Other Confounding Possibilities

Sometimes in a factorial experiment we have a double restriction imposed on the system. For example, in a 2 experiment (5 factors all at 2 levels, requiring a total of 32 runs) we may have 4 reactors which may be different. Accordingly we conform d in 4 blocks of 8, there being 8 runs on each of the 4 reactors. However, our batches of raw material may not be large enough to carry out the whole experiment. We then need to confoimd the experiment in an additional way. The problem is soluble if we make it the inverse of the first type of confounding. Thus, if the first confounding is in 4 blocks of 8 then the second must be in 8 blocks of 4. There is the further restriction that no interaction confounded in the second set must occur in the first set, and vice versa. 

To allocate the treatments, we can first set out them in the usual manner for confounding in 8 blocks of 4, as in Table 14.8. 

Batch 1 Batch 2 Batch 3 Batch 4 Batch 5 Batch 6 Batch 7 Batch 8 

We now superimpose Tables 14.8 and 14.9 on top of each other. Treatment (1) belongs to Batch 1 and Reactor 1, and is entered in Table 14.10 accordingly. Treatment pqrs belongs to Batch 1 and Reactor 2, and is entesed thus. Treatment rst belongs to Batch 1 and Reactor 4, and so on. 

Tt will be noted that, if we were confounding in 8 blocks of 4, the imposition of the second restriction leads to no increase in the number of first order interactions being lost. 

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No studies have demonstrated that selenium or its compounds are teratogenic in humans. Robertson (1970) reported on the outcome of pregnancies in a laboratory in which workers handled sodium selenite. Of the five pregnancies, four ended in spontaneous abortion and one resulted in an infant with bilateral clubfoot. The urinary selenium levels in all subjects were similar to those in other individuals living in the same area. The limited number of cases, possible exposure to other toxic agents, and other confounding factors leave the relationship between sodium selenite and developmental effects inconclusive. 

These studies have mostly been too short to be conclusive. The current data are difficult to interpret, because the risks of cancer are complex and include increasing age and obesity, which are common features of type 2 diabetes, along with many other confounding factors. The possibility that insulin is associated with a risk of cancer requires longer exposure data to be collected to provide useful information. 

These three studies indicate that exposure to low levels of lead may impact negatively upon children s hearing. However, the authors of the Robinson study did not state whether age and other possible confounding variables were controlled for. Similarly, in the NHANES study, age may have been a confounding variable. 

The information available regarding the association of occupational exposure to lead with increased cancer risk is generally limited in its usefulness because the actual compound(s) of lead, the route(s) of exposure, and level(s) of lead to which the workers were exposed were often not reported. Furthermore, potential for exposure to other chemicals including arsenic, cadmium, and antimony occurred, particularly in lead smelters, and smoking was a possible confounder (Cooper 1976 IARC 1987). These studies, therefore, are not sufficient to determine the carcinogenicity of lead in humans, and the following discussion is restricted to the most comprehensive of these studies. 

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