The term factor is used to indicate a condition controlled by the investigator. Thus if a drug is given at four dose levels, then drug is a factor with four treatments or levels. If the experiment involves both males and females, then gender or sex is a second factor with two levels, female and male. The treatments/levels can be quantitative, such as the dose levels of the drug, or qualitative such as diets A, B and C.
Factors and treatments
Treatments are fixed effects
Blocks effects are random effects
Factorial arrangement of treatments
Choice of treatments
An athymic nude mouse
A factor such as diet may consist of several treatments such as levels of protein designated A, B, C etc. The effect of any diet (in this case) is considered to be a “fixed” effect in that diet A is imposed by the experimenter, it is repeatable and can be given to an animal at any time in the future and is (or is expected to be) different from diet B.
Some experimental designs involve splitting the experiment up into two or more “blocks” or mini-experiments. This may be done for convenience or to take account of some natural structure among the experimental units. Blocks may be designated 1, 2, 3 or A, B, C etc., but any block effect is a “random effect” because it is not possible to repeat a Block 2 at any time since “block” is not something imposed by the experimenter.
Some factors, such as sex and strain, involve a classification rather than a treatment because an animal can not be assigned to male of female at random. The animal is either male or female. An experiment to determine, say, sex differences in feeding behaviour in rats is a survey rather than an experiment (in the statistical sense, although legally it may be an “experiment”). In order to avoid bias and get a true estimate of strain or sex differences the animals should be matched for all other characteristics. However, the method of statistical analysis does not differ between experimental and classification variables.
If the experiment involves more than one factor in such a way that the animal can receive a combination of the treatments from two or more factors, then a “factorial” experiment has been designed.
For example, if animals were assigned either to a low or a high protein diet (diet is therefore a factor with two levels), and each is then given a drug or a placebo (drug is therefore a factor with two levels), then the experiment will be a 2 x 2 factorial design with four treatment combinations (low protein & drug : low protein & the placebo: high protein and drug: high protein & the placebo). If the experiment was done in both males and females, then it would be a 2x2x2 factorial design. These designs are considered in more detail under 12. Experimental designs.
Factorial designs have many advantages in that they provide extra information at little extra cost because adding an additional factor does not mean that the size of the experiment necessarily has to be increased.
It is generally best to avoid having a factor with very many levels, particularly if the aim is to compare each mean with every other mean as this involves a lot of tests. Usually two to four levels are sufficient. However, the number of treatment combinations in factorial designs may be quite high.
Where drugs or chemicals are being tested the greatest response will usually be found with the highest dose. Intermediate dose levels can be used to see if the response is linear, or as an insurance in case the high dose proves to be excessively high. It is sometimes helpful if doses can be equally spaced on some scale as the statistical analysis can then use the method of “orthogonal polynomials” to test for linearity of response (however, this is an advanced statistical technique which will normally require professional advice and is not discussed here).