FAQ/AdjRes - CBU statistics Wiki

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  • = How do I know which elements contribute to a relationship in a two-way frequency table? =

Suppose we wish to compare the age frequency profiles of two groups. The data for the four age bands and two groups, willing to go in an ambulance and refused to go in an ambulance to hospital, are given below.

||||||||<style="TEXT-ALIGN: center"> || Ages 18-40 || Ages 40-65 || Ages 65-80 || Ages 80 and over || Refused || 51 || 24 || 13 || 18 || Complied || 27 || 25 || 31 || 26 ||

There is a relationship between age and group (chi-square(3) = ). Where, though, exactly is the relationship?

SPSS produces adjusted residuals which may be interpreted as z-values and referred to a standard normal distribution.

{{ WEIGHT BY CASE. CROSSTABS /TABLES=age by group /CELLS= ASRESID. }}

The adjusted residuals for the age group example are

||||||||<style="TEXT-ALIGN: center"> || Ages 18-40 || Ages 40-65 || Ages 65-80 || Ages 80 and over || Refused || -3.6 || 0.1 || 2.9 || 1.2 || Complied || 3.6 || -0.1 || -2.9 || -1.2 ||

We can use the CDFNORM function (in SPSS compute menu) to see the numbers in the cells deviate from what would be expected assuming there is no relationship between age and refusal. For cells (1,1) and (1,3)

{{ COMPUTE SIG=2*CDFNORM(-3.6). COMPUTE SIG2=2*(1-CDFNORM(2.9)). EXE. }}

The adjusted residuals -3.6 and 2.9 have two-sided p-values of 0.0003 and 0.004 respectively. This tells us that the 18-40 age groups tended to refuse and 65-80 group tended to comply.

If you are using version 12 of SPSS or later then you can evaluate the p-values for the adjusted residuals directly using the [http://www.spss.com/corpinfo/newsletter/0705_tip1.htm:Output Management System (OMS).]