Positive and Negative Classes
The classes, , are called positive classes because they contain all positive attributes. The classes are called negative classes because they have negative attributes. The classes and contain both positive and negative attributes, so they are called mixed or contrary classes.
If we have three attributes with their opponents or complements as and , then we can write the different class frequencies as in the table below:










Total



















Total




In this table the positive classes are and whereas the negative classes are. All other classes are mixed.
Order of Classes
The order of the class depends upon the number of attributes going into that class. If a certain class can give us information about only one attribute, it is called a class of order one.
The classes and are the classes of order one and the frequencies, and are the frequencies of order one. The classes , and are the classes of order two and the frequencies and are the frequencies of order two. The classes ,, and are the classes of order three and , ... are the frequencies of order three. The sample size n does not contain any attributes and is therefore called the frequency of order zero.