Application of Analysis of Means (ANOM) to Nested Designs for Improving the Visualization and Understanding of the Sources of Variation of Chemical and Pharmaceutical Processes

Analysis of means approach in advanced designs

“…Researchers commonly use hierarchically nested and split‐plot designs when there are multiple factors of interest and the experimental units are subsampled. Specifically, these designs have important applications in many disciplines, for example, Parra and Rodriguez‐Loaiza 1 reported an experiment that studied the validation efforts of a bulk pharmaceutical plant in order to identify and to minimize the overall variability of a synthetic process of a drug substance. It was believed that the quality of the product is related to the quality of the starting material; therefore, the study focused on the variability in assay values of starting materials.…”

“…Then, four containers were selected from each lot randomly, and three assay determinations were made on each container. The data obtained from the experiment presented in Parra and Rodriguez‐Loaiza 1 can be analyzed by using analysis of variance (ANOVA) based on the three‐stage hierarchically nested design. However, it is often too technical for nonstatisticians 2,3 .…”

“…ANOM is an appealing data visualization tool, which requires only basic knowledge in statistics to interpret its results. As Parra and Rodriguez‐Loaiza 1 indicated, the results of nested designs, traditionally presented in ANOVA tables, are not always helpful in communicating with operators, technicians, and managers, who may lack the sufficient statistical training. With the exponential growth of the data science community and the fundamentally interdisciplinary nature of statistics, ANOM has a great potential to play a vital role due to its appealing visual display and ease of interpretability.…”

“…Since ANOM methodologies adequate for analyzing data from hierarchically nested and split‐plot designs have not been developed, in this article, we aim to develop ANOM procedures that analyze data from experiments with nested designs (such as the aforementioned pharmaceutical study in Parra and Rodriguez‐Loaiza 1 ). The presence of random factors is a key challenging aspect in our discussion and we carefully incorporate both random and fixed factors in the suggested ANOM procedure.…”

“…For this reason, the ANOM procedure is barely implemented in nested and hierarchical designs, where random factors play a vital role. As Parra and Rodriguez‐Loaiza 1 explained, researchers frequently encounter random factor effects in nested designs. In those situations, it is appropriate for researchers to apply ANOVA; however, the presence of any random effects may not be suitable for ANOM.…”