Alternative Split-plot Models

Objective

As can be seen from Figure 2 of Split-plot Tools, the Split-plot data analysis tool supports two other RCBD models (RCB 1 and RCB 2) and a CRD model. We now describe these three models.

RCB 1 and 2 models

The RCB 1 model is the same as the RCB model, except that Whole plot × Subplot is used as the error term for the Subplot factor, and so the formula in cell W8 is =V8/V9 (instead of =V8/V10).

The analysis for the RCB 2 model of Example 1 of Split-plot Tools is shown in Figure 1.

Figure 1 – RCB 2 Split-plot Model

In this model, the Block × Split term is separated out from the Split-plot Error term. Cell W8 contains the formula =V8/V9 and W10 contains the formula =V10/V11. This is the model used in Montgomery (2001).

CRD model

The final model is the Complete Randomized Design (CRD) Split-plot model as described in Split-plot Design. For Example 1 of Split-plot Tools, the analysis is as shown in Figure 2.

Figure 2 – CRD Split-plot Model

Cell W5 contains the formula =V5/V6, cell W6 contains the formula =V6/V9, cell W7 contains the formula =V7/V9 and cell W8 contains the formula =V8/V9.

Links

↑ Split-plot design

Examples Workbook

Click here to download the Excel workbook with the examples described on this webpage.

References

Montgomery, D. C. (2012) Design and analysis of experiments. 8th ed. Wiley
https://faculty.ksu.edu.sa/sites/default/files/douglas_c._montgomery-design_and_analysis_of_experiments-wiley_2012_edition_8.pdf

Zhang, H. (2022) Split plot design
https://www.stat.purdue.edu/~zhanghao/STAT514/Lecture_Notes/LectureNotes20-Split-plot-Designs-.html#:~:text=A%20split%2Dplot%20design%20is,randomly%20assigned%20to%20split%2Dplots.

Hale, I. (2025) Split plot design
https://www.unh.edu/halelab/ANFS933/Readings/Topic12_Reading1.pdf