Thursday, December 07, 2006

Love Stats

Warning: Do not read this post unless you truly have nothing better to do. I mean, if you have to write a paper or do some reading for school, do that. If you need to catch up on some correspondence, I recommend you do that before reading my post too. How about your ceiling fan? When was the last time you dusted it? Why don't you take care of that also before saying you have enough time to waste on this post.

I started to think of some things yesterday as a result of my study of statistics and a conversation I had with the great Smith Field House janitor/philosopher Lafe. When you test a hypothesis and decide to reject or accept a hypothesis you either get it right, commit a type I error, or commit a type II error. A type I error is rejecting the null hypothesis when it is actually correct, and a type II error is not rejecting the hypothesis when it is actually incorrect. You can always interpret the stats in such a way that you decrease the chance of committing a type I error, but that always means increasing the chance of committing a type II error, and vice versa. You just have to decide which error has the worst consequences and decrease the probability of making that error. In the justice system the null hypothesis is "The person is innocent". A type I error would be saying a person is guilty when they are actually innocent, and a type II error would be saying a person is innocent when they are really guilty. In this case our government says a type I error is worse. Putting the burden on the prosecution to prove guilt and having well defined laws as to what will and will not be allowed as evidence means that fewer innocent people are found guilty and more guilty people are found "not guilty". That's a trade off that we're willing to accept in this nation.

Now on to the topic of love. The null hypothesis that a person can have is "I'm not in love". After getting to know a member of the opposite sex well, it is common to test to see if this original hypothesis is still true. After the test is made that person can either be right, decide they are not in love when they actually are (type I error), or think they are in love when they actually aren't (type II error). Which error is worse? I asked a number of people and it was interesting to hear their responses. Some people said that a type I error is the most tragic while dating, but that if marriage is a very real possibility, a type II error would have the worst consequences. Others said a type II error is always worse.

I believe that we all define "love" in such a way that we avoid one of these errors while increasing the probability of committing the other. People with a very broad definition of love want to avoid the mistake of not thinking they are in love, only to realize it later, when it might be too late to do anything about it. People with very strict definitions of love want to avoid thinking they are in love, only to later realize that what they felt wasn't love, and have to get out of whatever situation they're in. But, on the other hand people with broad definitions run a higher risk of committing a type II error and those with very strict definitions run a higher risk of committing a type I error.

Let's present these two different types of people with the same difficult situation where they just can't decide if they are in love or not. The person avoiding type I errors will say they are in love, because if they say they are in love, they are either right, or they committed a type II error. That's great. There is no chance that a type I error could be committed. The person avoiding type II errors will say they are not in love, because that way they are either right, or they committed a type I error which they consider to be less severe. No type II error could be committed.

Of course if we think things through, the probability lies in us being correct and not committing any error. I hate to make it sound like we will always be wrong and we must choose which type of mistake we want to make. Okay, that's all. If you followed any of this rambling, congratulations.

4 comments:

Lillian said...

Wow. Reading that after pulling an all-nighter produces kind of a euphoric "I know that's deep but I'm not sure I quite understand..." feeling. Nice.

Jacob said...

Yeah, well after my all-nighter last night, I find my reading skills deficient and my head aching. So I confess to not actually reading any more than lillian's comment.

Whitney said...

i followed it! and it's almost one! and i have stuff i need to do!
good work team.

Chelsea said...

I got it too.