T testsWritten by Robert Niles If you haven't read them yet, please take a moment to read my pages on standard deviation and margin of error. They lay out a few concepts you need to understand before thinking about ttests.You're back? Good. Now let's start. Often, you haven't the time or money to measure every single item in a collection of stuff. Sometimes, it's just not practical, either. Let's say you want to see how much force it takes to break new laptop computer. If you break them all, you won't have any left to sell. Not a good idea. Or a particularly smart business plan. That's why you measure a smaller sample. But the standard deviation of a small sample of data doesn't necessarily tell you anything useful about how wildly the larger group's values vary around their average. And that distribution's important. Because sometimes the average of a small sample comes in where you want it to, but the sample's values are so widely spread around that you can't be sure the larger group's average will come in about the same place as the sample's. That's where you use the ttest. It's a random variable that uses the standard deviation of the sample to help determine interesting stuff about the larger group it represents. The tscore factors in a bunch of related values. I'll list them here for reference, but please skip the four lines below if you fear that too much detail will cause you to freak out...
The number of values in your sample, minus one, is the "degrees of freedom" of your sample. (One question down, one to go.) Once you've computed your tscore, you will compare it to a tvalue that you look up in a table. You'll select the tvalue that corresponds to the same "degrees of freedom" as your sample, and the same margin of error that you're willing to accept. So if you expect the larger population be normally distributed (C'mon. I'm trusting you read that standard deviation page already), if the tscore you computed is greater the tvalue you looked up in the table, you can accept the assumption that the larger population's mean is larger than your guess. If you are hoping that the larger population's mean is less than your assumption, slap a negative sign on the value from the ttable and hope that your (then presumably negative) tscore is less than it. Okay, let's try this again with an example: The Burns Co. is now making laptop computers in its Shelbyville plant. Mr. Burns is too cheap to wreck too many computers in a test, so he's letting his quality assurance guru, Homer, smash five of them. Homer is to record from how high in the air he can drop each laptop on the floor before it won't work anymore. Mr. Burns' wants laptops that can survive a fall from his height of five feet, two inches.Sources: 
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