The Design and Analysis of Flotation Experiments

The fundamental principles and modern techniques of experimental planning and data analysis, applicable to any type of research, are particularly important in flotation experimentation. Since they constitute the modern science of experimentation, they should be among the working tools of any scientist, research engineer, or plant operator engaged in flotation investigates. This chapter is a review of these principles and techniques. Equipment and procedures for the actual conduct of experiments will not be discussed here since these subjects are well covered elsewhere in this volume. Neither will any attempt be made to impart a working knowledge of statistical methods of data analysis since this would be impossible in the space allotted, and many excellent texts are available to the diligent inestigator.1-4 The objective here is simply to interest the reader in the application of statistical techniques to flotation experimentation by illustrating their utility in situations frequently encountered, and to point out the principles of experimental planning necessary for their proper use. Any conscientious metallurgist engaged in flotation experimentation or operations is well aware of the inherent complexity of the flotation process, and of the often frustrating difficulties this introduces into experimentation. The raw materials normally treated by the process are complex both physi- cally and chemically, and often highly variable even when from the same source. The flotation process itself is characterized by a very large number of potentially important process variables. Many of these are beyond the con- trol of the metallurgist, and some cannot even be measured quantitatively with available instruments. Those which can be measured and controlled with reasonable precision often produce effects which are intricately interrelated. Not only are the variables many, but the physical and chemical mechanisms by which they function are imperfectly under stood. To compound the difficulty, experimental techniques are relatively crude. Controls are not very precise, and the human factor looms large in most flotation experiments. These situations lead inevitably to experimental data of a relatively low degree of precision or reproducibility. Some are inclined to think that these conditions are unique to flotation experimentation. They are not. The experimental problems met by the agronomist, the biologist, the social scientist, and others are equally complex. Investigators in these fields pioneered in the development of methods for handling just such situations by proper experimental planning and the application of statistical methods in the analysis of data. Their pioneering work has grown into a well established modern science of experimentation which has spread into every field of science. This science is based upon statistical