Pearson residuals insignificant

[Eva Horvathova]

I would like to kindly ask you how to interpret the result or what analysis should I proceed with if the Pearson chi2 is significant but at the same time no Pearson residuals are significant.
I studied whether there is an association between involvement in gardening and family income (5 groups) using tabchi command:

tabchi gardNow incomeFamGr , raw pearson cont

          observed frequency
          expected frequency
          raw residual
          Pearson residual
          contribution to chi-square

-------------------------------------------------------
          |                 incomeFamGr                
  gardNow |       0        1        2        3        4
----------+--------------------------------------------
        0 |      31      116      188      113       56
          |  23.262  105.646  191.423  119.215   64.454
          |   7.738   10.354   -3.423   -6.215   -8.454
          |   1.604    1.007   -0.247   -0.569   -1.053
          |   2.574    1.015    0.061    0.324    1.109
          | 
        1 |      17      102      207      133       77
          |  24.738  112.354  203.577  126.785   68.546
          |  -7.738  -10.354    3.423    6.215    8.454
          |  -1.556   -0.977    0.240    0.552    1.021
          |   2.421    0.954    0.058    0.305    1.043
-------------------------------------------------------

          Pearson chi2(4) =   9.8629   Pr = 0.043
 likelihood-ratio chi2(4) =   9.9300   Pr = 0.042

I think this situation should be quite common for boundary-significant results as the sum of all squared standardized residuals is the chi-square. But I have not found if it is OK to just say which variable contributes the most to the significance (according to the observed – expected frequencies or the contribution to chi-square) or if another analysis is possible.
Thank you for your help.

[Nick Cox]

tabchi is a community-contributed command from tab_chi on SSC, as you are asked to explain (FAQ Advice #12).

I regard Pearson residuals as heuristic, perhaps helping you to see some pattern or interesting detail.

They arenot encoding a series of post hoc significance tests, which would raise many questions, not least multiplicity.

Full disclosure: I am the author of tabchi and would never dream of adding stars or any such stuff to the output. The numbers are the message if there is one.

With some guesswork, I interpret this as follows.

1. You have income group as a predictor. That is presumably ordinal but the chi-square test ignores that ordering.

2. You have some (0, 1) indicator as response.

3. A graph suggests a clear pattern. (I see that your income group is coded 0 to 4, but I won't redo the graph. In fact plotting the mean of the indicator with graph dot shows exactly the same information.)

4. The Pearson residuals don't add much extra insight to the chi-square and graph, except that they are rising and falling systematically. They are not guaranteed to change in the same way as the percents.

5. You need some non-parametric test for trend.