# Dissertation Using T-Test

If your signal is 6 and the noise is 2, your t-value is 3.This t-value indicates that the difference is 3 times the size of the standard error.However, this post includes two simple equations that I’ll work through using the analogy of a signal-to-noise ratio.

If your signal is 6 and the noise is 2, your t-value is 3.This t-value indicates that the difference is 3 times the size of the standard error.However, this post includes two simple equations that I’ll work through using the analogy of a signal-to-noise ratio.

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For more information, go to Why should I use a paired t-test?

The 2-sample t-test takes your sample data from two groups and boils it down to the t-value.

Let's look at how each of these t-tests reduce your sample data down to the t-value.

Understanding this process is crucial to understanding how t-tests work.

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.If the signal does not stand out from the noise, it’s likely that the observed difference between the sample estimate and the null hypothesis value is due to random error in the sample rather than a true difference at the population level.Many people are confused about when to use a paired t-test and how it works. The paired t-test and the 1-sample t-test are actually the same test in disguise!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 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.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.The process is very similar to the 1-sample t-test, and you can still use the analogy of the signal-to-noise ratio.Unlike the paired t-test, the 2-sample t-test requires independent groups for each sample. For the 2-sample t-test, the numerator is again the signal, which is the difference between the means of the two samples.

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