Ok, I've come up with a way to explain why small changes are more important when there are fewer items at stake (ie. few spots available in competitive residencies).
Cancer treatment A
Cancer treatment B
Two study arms, one for A, one for B. Rare cancer, few participants. Let's put statistical significance aside for sake of argument.
In the initial experiment, 2 people get treatment A, one dies, one lives
Both treatment B people live.
Treatment A is only a 50% survival. Treatment B is 100% survival. Big difference. Again, not significant stats-wise, but stay with me here.
Next experiment. 3 people in each arm. 1 survives in A arm, 2 in B arm. A has 33% survival, B has 66%. I still want treatment B by a long shot.
Next, 4 people, 1 survives in A, 2 in B. That's 25% and 50%.
Now 5, that's 20% and 40%.
10 people in each: 10% and 20%.
See how as numbers go up, the percentages of 'success' become seemingly less important because they become 'closer' in low value?
That is applying in the match in Derm vs IM. If two people have a set low chance of matching, but one is twice the chance of the other, the difference in getting a derm spot could turn into a 25% and 50% comparison. With so many IM spots, a small increase in chances may just translate into a 10% and 20% comparison (or even less of a difference).
Not a perfect example since the stats are not in the significant range, but it sorta explains the concept I think.
I mean, even without using numbers, one should be able to conceptually justify this to themselves.
There is a reason why many IM applicants cancel interviews during the season because 'they already have enough', but a derm applicant will spend $5000 and interview at 5 places across the country in one week and not cancel a single precious interview unless it conflicts with another...not that the latter was me or anything.
It's that small extra chance that you need to bank on...if you don't take it, you'll always be left wondering.
