Main and Interaction effects in factorial designs

 

Main and Interaction effects in factorial designs

Consider the independent variables are ‘drug dosage’ and ‘gender’ and the dependent variable is ‘drug effectiveness’. Also, let drug dosage have 2 levels (low and high) and gender has 2 levels (male, female). After the experiment, we get the results like in the figure below. 

Let the blue lines correspond to male and red with the female.

We would like to ask the following questions?

1. Does dosage impact drug effectiveness?

2. Does gender impact drug effectiveness?

3. Does the interaction of dosage and gender impact drug effectiveness?

What do you think (take 5 mins)

To answer Q1, forget about the gender (colored lines) and consider only 1 independent variable (dosage) with the dependent variable like below,

We can see that the mean effect of low dosage (green star ⭐) is indifferent from the mean effect of giving a high dosage suggesting that dosage doesn't have an effect on drug effectiveness. 

To answer Q2, forget about the dosage and consider only 1 independent variable (gender) with the dependent variable like below,

You could see that both male and female have the same effect on average suggesting that gender doesn't impact drug effectiveness.

Now for question 3, we could see that the lines cross each other suggesting that there is some interaction going on. 

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Now consider the figure below and let's try to answer the same questions

For Q1, we can forget about the gender (colored lines) and consider only dosage with drug effectiveness like below,

You can see the mean effect of low dosage is statistically different from the mean effect of giving a high dosage suggesting dosage indeed has an effect on drug effectiveness.

Now for Q2, forget about the dosage and consider only gender with the drug effectiveness like below,

We can see that the mean effect of male and the mean effect of the female is different. Whether they are statistically significant can be proven with ANOVA. 

For Q3, Since the lines do not cross, it suggests that the effect from male and female are indifferent (tats why the lines are parallel)