![]() ![]() Instead, we have historically printed out tables of already-calculated p values for a range of degrees of freedom and t-statistics (you are likely to find such a table in the back of your intro to stats text book), or included algorithms in our software that do the heavy lifting of the p value calculation for us, as is suggested by the p() function in your question. That's a lot of intense calculation for what is otherwise a pretty simple test most of us casual t-test users are not up for that kind of time investment. Since the distribution is symmetrical, you don't have to separately calculate that - it will be exactly the same, so you can just double the value you got from 0.6595 to positive infinity. This gives you the area under the curve from 0.6595 up, but for a two-tailed test you also want it from -0.6595 down. You would enter these as the values over which to integrate, and then crunch through the calculus to evaluate the integral of the t PDF function. You want to get the area under the curve from 0.6595 up, i.e. In your example, your t statistic is 0.6595. Where nu (looks sort of like a "v") is the number of degrees of freedom and Gamma (looks sort of like an upside down "L") is the gamma function. ![]() Here's the function that defines the t-distribution (its probability density function, or PDF): If you've taken calculus, you may already know what needs to be done: The area under a curve is the integral of the function that defines the curve. Since the distribution is symmetrical, you can simply double that value to get the two-tailed p-value. So in order to calculate the p value that corresponds to a particular t-statistic at some degrees of freedom, you need to measure the area under the curve from that point on out. The p value is simply the proportion of the distribution - the area under the curve - that is at least as far from 0 as your t-statistic. way out in one of the tails), the you conclude that it is unlikely to have come from the null distribution. That mens you can compare that t-statistic to the rest of its null distribution - if it's a very unusual value for that distribution (i.e. So as long as you know how many degrees of freedom you have, you know theoretically what distribution your t-statistic came from under the null hypothesis. There is a defined theoretical distribution of t-statistics (the t distribution). If you want a one-tailed p value, then it's what proportion of t-statistics (for those degrees of freedom) are that high or higher (for the positive tail) or that low or lower (for the negative tail). ![]() The p value in a t-test (any t-test, not just two independent samples) refers to what proportion of t-statistics (for those degrees of freedom) are that extreme or more, assuming you want a two-tailed p value. First, a little background on the meaning of a p value ![]()
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