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). 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 whenever there is a weight and when 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
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.