# Contingency table (descriptive statistics)

Contingency tables let you visualize the relationship between two qualitative variables. Describe contingency tables in Excel using the XLSTAT software.

## What is a contingency table

A contingency table is an efficient way to summarize the relation (or correspondence) between two categorical variables V1 and V2. It has the following structure:

V1 V2 | Category 1 | Category j | … | Category m2 |

Category 1 | n(1,1) | n(1,j) | … | n(1,m2) |

… | … | … | … | … |

Category i | n(i,1) | n(i,j) | … | n(i,m2) |

… | … | … | … | … |

Category m1 | n(m1,1) | n(m1,j) | … | n(m1,m2) |

where n(i,j) is the frequency of observations that show both characteristic i for variable V1, and characteristic j for variable V2.

Descriptive statistics

In this tool, XLSTAT provides you with two criteria to characterize the relationship between the two variables:

- The Chi-square distance has been suggested to measure the distance between two categories. The Pearson chi-square statistic, which is the sum of the Chi-square distances, is used to test the independence between rows and columns.
- Inertia is a measure inspired from physics that is often used in Correspondence Analysis, a method that is used to analyse in depth contingency tables. The inertia of a set of points is the weighted mean of the squared distances to the center of gravity.

Many more indexes and tests are available in the "Correlation and association tests" feature to characterize the relationship between two categorical variables.

The following descriptive statistics are available within this tool:

- Inertia by cell.
- Chi-square by cell
- Significance by cell
- Observed frequencies
- Theoretical frequencies
- Proportions / row
- Proportions / column
- Proportions / total