What is Blocking in a 2k Factorial Design
The blocking and confounding techniques in 2k factorial design of experiment is described in Video 1.
In an ideal situation, a completely randomized full factorial with multiple numerous replications would make a lot of statistical theoretical sense, including reducing the confidence interval, the higher power of the findings, and so on. In fact, completely randomized design has been considered the most efficient over the years. However, when some obvious known nuisance factors/variables are present to introduce variation in the responses, blocking technique has been utilized to handle this kind of situations better for the Randomized Complete Block Design in the earlier Module. As the 2k design is primarily used to screen factors/variables, often a very large number of experimental units are required to complete even one full replication. For an example, 26 design with six variables requires 64 experimental units to complete one full replication. In the 2k design of experiment, blocking technique is used when enough homogenous experimental units are not available.
Ideally, experiments should be run by using completely randomized experimental units. However, often, there is not enough experimental units from one homogenous sample. For example, if there are not enough raw materials to produce all the experimental units for all replications, blocking is utilized to control the nuisance effects of the experimental units coming from, possibly non homogenous batches. Different batches do not necessarily mean non-homogeneity all the time. However, keeping track of the batch numbers as blocks (the statistical term) would provide an opportunity, if in case there is non-homogeneity from batch to batch. Therefore, a block is defined by a homogenous large unit, including, raw materials, areas, places, plants, animals, humans, etc. where samples or experimental units drawn are considered identical twins, but independent.
Let’s start with the basic 22 factorial design to introduce the effective use of blocking into the 2k design (Table 1). Let’s assume that we need at least three replications for this particular experiment. If one batch can produce enough raw materials for only four samples (experimental units), only one replication can be made from one batch. Therefore, three batches will be required to complete the three full replications for the 22 basic factorial design (Table 2).
Table 1. The Basic 22 Factorial Design of Experiments
Table 2. The Basic 22 Factorial Design of Experiments with three replications in blocks