As we highlighted in CHAPTER 2, the study of variation is at the heart of statistics. In almost all fields of mathematics, variation means non‐random (i.e. systematic) variation. Statisticians, however, take account not only of non‐random variation, but also of random (i.e. chance) variation in the real‐world data they work with. This contrast, indeed, distinguishes statistics from mathematics. What’s more, the two types of variation that statisticians deal with are almost always present simultaneously. Sometimes, it is the influence of the random variation which is dominant in a particular data set – as, for example, in day‐to‐day movements in the price of a particular share on the stock exchange. Sometimes, it is the other way round – as, for example, in the monthly value of sales of ice cream in a particular city, where the regular seasonal pattern city‐wide dominates random local variation.

It is useful, for what follows, to think of the patternless chance variation as being overlaid, like a veil, on some underlying pattern of systematic variation. A prime goal of statistical analysis is to get behind this veil of random variation in the data, so as to have a clearer picture of the underlying pattern (i.e. the *form*) of systematic variation in the variable or variables of direct interest. This goal is pursued with reference not just to the data at hand, but also (by using appropriate techniques of statistical ...

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