Two Attributes

The tall and short persons may further be divided into intelligent and non- intelligent persons. Intelligence may be denoted by B and \beta may be used for non intelligence. The following table shows different attributes and their combinations. When two attributes are involved, the division of the sample as below is called two- way classification.

Two-Way Classification
\left( {AB} \right)
\left( {\alpha B} \right)
\left( B \right)
\left( {A\beta } \right)
\left( {\alpha \beta } \right)
\left( \beta \right)
\left( A \right)
\left( \alpha \right)

The column totals are denoted by \left( A \right) and \left( \alpha \right) and the row totals are denoted by \left( B \right) and\left( \beta \right). The above table contains 2 rows and 2 columns and is therefore called 2 x 2 contingency table or 2 x 2 cross-tabulation briefly written as 2 x 2 cross-tables.

There may be more than two attributes. The symbols A,B,C are used for the attributes and \alpha ,\beta ,\gamma are used for the absence of the attributes A,B,C. Thus a means not A and \beta means not \beta and \gamma means not C.

Suppose that out of 60 tall persons, 30 are intelligent and out of 40 short persons, 20 are intelligent. We can write these frequencies in the following 2 x 2 contingency in the given table.

2 x 2 Contingency Table
\left( {AB} \right) = 30
\left( {\alpha B} \right) = 20
\left( B \right) = 50
\left( {A\beta } \right) = 30
\left( {\alpha \beta } \right) = 20
\left( \beta \right) = 50
\left( A \right) = 60
\left( \alpha \right) = 40
n = 100

From table above we can write some relation immediately.

(1) \left( A \right) + \left( \alpha \right) = n

(2) \left( B \right) + \left( \beta \right) = n

(3) \left( A \right) = \left( {AB} \right) + \left( {A\beta } \right)

(4) \left( \alpha \right) = \left( {\alpha B} \right) + \left( {\alpha \beta } \right)

(5) \left( B \right) = \left( {AB} \right) + \left( {\alpha B} \right)

(6) \left( \beta \right) = \left( {A\beta } \right) + \left( {\alpha \beta } \right)