The 2020 pandemic provided a perfect opportunity to spend time doing my favorite thing: Experimenting!
Read Part One of this three-part blog to learn what inspired me to investigate the impact of the following four factors on the bounciness of elastic spheroids:
A. Ball type: Hollow or Solid
B. Temperature: Room vs Freezer
C. Drop height: 3 vs 6 feet
D. Floor surface: Hardwood vs Rubber
Design-Expert® software (DX) provides the astonishing result: Neither the type of ball (factor A) nor the differing surfaces (factor D) produced significant main effects on first-bounce time (directly related to height per physics). I will now explain.
Let’s begin with the Pareto Chart of effects on bounce time (scaled to t-values).
First observe the main effects of A (ball type) and D (floor surface) falling far below the t-Value Limit: They are insignificant (p>>0.05). Weird!
Next, skipping by the main effect of factor B (temperature) for now (I will get back to that shortly), notice that C—the drop height—towers high above the more conservative Bonferroni Limit: The main effect of drop height is very significant. The orange shading indicates that increasing drop height creates a positive effect—it increases the bounce time. This makes perfect sense based on physics (and common knowledge).
Now look at a multi-view Model Graphs for all four main effects.
The plot at the lower left shows how the bounce time increased with height. The least-significant-difference ‘dumbbells’ at either end do not overlap. Therefore, the increase is significant (p<0.05). The slope quantifies the effect—very useful for engineering purposes.
However, as DX makes clear by its warnings, the other three main effects, A, B and D, must be approached with great caution because they interact with each other. The AB and BD interactions will tell the true story of the complex relationship of ball type (A), their temperature (B) and the floor material (D).
See by the interaction plot how the effect of ball type depends on the temperature. At room temperature (the top red line), going from the hollow to the solid ball produces a significant increase in bounce time. However, after being frozen, the balls behaved completely opposite—hollow beating solid (bottom green line). These opposing effects caused the main effect of ball type (factor A) to cancel!
Incredibly (I’ve never seen anything like this!), the same thing happened with the floor surface: The main effect of floor type got washed out by the opposite effects caused by changing temperature from room (ambient) to that in the freezer (below 0 degrees F).
Changing one factor at a time (OFAT) in this elastic spheroid experiment leads to a complete fail. Only by going to the multifactor testing approach of statistical DOE (design of experiments) can researchers reveal breakthrough interactions. Furthermore, by varying factors in parallel, DOE reveals effects far faster than OFAT.
If you still practice old-fashioned scientific methods, give DOE a try. You will surely come out far ahead of your OFAT competitors.
P.S. Details on elastic-spheroid experiments procedures will be laid out in Part 3 of this series.