p values differing amongst two groups in comparison
this is a board exam practice question, so I apologize in advance for leaving out all the details. I don't even know if this is a legitimate study.
this was a study based on serum glucose levels and the association with developing dementia, comparing those WITH diabetes and those WITHOUT Diabetes. The results appear to be counterintuitive. I noticed both p-values are not equivalent, though both less than the arbitrary 0.05. My overall question is one trying to develop a larger understanding of potential loop hole data biases. Is having two VERY different p levels (though both less than 0.05) justifiable when comparing between two groups? see below to make sense of what I am saying.
Average glucose level (left);Hazard ratio for dementia (95% confidence interval) (Right)
Participants without diabetes
95 mg/dL 0.85( 0.77-0.96)
100 mg/dL . 1.00
105 mg/dL 1.11 (1.03-1.18)
110 mg/dL 1.14 (1.03-1.27)
115 mg/dL 1.12 (1.04-1.31)
Participants with diabetes
150 mg/dL 1.10 (0.92-1.30)
160 mg/dL 1.00
170 mg/dL 1.01 (0.92-1.12)
180 mg/dL 1.16 (0.98-1.29)
190 mg/dL 1.38 (1.12-1.68)
According to these results, those WITHOUT diabetes have an association with dementia at glucose levels lower than those WITH diabetes.... so its like saying: "at a certain point, both groups have a greater risk of dementia when average glucose levels reach a certain point, but those WITH Diabetes can tolerate higher levels before becoming at risk"
Im curious too see someone's thoughts on this result and whether not each group having different p values would cause those in "statistics-world" to be squeamish.