Why is my highest coefficient not significant but lower ones are? (Poisson regression) 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 ***

My calculations:
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!

low (vs. high) has a restricted range (i.e., only 2 values).  Number of children presumably has a much wider range.  The narrower the range of an $X$ variable, the less power there is to test it.  That's a general principle.  Specific to this example, it sounds like the underlying variable (income) was subjected to a median split, or something similar.  If so, you should be aware that categorizing a continuous variable has long been considered poor statistical practice.
