Tuesday, March 3, 2009

Hypothesis Testing

So how is hypothesis testing like life? I'm going to provide an example that my dog, Lucy, would provide if she was explaining hypothesis testing to you.

In case you forgot who she was or what she looks like...

1. Determine the appropriate null and alternative hypothesis

Ho: The holes in the kitchen rug occurred naturally
Ha: It was me that chewed the kitchen rug...HA!!

2. Check conditions
  • Randomization - I will randomly select a spot on the rug
  • Independence - my decision to chew on this rug is independent of my decision to chew other rugs
  • Success / Failure - np, nq >= 10. I'm just a dog and I can't do that math. Mr. C's Stat students will always check this condition, as this tells them that the Normal model is appropriate.

3. Determine the likelihood of observing the sample proportion that we did through natural sampling variation

The probability that it was not me that chewed the rug is 0.5. We observed a sample probability of 0.99 that it was me that chewed on the rug (my parents caught me). The z-score for this sample proportion is 9.8, and the probability of observing that sample proportion or more (a one-tailed upper tail test) is 5.7 x 10^-23, which is essentially zero. My stat teacher owner helped me with the math here.

4. Interpret the p-value

The probability of observing a sample proportion of .99 or more is 5.7 x 10^-23. This is very unlikely to happen just by chance alone. That is, those pieces of rug missing are unlikely to happen naturally, somebody (ME) must have chewed on them when their owners weren't looking. We reject that the holes in the kitchen rug occurred naturally in favor of the fact that it was me, Lucy, that caused the holes in the kitchen rug.

There you go, time for bed!