## The Model, What and Why

We are attempting to 'model' what really happened with an experiment; so that we can predict what is 'likely' to happen if we repeat our experiment, study, research, etc.

As an aside; it is this 'likely' that forms the basis of Fisher's concept of Maximum Likelihood. That is, find those parameter estimates which Maximise the Likelihood of obtaining the actual data we got in our study.

There are 2 aspects to the 'model'

1. The biological model.
You, as the researcher, have to think whether the biological (experimental) model you are proposing is adequate and realistic. Does it include all the things, or factors, that affect an observation? For example, if we were studying growth rate of piglets from birth to weaning we know that maternal effects are very important biological effects (particularly so early in life) and so they MUST be considered in our model; this is from a biological (research) standpoint.

Write down and note these factors that you consider important. Note them and record what they are for all, each, and every observation. For example, following our previous example of piglets, if we know that maternal effects are important, then we should record for each piglet the date of birth, the sex of the piglet and the dam (sow) identity or registration number (and not just sow 1, 2, etc), and perhaps the age or parity of the dam as often that has an effect.

If we were conducting a nutrition experiment with humans, looking at their diet, we might have two groups, one eating diet A and the other eating diet B. Our experimental treatment (or diet) has 2 levels (A and B). But there may be/probably are other things that might affect the response to the diet. These might include the sex of the person (female or male), the age of the person, the amount of exercise that they do, etc. One should try and record all these things.

Basically, for either of the above 2 cases one must think of and record all the things that one knows about the experimental conditions. One must record everything that is not exactly the same for each and every animal or person (experimental unit) so that these factors can be included in the biological and statistical model. You cannot just say "I'm not interested in that so I'll ignore it and therefore it is random".

Identification and recording are the essence of research studies which allow us to summarize the raw data into useful statistics, so that we can make useful predictions.

2. The statistical model.
Having considered the biological (experimental) model one has to (You have to) translate this into a statistical model and then a statistical method of analysis.

For example, is it a regression factor? Should there be linear and quadratic regressions? Should one use a Maximum Likelihood method of estimation, or a Least-Squares method? Are the variances homogeneous? Are the data Normally distributed? Do we have a nested model, or a factorial model; do we have repeated measurements (and if so what is the covariance structure of them)?