Assumptions and approximations

This is a section from my text book An Introduction to Medical Statistics, Fourth Edition. I hope that the topic will be useful in its own right, as well as giving a flavour of the book. Section references are to the book. 

1.4 Assumptions and approximations

Many statistical calculations give answers which are approximate rather than exact. For example, if we carry out a clinical trial and obtain a difference in outcome between two treatment groups, this applies only to the people in the trial. It is people not in the trial, those who are yet to come and to be eligible for the trial treatments, for whom we want to know the difference. Our trial can only give an approximate estimate of what that might be. As we shall see, statistical methods enable us to get an idea of how precise our estimate could be, but this, too, is only approximate. It depends on some assumptions about how the data behave. We have to assume that our data fit some kind of idealized mathematical model. The great statistician George Box said that ‘essentially, all models are wrong, but some are useful’. We might add that, in medical statistics, all answers are approximate, but some approximations are useful. The important thing will be to have an idea of how good our approximations are. We shall spend quite a lot of time investigating the assumptions underlying our statistical methods, to see how plausible they are for our data.

Adapted from pages 2–3 of An Introduction to Medical Statistics by Martin Bland, 2015, reproduced by permission of Oxford University Press.

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