I'm looking to see if income level affects the number of pets a person has, controlling for number of children. I have run a GLM (Poisson family) model, and found that if a person is categorised as 'Low' income, their number of expected pets decreases by 21.3%. I also found that for every child a person has, their number of expected pets increases by 4.03%.
However, the 21.3% decrease is not significant, and the 4.03% increase is significant. I'm wondering if this is incorrect/whether I have done something wrong? I am aware I may be confused about how statistical significance works, so just want to check whether the below makes sense!
The R outputs for estimates and p-values look like this:
Estimate Pr(>|z|) Level_of_IncomeLow: -0.239043 0.0830 . Num_of_children 0.039527 7.54e-10 ***
Exponent of -0.239043: 0.787381 1-0.787381=0.212619 = 21.3% decrease Exponent of 0.039527: 1.040319 = 4.03% increase
Essentially, is it okay that the larger effect is not statistically significant, but the smaller effect is? It just feels wrong!