B.pharmacy 8th semester
Biostatistics BP801T according to AKTU AND PCI SYALLABUS.
Today topic is blocking and confounding
Blocking
Technique has been utilized to handle 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.
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.
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).
23 blocking
Let’s expand the 22 basic factorial design to a 23 design for three variables in Table 3. Eight experimental units will be required to complete a full replication of the 23 design. However, if only four samples or experimental units can be produced from one batch, there are not enough samples or experimental units to complete the full replication of the 23 factorial design. Therefore, two batches/blocks are required to complete the full replication of the 23 factorial design. Therefore, one (2-1 = 1) degrees of freedom is lost due to the two blocks. One effect won’t be possible to estimate from this experiment. Generally, higher-order interaction terms are practically meaningless. Therefore, the higher-order interactions are sacrificed when there are not enough experimental units are available.
For an example, in a 23-factorial design of experiment, the three-way interaction (ABC interaction) is sacrificed by confounding with the block, meaning that it won’t be possible to distinguish the effect of ABC interaction from the block effect. To make the ABC interaction indistinguishable from the block, all the “positive terms” and the “negative terms” in the contrast of ABC is run in separate blocks. The indistinguishable effects are known as confounded effects. Of course, the run orders are selected randomly within the block, rather than the standard order, as in any other experimental designs. The entire systematic process of making some effects indistinguishable by blocking is known as confounding.
Unconfounding
The method using either -1/+1 or 0/1 coding systems described above can be generalized for the 2k design in 2p blocks (p= number of independent confounded effects). Table 16 shows the number of factors, number of blocks, the number of samples can be taken from a block, the block generator, and the confounded interactions with the blocks. A few guidelines to choose the effects to generate the blocks are provided below.
As there is less interest in the higher-order interaction terms, they should be the potential candidates for the confounding effects to reduce the primary information loss. The goal is to keep as many lower-order interactions as possible unconfounded.