Model Interpretation for Chi-Square and Post Hoc Tests:

  I’d like to study about the relationship btw total personal income(explanatory) and depression(response) by using NESARC.

‘S1Q10A’: Total personal income in last 12M (Quantitative) ‘DMAJORDEPSNI12′: Major depression in last 12M (Illness-induced ruled out)

  I refined Quantitative data(‘S1Q10A’ ) into 3-levels as ‘low’, ‘medium’, ‘high’ according to the amount of personal income. The ‘low’ level was set up to 30%, 'medium’ level was up to 70% and more than 70%(30% top of personal income) are categorized as 'high’.

  Chi Square test of independence revealed that they were significantly associated, chi2: 195.14, p-value: 4.27e-43, dof: 2

  Post hoc comparisons also told that any pairs among income categories are not associated. 

Here’s the results. 

========== chi-square test =================================
Income Level   low      medium   high
Depression                       
0                      9419    16032     12233
1                      1051    1211        685
Income Level   low           medium    high
Depression                                
0                      0.899618  0.929769  0.946973
1                      0.100382  0.070231  0.053027
*** chi-squre value, p-value, dof
chi2: 195.14
p-value: 4.23610993039e-43
dof: 2

========== Post hoc test ===================================

low vs medium——————-
*** chi-squre value, p-value, dof
chi2: 78.60
p-value: 7.60330301415e-19
dof: 1

low vs high——————–
*** chi-squre value, p-value, dof
chi2: 188.03
p-value: 8.54030265154e-43
dof: 1

medium vs high——————–
*** chi-squre value, p-value, dof
chi2: 36.82
p-value: 1.2984866455e-09
dof: 1