What about multiple testing?
If alpha=0.05 then
- if you test 100 hypotheses then 5 will be false positives (i.e. appear as significant wrongly)
- if you test 1,000,000 hypotheses then 50,000 will appear as false positives
IF the tests are INDEPENDENT
GAM hypotheses are not independent hence need to use Monte Carlo Test to check on this aspect or ignore it!