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.
As the difference between the sample mean and the null hypothesis mean increases in either the positive or negative direction, the strength of the signal increases. The equation in the denominator is a measure of variability known as the standard error of the mean.
This statistic indicates how accurately your sample estimates the mean of the population.
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.
However, this post includes two simple equations that I’ll work through using the analogy of a signal-to-noise ratio.
Minitab statistical software offers the 1-sample t-test, paired t-test, and the 2-sample t-test.
If you understand how t-tests calculate t-values, you’re well on your way to understanding how these tests work.
In this series of posts, I'm focusing on concepts rather than equations to show how t-tests work.
You just need to figure out whether it makes sense to calculate the difference between each pair of observations.
For example, let’s assume that “before” and “after” represent test scores, and there was an intervention in between them.