The chi square distribution is a probability density function used in statistics to determine the probability that numerical differences in data are significant and real (as opposed to just being due to random errors or chance). Chi is a Greek letter designated by x. In practice, the x² distribution is expressed as a family of curves or a table of critical x² values that correspond to a particular probability level. Tables of these "expected" or "theoretical" x² values are published in reference books. During a x² test, an "observed" x² value is calculated for the data in question and compared to the table values to determine the probability that the numerical event in question is statistically significant.

The chi square distribution is closely related to another commonly used probability density function, the normal distribution, which shows the distribution of many random variables. Normal or...