A Simple Step-by-Step Guide to the Design and Analysis of Unreplicated Split-Plot Experiments Through a Case Study on Molybdenum Recycling from CIGS Solar Cells

Journal article, 2025

Considerable effort has been put over the last few decades into clarifying the correct design and analysis of split-plot factorial experiments. However, the information found in the literature is scattered and sometimes still not easy to grasp for non-experts. Because of the importance of split-plots for the industry and the fact that any experimenter may need to use them at some point, a detailed and step-by-step guide collecting all the available information on the fundamental methodology in one place was deemed necessary. More specifically, this paper discusses the simple case of an unreplicated split-plot factorial experiment with more than one whole-plot (WP) factors and all factors set at two levels each. Explanations on how to properly design the experiment, analyze the data, and assess the proposed model are provided. Special attention is given to clarifications on the calculations of contrasts, effects, sum of squares (SS), parameters, WP and sub-plot (SP) residuals, as well as the proper division of the proposed model into its sub-designs and sub-models for calculating measures of adequacy correctly. The application of the discussed theory is showcased by a case study on the recycling of molybdenum (Mo) from CIGS solar cells. Factors expected to affect Mo recovery were investigated and the analysis showed that all of them are significant, while the way they affect the response variable was also revealed. After reading this guide, the reader is expected to acquire a good understanding of how to work with split-plots smoothly and handle with confidence more complex split-plot types.