From experimental design to images to particle size histograms to multiway analysis. An example of peat dewatering

The efficiency of peat dewatering by filtering slurries is dependent on the sizes of fine and colloidal particles that clog the filter. A designed experiment was carried out to check the use of different treatments on particle coagulation. The resulting particle sizes were studied under the microscope by automated digital image analysis, leading to area histograms for 21 size classes. Seven treatments on five peat types give a two‐way ANOVA in all‐qualitative variables, but the 21 response variables are a bit too much for an ANOVA or MANOVA analysis. The data can also be arranged in a 5 (peat types) × 7 (treatments) × 21 (size classes) three‐way array. This array is analyzed by PARAFAC and gives an effective three‐way rank of 4. The three‐way data have no obvious underlying trilinear structure, and curve resolution results are not expected. The three‐way analysis gives a very parsimonious model that is easily interpreted as a function of the problem definition. The emphasis is on visualization of the results. Copyright © 2000 John Wiley & Sons, Ltd.