One of the first concepts students of statistics learn -- often as early as elementary school -- is the mean of a set of numbers. This is the average of the numbers, where the student adds together the values of a set of "n" numbers then divides the sum by that same number "n." The purpose of a T-test, is to determine if a set of means differ from each other with statistical certainty.
One of the concepts in statistics, on which statistical tests such as a T-test, rely, is called the normal distribution. This is more commonly known as the bell curve, along which sample numbers should logically distribute themselves, when sampling real world data. While random samples that are not normally distributed can be useful when learning how to perform statistical tests, T-test, that assess real world data need normally distributed data to yield valid results. Researchers can visually inspect the distribution of data before they run a T-test, to ensure the results will be valid.
To perform a T-test, a researcher needs two sets of data to compare. One group will be called the "independent variable" and the other will be called the "dependent variable." This nomenclature also applies when the "variable" in question is a set of data. The T-test, produces a score by dividing the difference in means between the independent and dependent variables by the difference in variance -- the variability between the individual numbers within the numbers in each data set -- between the independent and dependent groups.
The raw number a T-test produces is not useful in and of itself. After calculating a score from a T-test, also known as the T-value, the researcher will compare the result to a standard statistical chart that gives the minimum T-values, in order to consider the difference in means between two groups to be statistically different. This minimum score will depend on the alpha level -- a number representing the chance that the results are the result of pure chance -- which the researcher selected for his study and the number of data samples in each group.