# Paired t-test

What is the equation for a paired t-test?

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#### hypnagogue

Staff Emeritus
Gold Member
It's the same as a normal t-test. You just have to keep in mind that you're testing against the null hypothesis H0: &mu;D = 0, where &mu;D is the population mean of differences between pairs of observations. So it's

t0 = d(bar) / (sd / &radic;n)

where d(bar) and sd are the sample mean and sample standard deviation for the differences between each pair.

edit: And just to be clear, n is the number of pairs of observations.

Basically, you treat this like a regular t-test problem, except your random variable is the difference between each pair of observations.

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