Multiway Tables with Control Variables
When only two variables are crosstabulated, we call the resulting table a two-way table. However, the general idea of crosstabulating values of variables can be generalized to more than just two variables. A third variable could be added to the data set. This variable might contain information about the state in which the study was conducted (either Nebraska or New York).
| Gender | Soda | State | |
|---|---|---|---|
| case 1 | Male | A | Nebraska |
| case 2 | Female | B | New York |
| case 3 | Female | B | Nebraska |
| case 4 | Female | A | Nebraska |
| case 5 | Male | B | New York |
| ... | ... | ... | ... |
The crosstabulation of these variables would result in a 3-way table:
| State: New York | State: Nebraska | |||||
|---|---|---|---|---|---|---|
| Soda: A | Soda: B | Soda: A | Soda: B | |||
| G: Male | 20 | 30 | 50 | 5 | 45 | 50 |
| G: Female | 30 | 20 | 50 | 45 | 5 | 50 |
| 50 | 50 | 100 | 50 | 50 | 100 | |
Theoretically, an unlimited number of variables can be crosstabulated in a single multi-way table. However, research practice shows that it is usually difficult to examine and "understand" tables that involve more than 4 variables. (Even though the Crosstabulation option will produce tables of much greater complexity, it is recommended to analyze relationships between the factors in such tables using modeling techniques such as Log-Linear Analysis or Correspondence Analysis).