Factorial Experiment Design Activity
With the rising costs of fuel, you’ve decided to explore factors that might improve fuel economy. The factors I explored were:
A – Switching to higher octane fuel
B – Leaning out the fuel mixture under part-load conditions
Table 1: Fuel economy data for four different fuel tank fill-ups under each condition
A / B / I / II / III / IV- / - / 32 / 31 / 30 / 33
+ / - / 30 / 28 / 29 / 30
- / + / 32 / 34 / 36 / 34
+ / + / 32 / 31 / 33 / 33
A- represents original fuel octane, A+ represents switching to 91 octane
B- represents original air/fuel ratio, B+ represents increasing (lean) air/fuel ratio
1) Calculate (1), a, b, and ab
2) Calculate MEA, MEB, and the Interaction Effect (AB)
3) What can you say about the effects of changing fuel octane, and fuel mixture?
4) Do you think there is a statistical difference? Why/Why not?
Table 2: Suppose the data looked like
- / - / 31.5 / 31.5 / 31.5 / 31.5
+ / - / 29.25 / 29.25 / 29.25 / 29.25
- / + / 34 / 34 / 34 / 34
+ / + / 32.25 / 32.25 / 32.25 / 32.25
5) Even though (1), a, b, and ab haven’t changed, do you feel more confident in your comments from question 3? Why so/why not? What if there was more data, but it was scattered like the first table?
6) What statistical concepts do you expect will be helpful in determining when you could say there was a difference?
Unsatisfied with the previous experiment, you’ve tried looking at a different factor.
A – Switching to higher octane fuel
B – Raising the compression ratio of the engine
Table 3: Fuel economy data for four different fuel tank fill-ups under each condition
A / B / I / II / III / IV- / - / 32 / 31 / 30 / 33
+ / - / 30 / 28 / 29 / 30
- / + / 33 / 33 / 32 / 31
+ / + / 36 / 35 / 38 / 35
A- represents original fuel octane, A+ represents switching to 91 octane
B- represents original compression ratio, B+ represents a higher compression ratio
7) Calculate (1), a, b, and ab
8) Calculate MEA, MEB, and the Interaction Effect (AB)
9) Is there an interaction dependence for the two factors? What do you think the number AB represents?