Somewhere along the way I remember being taught that you can never really prove the null hypothesis. Instead, you can either prove or disprove the alternative. In proving the alternative, you can reject the null. In disproving the alternative, you still can’t assume that the null is correct. It just allows you to cross one potential theory off your list. Very tricky.
It’s possible that I’m mixing some of this up (or maybe even making it up) … can’t be 100% certain. The part of my brain that houses this particular piece of information is buried deep deep deep. To retrieve even the tiny bit I’ve come up with so far, I had to wade through some very thick and scary cerebral cobwebs. I think it had something to do with t tests (or was it F tests?) and I seem to remember something about type 1 errors and type 2 errors. Also something to do with tails and directions. Maybe p-values?!?! Does that sound right? I also remember that the guy who taught me this information during a hot sticky summer semester very long ago was a visiting professor from southern california who happened to be blond and tanned and beachy and not much older than me. Yup … remember him perfectly.
Here’s the theory I’m testing:
H0 = getting another tattoo will not negatively impact my career
Ha = getting another tattoo will negatively impact my career
So … I’m scheduled to get my second tattoo next weekend. I’m totally excited … I can picture it on my skin and know it belongs there. We’ll see what my guy comes up with, but we’re leaning towards something pretty big and dramatic … maybe a half-sleeve (apparently REAL tattoo people laugh when you say “half-sleeve” and point out that it’s either a sleeve or it’s not a sleeve). The problem is that I’m having trouble finding anyone who thinks this is a good idea. My research to-date (largely survey-based and qualitative) is lending a lot of support to the alternative hypothesis. However, here’s something to consider. What if I have the equation wrong? What if I’m really testing this hypothesis:
H0 = not getting another tattoo will improve my career prospects
Ha = not getting another tattoo will not improve my career prospects
Choosing the null and the alternative is a very complex exercise. The (admittedly weak) counter-argument I am making is that nobody can prove to me that not getting a tattoo will improve my career prospects (the null above). I’ve thrown a double negative into the alternative hypothesis just to keep everyone on their toes but … I think the logic works. Either way, I think proving this one is going to be somewhat elusive. I honestly can’t imagine someone coming out and saying “sorry but you aren’t going to get that awesome, really cool job that you desperately want because you have a tattoo”. So … perhaps I’m not going to solve this one with stats.
The fact is that I don’t necessarily want to follow a traditional career path … just blend in and make jumps to the next tier on the corporate ladder at regular (almost predetermined intervals). I want to stand out and do things differently. I want to get ahead, but I want to do it by being authentic. The woman I admire and respect most in my organization is always telling me that being edgy is good. This would qualify. So … there. Doing it.
In the meantime … if you want to know how badly I messed up the stats stuff, read this article – http://liesandstats.wordpress.com/2008/10/25/you-cant-prove-the-null-by-not-rejecting-it/.