John runs the same 3 mile route every day. If he takes his dog, it adds 25 seconds to his running time. If it is cold, it adds 10 seconds to his running time. Suppose he ran one cold morning with his dog. What change in time would represent NO interaction between the two variables? (dog and temp).
a. increase 25 seconds
b. increase 35 seconds
c. none of the above
d. increase 10 seconds
If there were some interaction, you would expect one or the other times to change so that the sum of the two would be different.
As a (silly?) example
Time = t
0 + 25 d + 10 c + a d c /25
where d and c takes on values of 0 (didn't happen that day) or 1 (did happen that day) and a is some constant.
-If it is not cold and he takes his dog, it adds 25 seconds.
-If it is cold but he doesn't take his dog it adds 10 seconds.
-If it is cold and he takes his dog and a=1, there is interaction between d an c and it adds 35 seconds.
So, if a were zero, would there be any interaction? If a were zero, what would the added time be?
BTW, in the real world I would agree there is not enough information. However, one could say there was (or was not) any apparent interaction from the information given.
