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22 QUALITATIVE DATA ANALYSIS<br />

Figure 2.3 Categorizing using inclusive categories<br />

varies in kind or amount. This type of variable is often called a ‘nominal’ variable<br />

because its values (or categories) are ‘names’ rather than numbers.<br />

With nominal variables, the values we use must be mutually exclusive and<br />

exhaustive. ‘Mutually exclusive’ means no bit of <strong>data</strong> fits into more than one<br />

category. For example, suppose we classified a box of apples according to colour,<br />

and assumed that the apples are either red or green. ‘Colour’ is then our variable,<br />

with two values ‘red’ and ‘green’. What if we encounter some apples which are red<br />

and green? Our values are no longer mutually exclusive. ‘Exhaustive’ means you can<br />

assign all your <strong>data</strong> to one category or another; there’s nothing that won’t fit<br />

somewhere into a given set of categories. Suppose we encounter some yellow apples<br />

lurking at the bottom of the box. Our categories no longer exhaust all possible values<br />

for the variable ‘colour’. To make our values exhaustive and mutually exclusive, we<br />

would have to add new categories for the yellow and red/green apples.<br />

Classifying in this way adds to our information about the <strong>data</strong>. For any bit of<br />

<strong>data</strong> which we assign one value, we can infer that we cannot assign the same bit of<br />

<strong>data</strong> to other values of the same variable. Our categories have become exclusive. For<br />

example, suppose our categories refer to ‘primary’ and ‘secondary’ schools. ‘Schools’<br />

becomes our variable and ‘primary’ and ‘secondary’ its mutually exclusive values.<br />

The observations can no longer be assigned to either category (Figure 2.4). If we<br />

encountered another bit of <strong>data</strong> which fits our variable but not our values, such as a<br />

‘middle’ school, then we would have to modify our classification to keep it exclusive<br />

and exhaustive.<br />

At this level of measurement, we have adopted a more rigorous measure of both<br />

the qualitative and quantitative aspects of our <strong>data</strong>. At a conceptual level, our<br />

criteria for categorizing (or counting) a school as either primary or secondary have to<br />

be clear: they cannot be fuzzy and overlapping. As these categories are both values of<br />

the variable ‘schools’, we are also clear about what they have in common. In terms<br />

of counting numbers, if we add our observation to one category, we automatically

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