Definition:Contingency Table
Definition
A contingency table is an array of $r$ rows and $c$ columns in which:
- each row and each column is associated with a specific attribute
- the number $n_{i j}$ in row $i$ and column $j$ is a count of the number of units having that combination of attributes.
It is then commonplace to perform a chi-squared test to investigate how the data may differ between categories.
Row and column categories may be either nominal or ordinal.
Cell
The element in row $i$ and column $j$ of a contingency table is referred to as cell $\tuple {i, j}$ of that contingency table.
Marginal Total
The marginal totals of a contingency table are the totals of each of the rows and columns of that contingency table.
Examples
Arbitrary Example
The following is an example of a contingency table:
$\quad \begin{array}{r|ccc|c}
& \text {Superior} & \text {Average} & \text {Poor} & \text {Factory totals} \\
\hline
\text {Factory A} & 12 & 20 & 8 & 40 \\
\text {Factory B} & 14 & 39 & 7 & 60 \\
\hline
\text {Category totals} & 26 & 59 & 15
\end{array}$
Also see
- Results about contingency tables can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): contingency table
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): contingency table