in final week of biostats, and, as usual, it’s pretty exciting (once I stop procrastinating and sit down to my lectures).
last week we saw how admissions to UC Berkeley’s graduate programs, which aggregated into male/female, accepted/not accepted groups, seemed to expose a glaring bias towards accepting males (i.e., more males accepted than females). as it turns out, it only looks like men were favoured in applications, whereas in fact most women were applying to programs that had lower acceptance rates, whereas men applied to ones easier to get into. when comparing the acceptance rates, women + men were equal, and in one case women were actually favoured. this illustrates the importance of isolating confounding variables/effects. in order to do this, you take stratified samples, compare, then verify if effects are still similar, then apply relative weights and pool together to see if concurs with the partial effects.
in this week’s lessons the prof explains why relative odds ratios are so popular/important, which is that the probability/odds of a certain outcome given a certain risk factor, it is equivalent to the odds of the risk factor given the outcome. below is a visual representation and the mathematic proof of why this is true. (this example is based on a study concerning infant mortality in the first 180 days of life and night blindness in the mothers.)
the practical implication of this trait, called the invariance of odds ratio, is that you can used case-control studies in order to approximate relative risk. e.g., you can find out what the relative lung cancer risk of smoking is by going to the hospital and counting up how many lung cancer patients smoked and didn’t smoke. this is valuable because that kind of study is much simpler and often cheaper than working in the opposite direction.
this is one of the instances where math (the art of tinkering with numbers) reveals some really cool shit about how the world works, which I find very exciting. data about the world are just sitting around, waiting to be seen in just the right way so as to reveal the answers about which we care about quite a lot (does smoking cause cancer or not? does x easily-fixed risk factor cause death in impoverished people or not? are college admissions distorted by sexism?).
my master’s is definitely going to have to include statistics. in fact, my aim at this point is to do the highest level of stats possible given the (non-stats) background I have currently.
in other news, I had been obsessing about how I haven’t been running this summer. every time I got dressed in the morning, every time I looked at the musculature of the summer-exposed arms and legs of athletic people, every time I log the exercise I’ve done (yoga, 7-minute workout, bike 3hrs), I felt the smart of knowing that weeks kept going by of me not running on a regular basis, in a way that was not so much about what had not happened but a sinking feeling that running is just not something I can or will ever do. this is something that I do a lot; my default expectation in meeting people/embarking on projects/taking a class/learning a skill is failure. it takes me weeks of pushing forward blindly, unconvinced, before I will blink and realize I’m not only doing it, but doing it half decently. with the running, it took me realizing that I was committed to the idea that I simply will never be a runner, and so far this week I’ve gone running every other day. obviously it’s just the first week, but the difference is in how I feel about my capacity to do it, if I want to. as I said, this irrational automatic response is present in all aspects of my life, so I hope to counter it in other parts slowly; first realizing I’m doing it, then actively reminding myself that this is irrational because it is unfounded in reality, and then taking steps to show myself otherwise. if we are what we repeatedly do, then I will learn by painstakingly repeating this cycle of steps.