Chi-Square

Chi-square is a statistical test to check if the frequency values obtained by a survey and recorded in some cross-table, are significantly different from the theoretical ones (the "expected" values).

Generally, T-LAB applies this test to (2 x 2) tables and the threshold value is 3.84 (df = 1; p. 0.05) or 6.64 (df = 1; p. 0.01).

For example, in order to verify the significance of a word ("x") occurrences within a context unit ("A") the test is applied to a table as follows:

The chi-square formula, in its simplified version, is the following:

where "O" and "E" stand respectively for the observed frequencies and the expected ones.

For each cell, the expected (E) occurrences are calculated as follows: (Ni x Nj)/Nij.

Following the above example the CHI value is equal to 19.38.

Since it is greater than the critical value, the null hypothesis (absence of meaningful difference) can be rejected.