Characterized

Terms and Notation

Before we can turn to statistical procedures, we have to introduce some terms and notions, together with some basic notation, with which we can refer to data.

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object, case

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Data describe objects, cases, people etc. For example, medical data usually de- scribes patients, stockkeeping data usually describes components, devices or gen- erally products, etc. The objects or cases are sometimes called the statistical units. (random) sample
The set of objects or cases that are described by a data set is called a sample, its size (number of elements) is called the sample size. If the objects or cases are the outcomes of a random experiment (for example, drawing the numbers in a lottery), we call the sample a random sample.

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attribute, feature

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The objects or cases of the sample are characterized by attributes or features that refer to different properties of these objects or cases. Patients, for example, may be described by the attributes sex, age, weight, blood group, etc., component parts may have features like their physical dimensions or electrical parameters. attribute value
The attributes, by which the objects/cases are described, can take different values. For example, the sex of a patient can be male or female, its age can be a positive integer number, etc. The set of values an attribute can take is called its domain.
Depending on the kind of the attribute values, one distinguishes different scale types (also called attribute types). This distinction is important, because certain charac- teristic measures (which we study in Sect. A.2.3) can be computed only for certain scale types. Furthermore, certain statistical procedures presuppose attributes of spe- cific scale types. Table A.1 shows the most important scale types nominal, ordinal, and metric (or numerical), together with the core operations that are possible on them and a few examples of attributes having the scale type.