DOE - confounding

Question 1

Define confounding in a factorial experiement

Answer 1

When the number of factors or number of levels increase, the number of treatment combinations increase very rapidly. It is not possible to accommodate all these treatment combinations in a single homogeneous block.

For example, a 2^5 factorial experiemnt would have 32 treatments combinations and the blocks of 32 plots are quite big to ensure homogenity within them.

A new technique is therefore necessary for designing experiemnts within a large number of treatments. One such device is to take blocks of size less than the number of treatments and have more than one block per replication, so that the treatment combinations are then divided into as many groups as the number of blocks, per replication.

The different group of treatments are allocated to the blocks.

Evidently the interction confounded has been lost, but the other interactions and main effects can now be estimated with better precision because of reduced block size.

This device of reducing the block size by taking one or more interaction contrasts identical with block contract is called as confounding.

Question 2

In what context is confounding preferred in factorial experiments?

Answer 2

Preferably only higher order interactions are confounded, that is interaction with 3 or more factors are confounded because their loss is immaterial. As an experiementer is generally interested in the main effects and two factor interactions as far as possible.

Question 3

Advgs and disadvgs of confounding in a factorial design

Answer 3

• The block size is reduced so homogenity is increased, in turn increasing the efficiency.
• Since the number of experiemntal runs is reduced, confounding can help lower the cost and time associated with experimentation, since it is simpler to do it.
• Biased estimates of main effects and interactions
• loss of info about certain effects
• all this leads to misinterpretation of results

Question 4

Balance confounding

Answer 4

Balance confounding occurs when one effect (e.g., an interaction) is confounded with another effect, but the confounding is balanced across all treatment combinations, ensuring that each effect is estimated independently.

Question 5

Complete Confounding

Answer 5

if the same interaction is confounded in all other replications then the interaction is said to be complete confounding

Question 6

Partial confounding

Answer 6

When an interaction is confounded in one replicate and not in another, the experiment is said to be partially confounded.

Question 7

general rule for confounding in 2^n series

Answer 7

involves
1. choosing effects to confound
2. determining the defining contrast
3. and assigning treatment combinations to blocks based on signs of the chosen effects in the defining contrast

Question 8

rule to find which effects have been confounded

Answer 8

odd common positive and the even common positive, the no common positive rule