Cell chi-square test
The cell chi-square test looks at each table cell and tests whether it is significantly different from its expected value in the overall table. For example, if it is thought that variations in political opinions might depend on the respondent's age, this test can be used to detect which cells contribute significantly to that dependence.
Unlike the chi-square test, which is carried out on a whole set of rows and columns, the cell chi-square test is carried out independently on each table cell. This is done by treating each cell as belonging to a two-by-two table, known as a contingency table, as follows:
|
|
Base
|
In column
|
Not in column
|
|
Base
|
B
|
C
|
B-C
|
|
In row
|
R
|
V
|
R-V
|
|
Not in row
|
B-R
|
C-V
|
B-R-C+V
|
For each cell, the values B, C, R and V are taken from the table. The other values are calculated from these values.
The formula applied to this two-by-two table is the standard Pearson chi-square formula, with the Yates' correction for small samples when relevant as the p value associated with the Pearson chi-square test can be distorted if any cells in the table have very low expected counts (below 5).
Note Although the significance level of the cell chi-square test is accurate for any given cell, the cell tests cannot be used instead of the chi-square test carried out on the overall table. Their purpose is simply to point to the parts of the table where dependencies between row and column categories may exist.
See also