Posted by
Rich Ulrich on
May 27, 2011; 6:08pm
URL: http://spssx-discussion.165.s1.nabble.com/Interpreting-Contingency-table-analysis-z-tests-results-PLEASE-HELP-tp4412140p4432889.html
Yes, the z's for the cells are a remark on the relation to the 'average' difference.
So, acacia/euc is not extreme because it falls in the middle.
Further, z for the low proportion for wetland is not as extreme because
the N is smaller and thus the power is weaker.
I'm going to call the groups A B C D and E, for the ordered means
(1.7, 2.2, 3.1, 12.8, 20.4). The first thing to conclude is that
(A B C) are the same and that all the cases are in (D E).
Using the z's as tests, (A B C) (D E) is the way that you could show
differences, in one style of post-hoc reporting. If that was the full
result. I don't remember if you stated it, but it is possible that D
is not "different" from (A B C). In that case, the post-hoc report
could be (A B C D) (D E).
This would say that D is "not different" from the first three, and it also is
not different from the last. Traditionally, these have often been shown
by underlining the means that "do not differ." - This style of report was
designed for ANOVA, using tests based on the pooled variance, for groups
with equal Ns; it does not work consistently for 2x2 tables, for grossly
unequal Ns, or for other paired comparisons that are may have different
error terms for various comparisons. (re: smallest sample here. But it
seems like it might work here.
MOST of the detections are in D and E. The simple difference between
them is not (I think you report) tested as different in a 2x2 table. Okay.
So, at the conventional test level, they do not differ. However, the
"effect size" of their measured difference is still somewhat large. It also
is "sensible" in that the mixed environment is less extreme than the pure
one. So you might expect a difference to be confirmed if the sampling was
more extensive.
--
Rich Ulrich
From:
[hidden email]To:
[hidden email];
[hidden email]Subject: RE: Interpreting Contingency table analysis & z-tests results - PLEASE HELP!
Date: Fri, 27 May 2011 18:43:24 +1000
Thanks very much for your reply Rich,
I'm still a little confused as to how to interpret the z-tests - do they indicate which rows (habitats in my case) have the greatest difference between the numbers of the categories of the columns (no. of surveys that detected/didn't detect in my case)? If so, is this relative to the 'average' difference between column categories across all rows?
[snip, some]
... But I had interpreted the z-tests as indicating that Acacia was contributing to the significance of the chi-square
but not Acacia/Euc - despite 12.8% being >4 times the three other habitats (1.7-3.1%), and in a 2x2 table Acacia vs Acacia/Euc was not significant.
In summary, the species is detected significantly more frequently in two habitats (Acacia + Acacia/Euc) and these are frequented either equally OR Acacia more so than Acacia/Euc. It is the latter part that is troubling me (hence the follow up 2x2 table).
[snip, rest]