1.1 Introduction

Experiments are carried out by investigators in all fields of study either to discover something about a particular process or to compare the effects of several factors on some phenomena.
An important distinction in the model assumptions and associated analysis arises over whether the conclusions from the statistical analysis are to apply to a fixed number of populations in the experiments whether they are to apply to a wider class of populations of which those involved in the experiments are just representatives.

First part the populations are fixed where as the second they are considered randoms. For the first part we use a fixed effect model and the second part we use a random effect model.

Fixed effects model

If we consider an experiment comparing the effects of three drugs, each is a new compound developed in the laboratory. Information is desired on the comparative effects of these drugs. Other situations usually considered as fixed effects are treatment regiments, types of disease, different methods doing something.

Random effects

Consider for instance a large company which employs a large number of personal officers who interviews applicants for jobs in the firms. At the end of an interviews, the personal officers assign a rating between 0 and 10 individually. Indicating the applicants potential value for the job.

Suppose that five personal officers where selected at random and each was assigned ten candidates at random to do the rating.

\(X_{ij}=\) rating of the i\(^{\text {th}}\) candidate by the j\(^{\text {th}}\) officers.

In this case the company would not wish to make inferences concerning the five personnel officers who happened to be selected out rather about all the personnel officers.

If a smaller company has only five personnel officers who are included in the study and interest is limited to five the model used is fixed effect.

It important to point out that we do have fixed or random factors in the world, but rather different structural models we impose on the world when we design the experiment. Thus, the variable becomes fixed or random only in the context of actual experiment.

Randomisation

Analysis of variance model usually result from planned experiments. Often variability among experimental units may mask an obscure the treatment effects of interest.
This nuisance factor (variability) of experimental unit difference can be minimised by randomisation. Randomisation is the corner stone underlying the use of statistical methods in experimental design. By randomisation we mean that both the allocation of experimental units and the other in which the individual runs or trials of the experiment are to be performed randomly determined.

Blocking

This is a technique used to increase the precision of an experiment. A blocking is a group of experimental units which are more homogeneous than the entire set of experimental units.