The Design and Analysis of Launching Cats

Hi folks! It was wonderful to meet with so many new prospects and long-standing clients at the Advanced Manufacturing Minneapolis expo last week. One highlight of the show was running our own design of experiments (DOE) in-booth: a test to pinpoint the height and distance of a foam cat launched from our Cat-A-Pult toy. Visitors got to choose a cat and launch it based on our randomized run sheet. We got lots of takers coming in to watch the cats fly, and we even got a visit from local mascot Goldy Gopher!

But I’m getting a bit ahead of myself: this experiment primarily shows off the ease of use and powerful analytical capabilities of Design-Expert® and Stat-Ease® 360 software. I’m no statistician – the last math class I took was in high school, over a decade ago – but even a marketer like me was able to design, run, and analyze a DOE with just a little advice. Here’s how it worked.

Let’s start at the beginning, with the design. My first task was to decide what factors I wanted to test. There were lots of options! The two most obvious were the built-in experimental parts of the toy: the green and orange knobs on either side of the Cat-A-Pult, with spring tension settings from 1 to 5.

However, there were plenty of other places where there could be variation in my ‘pulting system:

• The toy comes with 5 Cat-A-Pults: are there variations between each 'pult?
• Does it matter what kind of surface the Cat-A-Pult is on, e.g., wood, concrete, or carpet?
• The toy came with 5 colors of foam cat; would the pigment change the cat’s weight enough to matter?
• What about where on the plate we apply launch pressure, or how much pressure is applied?

Some of these questions can be answered with subject matter knowledge – in the case of launch pressure, by reading the instruction manual.

For our experiment, the surface question was moot: we had no way to test it, as the convention floor was covered in carpet. We also had no way to test beforehand if there were differences in mass between colors of cat, since we lacked a tool with sufficient precision. I settled on just testing the experimental knobs, but decided to account for some of this variation in other ways. We divided the experiment into blocks based on which specific Cat-A-Pult we were using, and numbered them from 1 to 5. And, while I decided to let people choose their cat color to enhance the fun aspect, we still tracked which color of cat was launched for each run - just in case.

Since my chosen two categoric factors had five levels each, I decided to use the Multilevel Categoric design tool to set up my DOE. One thing I learned from Mark is that these are an “ordinal” type of categoric factor: there is an order to the levels, as opposed to a factor like the color of the cat or the type of flooring (a “nominal” factor). We decided to just test 3 of the 5 Cat-A-Pults, trying to be reasonable about how many folks would want to play with the cats, so we set the design to have 3 replicates separated out into 3 blocks. This would help us identify if there were any differences between the specific Cat-A-Pults.

For my responses, I chose the Cat-A-Pult’s recommended ones: height and distance. My Stat-Ease software then gave me the full, 5x5, 25-run factorial design for this, with a total of 75 runs for the 3 replicates blocked by 'pult, meaning we would test every combination of green knob level and orange knob level on each Cat-A-Pult. More runs means more accurate and precise modeling of our system, and we expected to be able to get 75 folks to stop by and launch a cat.

And so, armed with my run sheet, I set up our booth experiment! I brought two measuring tapes for the launch zone: one laid along the side of it to measure distance, and one hanging from the booth wall to measure height. My measurement process was, shall we say, less than precise: for distance, the tester and I eyeballed the point at which the cat first landed after launch, then drew a line over to our measuring tape. For height, I took a video of the launch, then scrolled back to the frame at the apex of the cat’s arc and once again eyeballed the height measurement next to it. In addition to blocking the specific Cat-A-Pult used, we tracked which color of cat was selected in case that became relevant. (We also had to append A and B to the orange cat after the first orange cat was mistaken for swag!)

Over the course of the conference, we completed 50 runs, getting through the full range of settings for ‘pults 1 and 2. While that’s less than we had hoped, it’s still plenty for a good analysis. I ran the analysis for height, following the steps I learned in our Finding the Vital Settings via Factorial Analysis eLearning module.

The green knob was the only significant effect on Height, but the relatively low Predicted R² model-fit-statistic value of 0.36 tells us that there’s a lot of noise that the model doesn’t explain. Mark directed me to check the coefficients, where we discovered that there was a 5-inch variation in height between the two Cat-A-Pult! That’s a huge difference, considering that our Height response peaked at 27 inches.

With that caveat in mind, we looked at the diagnostic plots and the one-factor plot for Height. The diagnostics all looked fine, but the Least Significant Difference bars showed us something interesting: there didn’t seem to be significant differences between setting the green knob at 1-3, or between settings 4-5, but there was a difference between those two groups.

With this analysis under my belt, I moved on to Distance. This one was a bit trickier, because while both knobs were clearly significant to the model, I wasn’t sure whether or not to include the interaction. I decided to include it because that’s what multifactor DOE is for, as opposed to one-factor-at-a-time experimentation: we’re trying to look for interactions between factors. So once again, I turned to the diagnostics.

Here's where I ran into a complication: our primary diagnostic tools told me there was something off with our data. There’s a clear S-shaped pattern in the Normal Plot of Residuals and the Residuals vs. Predicted graph shows a slight megaphone shape. No transform was recommended according to the Box-Cox plot, but Mark suggested I try a square-root transform anyways to see if we could get more of the data to fit the model. So I did!

Unfortunately, that didn’t fix the issues I saw in the diagnostics. In fact, it revealed that there’s a chance two of our runs were outliers: runs #10 and #26. Mark and I reviewed the process notes for those runs and found that run #10 might have suffered from operator error: he was the one helping our experimenter at the booth while I ran off for lunch, and he reported that he didn’t think he accurately captured the results the way I’d been doing it. With that in mind, I decided to ignore that run when analyzing the data. This didn’t result in a change in the analysis for Height, but it made a large difference when analyzing Distance. The Box-Cox plot recommended a log transform for analyzing Distance, so I applied one. This tightened the p-value for the interaction down to 0.03 and brought the diagnostics more into line with what we expected.

While this interaction plot is a bit trickier to read than the one-factor plot for Height, we can still clearly see that there’s a significant difference between certain sets of setting combinations. It’s obvious that setting the orange knob to 1 keeps the distance significantly lower than other settings, regardless of the green knob’s setting. The orange knob’s setting also seems to matter more as the green knob’s setting increases.

Normally, this is when I’d move on to optimization, and figuring out which setting combinations will let me accurately hit a “sweet spot” every time. However, this is where I stopped. Given the huge amount of variation in height between the two Cat-A-Pults, I’m not confident that any height optimization I do will be accurate. If we’d gotten those last 25 runs with ‘pult #3, I might have had enough data to make a more educated decision; I could set a Cat-A-Pult on the floor and know for certain that the cat would clear the edge of the litterbox when launched! I’ll have to go back to the “lab” and collect more data the next time we’re out at a trade show.

One final note before I bring this story to a close: the instruction manual for the Cat-A-Pult actually tells us what the orange and green knobs are supposed to do. The orange knob controls the release point of the Cat-A-Pult, affecting the trajectory of the cat, and the green knob controls the spring tension, affecting the force with which the cat is launched.

I mentioned this to Mark, and it surprised us both! The intuitive assumption would be that the trajectory knob would primarily affect height, but the results showed that the orange knob’s settings didn’t significantly affect the height of the launch at all. “That,” Mark told me, “is why it’s good to run empirical studies and not assume anything!”

We hope to see you the next time we’re out and about. Our next planned conference is our 8th European DOE User Meeting in Amsterdam, the Netherlands on June 18-20, 2025. Learn more here, and happy experimenting!