The chi-square statistic (or -statistic) measures agreement between the observed and hypothetical frequencies. This statistic is computed from two entities: hypothetical probabilities of the values of a discrete random variable , and the observed frequencies of these values - the numbers of observations of each type. The chi-square statistic is the heart of the chi-square test .

The chi-square statistic is computed according to the following formula:

where

is the number of observed events of the th type;

is the hypothetical probability of the event of the th type.

Sampling distribution of this statistic approaches the chi-square distribution with degrees of freedom when the number of observations grows infinitely. This explains the name of the statistic.

There are other statistics that obey the chi-square distribution and, therefore, might be called "chi-square statistics" too. But the statistic described here is the most famous one - it is discussed even in introductory texts in statistics and widely used in practice.

This course will teach you the principal statistical concepts used in medical and health sciences. Basic concepts common to all statistical analysis are reviewed, and those concepts with specific importance in medicine and health are covered in detail.

This course will teach you the analysis of contingency table data. Topics include tests for independence, comparing proportions as well as chi-square, exact methods, and treatment of ordered data. Both 2-way and 3-way tables are covered.