The Student’s t-Test is a statistical hypothesis test based on the t-distribution which assesses whether the means of two different groups are statistically different from each other. Thus, the Student’s t-Test can be used to determine if two different sets of data are similar or in fact very different. If the scaling term of the data is known, then normally the z-Test would be utilized to assess the differences; however, if the scaling term is not known, then the t-Test can be used instead. This phenomenon occurs because the t-distribution takes the shape of the normal distribution without standardizing the mean to 0 and the standard deviation to 1 with the scaling term.
In statistics, the Student’s t-Test can be used in a variety of ways as long as the data collected originates from two different sources. For example, the t-Test can be used to assess the differences between one sample and a population, two different samples from two different populations (where the variances are equal) and two samples from the same population (one before a particular treatment and one after it).
The actual test statistic for the t-distribution is very similar for the z-statistic and it is as follows:
t = (x- µo)/(s/(n^1/2))
X is the sample mean
µo is the population mean
s is the sample standard deviation
n is the sample size
Thus, understanding the very basics of the Student’s t-Test is critical for accurately assessing the differences between two data sets.