# Second Order Rao-Scott Test of Independence of a Contingency Table

The *Second Order Rao-Scott Test of Independence of a Contingency Tables*^{[1]} is a generalization of Pearson's Chi-Square Test of Independence for Contingency Tables for *complex samples* (e.g., when weights are applied to a table). In Q, it is only performed for 2×2 tables where **Design effect** is set to **Auto** or **Taylor series linearization** with Pearson's Chi-Square Test of Independence using Weight Calibration used in other situations.

This test is used by Q whenever there is a weight and Q is conducting a test of significance on the cells of a table (either Column Comparisons or Cell Comparisons) where the rows and columns are either Pick One, Pick Any, Pick Any - Compact or Date questions.

Where Weights are used, the standard error is computed using a *Taylor series linearization*, with an additional adjusting for Extra Deff if required

## See also

- Independent Sample Tests - Comparing Two Proportions
- Planned ANOVA-Type Tests
- Pearson Chi-square Test of Independence

## References

- ↑ Rao, J. N. K. and A. J. Scott (1984). 'On Chi-Squared Tests for Multiway Contingency Tables with Cell Proportions Estimated from Survey Data.' The Annals of Statistics 14.