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arxiv: 1907.10684 · v1 · pith:A5BOCRQQnew · submitted 2019-07-24 · 📊 stat.AP

Teaching Split Plot Experiments With a Boomerang Tin

Thomas Muehlenstaedt , Maria Lanzerath This is my paper

Pith reviewed 2026-05-24 16:30 UTC · model grok-4.3

classification 📊 stat.AP
keywords split-plot designdesign of experimentsteaching statisticshands-on learningboomerang tinrubber band toywhole plotsubplot
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The pith

A boomerang tin toy supplies a hands-on setup for teaching split-plot experimental designs.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows how a rubber-band toy that stores and releases energy can be turned into a classroom exercise for split-plot designs in design of experiments. An actual experiment is described, run, and analyzed so instructors have a concrete reference. The approach lets students directly observe the practical difference between whole-plot and subplot factors and their separate error structures.

Core claim

The boomerang tin experiment sets up whole-plot factors that are costly to reset and subplot factors that can be varied more easily, then analyzes the resulting data with the appropriate mixed model to illustrate the split-plot structure for teaching purposes.

What carries the argument

The rubber-band energy mechanism that separates hard-to-change whole-plot factors from easier-to-vary subplot factors.

If this is right

  • Instructors obtain a ready-to-use example that includes the physical setup, design matrix, and analysis code.
  • Students experience the cost of resetting whole plots in real time rather than only in abstract terms.
  • The same toy can be reused across multiple class sessions to compare different design choices.
  • Analysis results can be discussed immediately after data collection while the physical process is still fresh.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The method could extend to other toys or devices where some controls are physically harder to adjust than others.
  • Similar classroom props might help teach related topics such as blocking or repeated measures.
  • If the toy is inexpensive and portable, it lowers the barrier for statistics courses that lack access to industrial equipment.

Load-bearing premise

The toy produces measurable responses whose variance cleanly separates into whole-plot and subplot error terms without extra mechanical noise.

What would settle it

Re-running the described design and finding that a single-error-term model fits the data as well as the split-plot model, or that the two variance components cannot be distinguished.

Figures

Figures reproduced from arXiv: 1907.10684 by Maria Lanzerath, Thomas Muehlenstaedt.

Figure 1
Figure 1. Figure 1: Boomerang tin, disassembled (left) and assembled (right) [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Experimental setup of the starting ramp rolling the boomerang tin. [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: DoE table including results. For both models, the significance test of the overall model turns out to be highly significant, indicating that the models in fact do explain output variation [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Actual by predicted plots for both outputs [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Fixed effect tests for both outputs Y1 and Y2. We check the model assumptions (linearity, independence, normality, homoscedasticity) of the fitted linear model in order to decide if the model analysis is valid or if some other model is needed. This step should never be forgotten. A residual by predicted plot is used to check the latter two. If e.g. the model assumption of homoscedasticity is fulfilled, the… view at source ↗
Figure 6
Figure 6. Figure 6: Prediction profiler for both outputs Y 1 and Y2. of measurement variability and retrieve reliable results right from the beginning. We found it works well to give the students a set of steps to follow in the exercise and suggest a plan like the list below. The instructor can use the timing to help keep the small group teams on track and adjust the timing as needed. 1. Determine goals of experiment (5 minut… view at source ↗
Figure 7
Figure 7. Figure 7: Residual plots for both outputs Y1 and Y2. exercises for teaching DoE concepts, they do not lend themselves very well toward split–plot experiments. We believe the boomerang tin is a suitable alternative due to its potential to add hard–to–change factors. As a hands–on exercise quickly takes a significant length of time in class, a thorough prepa￾ration by the teacher dramatically helps manage time while p… view at source ↗
read the original abstract

This article presents an example on how to teach split-plot experimental designs based on a hands-on exercise. This is a toy called boomerang tin which utilizes a rubber band to store and release energy. The set up and mechanisms of the hands-on example are explained followed by a description of how it can be leveraged in teaching split plot DoE. An actual design is set up, analyzed and discussed to provide reference for its usage in class.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The manuscript presents a hands-on teaching example for split-plot experimental designs using a boomerang tin toy that stores and releases energy via a rubber band. It describes the toy's setup and mechanisms, explains its use in illustrating split-plot DoE, and provides details of an actual experimental design that was set up, run, and analyzed to serve as a classroom reference.

Significance. If the physical responses separate whole-plot and subplot error strata as intended, the example supplies a concrete, low-cost classroom activity that can help students distinguish error terms in split-plot structures; such tangible demonstrations are useful additions to statistics education literature when they are reproducible.

minor comments (2)
  1. The description of the actual design (factors, levels, response variable, and analysis output) is referenced but would benefit from explicit listing of the whole-plot and subplot factors and the model equation used, to facilitate direct replication by instructors.
  2. Figure captions and any tables summarizing the ANOVA or variance components should be checked for self-contained clarity so that readers can interpret the error-strata separation without returning to the main text.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive review and recommendation to accept the manuscript.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper is a purely descriptive teaching note that presents a hands-on classroom exercise with a boomerang tin to illustrate split-plot experimental design structure. It describes the physical setup, the actual design that was run, the analysis performed, and how the example can be used in class. No model derivation, quantitative prediction, uniqueness theorem, or fitted parameter is advanced; the central claim is simply that the exercise can be used for teaching. Because no derivation chain exists, no step reduces to its own inputs by construction, self-citation, or renaming.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities are introduced; the paper is a descriptive account of an educational activity.

pith-pipeline@v0.9.0 · 5587 in / 1028 out tokens · 19258 ms · 2026-05-24T16:30:26.348888+00:00 · methodology

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Reference graph

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