P-Test

Add a couple of "e"s and you’ve got the kind of test Olympic athletes subject themselves to to prove they’re not using banned performance-enhancing substances.

Without the additional "e"s, a p-test, or hypothesis test, is a method we use when we need to test to see if an idea we had or a claim somebody made has enough evidence for us to feel like it might be true.

More specifically, the p-test is used to test the validity of a statement about a population proportion.

Let’s break that down.

We might have heard somewhere that 11% of the population is left-handed (that 11% is our proportion). By population, we mean, like...everybody...not just the people in our town...everyone in America, for example (or even the world). Unfortunately, we can’t survey everyone to see which hand is dominant. It’d take too long and might well be impossible to talk to everyone anyway.

So we take a sample of people and determine what percentage of that group are lefties. Using that sample percentage (say, 6% lefties in our sample) and a couple of other formulas, we check to see how likely it is to get our sample result in a world where we expect there to be 11% lefties all the time. If getting a sample with only 6% is really unlikely in that 11% lefty world, we have some evidence to support the idea that the 11% figure might be wrong. Not proof though...just evidence to support that idea. Conversely, if getting a sample of 6% lefties in an 11% world isn’t that unlikely because random stuff happens, then we have evidence to suggest that the 11% figure is probably accurate.

P-tests are often used in product testing. If our machines are supposed to create a bag of M&Ms that is 20% brown candies, and we get reports that the bags are like 50% brown, we might run a p-test on some sampled bags to see if there’s evidence to support the idea that our machines are putting too many browns in each bag. Most p-tests are done using some form of technology, like a graphing calculator, spreadsheet, or website built just for that purpose.