Model Building in Statistics

One of the core processes in statistical analysis is ‘Model Building’. We often collect data and use this data to make a model. For example, the simplest model that we build is the ‘average’. The model is then used to assess each case (i.e. new case or existing). I will explain this with an example. Suppose that we have the data on age of 10 students. Lets say the ages of the students, admitted to a Master of Psychology programme at a university are as under: 24, 32, 26, 29, 22, 18, 25, 27, 36, 23.

The ‘mean’ of ‘average’ of these values is 26.2 years. So now this average value becomes our model. We will use this model to represent the age of students entering a Master of Psychology programme at the university. So given that our model ‘age’ is 26.2 years, if we come across a new student whose age is, lets say, 60 years, we immediately know that the age of this new person is much more than the average age of students entering the Master of Psychology programme. As an another example, suppose that your car on an average runs 12 kilometres per litre of petrol. Your model then ’12 kilometres’. If you find that on a particular fill of 10 litres of petrol, your car only ran 80 kilometres, suggesting an average of 8 kilometres, obviously you will get concerned about servicing the car. In summary, in statistics we make models based on the data that we have. Model building is amongst the initial steps of statistical analysis.

Note that the model can be of any type, for example, it can be mean, median or mode. Or it can be an equation, such as of a straight line or a curve. Once we have made the model, we try to see how this model fits to our existing data. In the above example of ‘age’ of students, we apply the the model 26.2 years to each case and see how far is each case from the model. For example, the first case has an age of 24 years. So this case is 2.2 years far from the model (26.2 – 24). In cases where these differences are very high, we know that our model does not fits the actual data well, and so we probe the cases where the differences between model and actual data is too large.