach than a multiple regression. I literally have no idea haha..
You can think of them as very similar, with the differences primarily relating to the focus. Some software packages will give you different output picking one over the other. The important thing to remember is that covariates should be reasonably correlated with the DV, uncorrelated with the factors (the variables of interest), and should not have any interaction with the factors (but include interaction if it exists).

Also, one of the issues when you code categorical variables as things other than "0" and "1" is that you make the interpretations of estimated coefficients less natural. The 0/1 convention allows you to interpret a particular coefficient as a difference in means between one group and the baseline.

I forgot to ask a couple things. First, were participants randomization to the treatments? If I understood your original post, your total sample size is 160 (3x2=6 groups with 20 per group). Is this accurate?

How many covariates do you plan to include? Can you shed some light on what they are as well as the DV?

5. ## Re: SPSS: regression analysis for 3x2 experiment. How to test for interaction

I indeed have 6 x 20 people!

- I plan to include 9 covariates (4 categorical, of which 3 have more than two categories; 5 ordinal variables that are constructed from Likert scales).
- The DV is a continuous variable with a range between 0 and 100 (risk).
- Then I also would like to investigate the presence of a mediator (another continuous variable called group cohesion) between competition and risk. However, I have no idea how to do that whit the moderator included (accountability). For now I used Baron & Kenny..

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