# Testing for interaction between two categorical independent variables and a dependent variable

This is a contrived example for clarity, but it reflects a real problem that I'm dealing with:

Say that I want to analyse miles-per-gallon (ratio) for cars of different color and interior type (both categorical):

colors: red, green, blue

interior types: leather, cotton, synthetic

I don't necessarily compare the same number of cars in each category:

Scenario 1:
+-------+----------+----------+-------------+
| MPGs  | Leather  |  Cotton  |   Synthetic |
+-------+----------+----------+-------------+
| Red   | 10,11,12 | 11,12,13 |       13,14 |
| Green |       10 | 10,11,12 |    11,12,13 |
| Blue  |   8,9,10 |  9,10,11 |    10,11,12 |
+-------+----------+----------+-------------+


In the above example, it's seems that red has higher mpg than green or blue, independent of interior style, and that synthetic has higher mpg than leather or cotton, independent of color.

Scenario 2:
+-------+----------+----------+-------------+
| MPGs  | Leather  |  Cotton  |   Synthetic |
+-------+----------+----------+-------------+
| Red   | 10,11,12 | 11,12,13 |       13,14 |
| Green |       10 | 11,12,13 |    10,11,12 |
| Blue  |   8,9,10 |  9,10,11 |    10,11,12 |
+-------+----------+----------+-------------+


The above is similar to before, except that now, if the car is green, then cotton seems to have the highest mpg.

Basically, I need to find out if I can look for the best interior type independently of the car's color. My motivation for asking this is that if I can ignore color, then each interior type has about 9 observations, thus I can be more certain which is best. But if I can't, then each [color,interior type] group has only about 3 observations, which means I'm less confident about which is best.

So I have two questions here:

1. What am I doing here? Is this really a test for interaction?

2. What statistical test can be used here?

Thanks!