= Category membership
<Category membership> concerns whether an object or event is assigned to a specified category. It is distinct from its judged <typicality>, how confident a person is about the judgment and how quickly the judgment is made. A category can have a precise membership rule while its examples differ in familiarity.
For example, 3 and 97 are both <odd integers>: each has the form $2k+1$ for an <integer> $k$. A participant might nevertheless consider one a more typical example or identify it faster. Those responses concern the <categorization> process, rather than making one <integer> mathematically more odd than the other.
<Sharon Lee Armstrong> and collaborators compared <typicality> judgments and <category verification> for everyday categories and well-defined categories including odd and even numbers. Their experiments show why graded responses alone cannot establish that the underlying membership conditions are graded. Distinguishing membership, <typicality> and <reaction time> avoids drawing a stronger representational conclusion than the task supports.<What some concepts might not be by Sharon Lee Armstrong and others>[1983, abstract and Experiments I–III: well-defined categories, typicality and membership judgments]{ref}
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