Interpreting Contingency table analysis & z-tests results - PLEASE HELP!

Posted by DP_Sydney on May 20, 2011; 9:18am
URL: http://spssx-discussion.165.s1.nabble.com/Interpreting-Contingency-table-analysis-z-tests-results-PLEASE-HELP-tp4412140.html

Hi all,

 I have completed a 5x2 contingency table in SPSS which returned a significant chi-square value (P<0.001). My columns are species detected/not detected in surveys and the rows are different habitats (see data below). I expected the proportion of detected to not-detected to differ between habitats. So all good here.

 I followed this up with z-tests (under the 'Custom Table' option) which detected significant differences in column proportions for three of the habitats (=rows) (B,C,D). B and C had lower proportions of surveys detecting the species and D had greater than expected.

 However, the 'reporting rate' of the species (i.e. the number of surveys that detected the species as a percentage of total surveys, which equals the row percentage in the contingency table) was highest in habitat D (20.4% - no surprises there), AND in E (12.8%) which showed no significant difference in proportions. All other row percentages were below 4%.

 Furthermore, in a 2x2 table just comparing habitat D and E (which from a priori reasons were the only habitats I expected to have a greater proportion of detected surveys - which they did as row percentages but not in z-tests) there was no difference between them (exact p = 0.079).

 I'm confused about how to interpret these results. What exactly does a significant z-test tell me about the proportions of detected/not-detected? Does a significantly greater than expected proportion of detected in habitat X not equate to a significantly lower than expected proportion of not-detected in habitat X? Can I still take note of the fact that in the habitat of row 5 the 'reporting rate' was still high relative to other habitats except D?

The data are as follows (standardised residuals in parentheses)
                        Detected            Not Detected           % detected (row %)
A   Obs              1 (-1.6)             45 (0.5)                   2.2
     Exp              4.4                   41.6
B   Obs              4 (-2.3)             123 (0.8)                  3.1
     Exp              12.2                  114.8
C   Obs              3 (-3.4)             175                         1.7
     Exp              17.1                  160.9
D   Obs              40 (4.9)             156 (-1.6)                20.4
     Exp              18.8                  177.2
E   Obs              18 (1.2)             123 (-0.4)                12.8
     Exp              13.5                  127.5

Hope anyone can help! :-)

Thanks in advance,

Dean