*If you understand how t-tests calculate t-values, you’re well on your way to understanding how these tests work.*

In statistics, t-tests are a type of hypothesis test that allows you to compare means.

They are called t-tests because each t-test boils your sample data down to one number, the t-value.

I'll show you the formula first, and then I’ll explain how it works. A common analogy is that the t-value is the signal-to-noise ratio. You simply take the sample mean and subtract the null hypothesis value.

If your sample mean is 10 and the null hypothesis is 6, the difference, or signal, is 4.

We include the noise factor in the denominator because we must determine whether the signal is large enough to stand out from it.

Both the signal and noise values are in the units of your data.In this case, you’d need to use another test, such as the 2-sample t-test, which I discuss below.Using the paired t-test simply saves you the step of having to calculate the differences before performing the t-test.However, if there is a difference of the same size but your data have more variability (6), your t-value is only 1. In this manner, t-values allow you to see how distinguishable your signal is from the noise.Relatively large signals and low levels of noise produce larger t-values.As we saw above, a 1-sample t-test compares one sample mean to a null hypothesis value.A paired t-test simply calculates the difference between paired observations (e.g., before and after) and then performs a 1-sample t-test on the differences.A larger number indicates that your sample estimate is less precise because it has more random error.This random error is the “noise.” When there is more noise, you expect to see larger differences between the sample mean and the null hypothesis value .If there is no difference between the sample mean and null value, the signal in the numerator, as well as the value of the entire ratio, equals zero.For instance, if your sample mean is 6 and the null value is 6, the difference is zero.

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