Chi square test and census pumf individuals

Question

A researcher has used a stratified cluster sample for Census 2001 Individuals data. As he explained it to me and as I think I understand it, this type of sample cannot be analyzed with SPSS. He mentioned that in censuses of the past there were certain tables that were used but which have now been replaced with a conversion factor.

He has studied the documentation around page 180, but there is no explanation of how to analyze the results by using the chi square test which is the one the researcher has planned to use. Can anyone help with this?

Answer

Our methodologist has provided the following information that was requested.

If the researcher took his sample from the 2001 PUMF, then the conversion factors are the factors he's looking for (these are design-effects). In previous censuses, we were calling them "Quality Factors". But they are the same thing. Their function is to convert, by squaring them, simple random sampling variances into variances obtained from the PUMF design plan. We modified the way it was introduced to simplify basic estimations.

The researcher is asking something not simple, though. In fact, simple random chi-square statistics are bias because of the PUMF sampling plan (as the researcher rightfully noted). To transform or to convert these statistics into chi-squares that take into account the sampling plan, he has to divide his chi-square statistics by the corresponding design-effects (conversion factors). But this is only an approximation [see 1, pp. 500 - 507]). The resulting statistics will behave better under the null hypothesis.

References:
[1] Särndal, C.E., Swensson B., Wretman J. Model Assisted Survey Sampling. Springer-Verlag. 1992.