Student's t Distribution

"Student's t distribution" was created by William Gosset in 1908. His employer was Guinness Breweries, a business that sought after the best yielding barley crops that could be produced. William Gosset, already passionate with the excitement of laboratory chemical, biological analyses and statistical analysis, began his interest in discovering those best yielding and insensitive barley crops for Guinness. With further research in statistics, he desired to publish his new findings. Guinness at the time was gaining industrial advantage over other breweries by using statisticians such as Gosset, which was not publicly announced. So the brewery had Gosset use the pseudonym "Student" instead.

Now with that historical context, the description of the Student's t distribution: It is utilized as a statistical distribution when the sample population size is small OR when the population variance is unknown. Usually, you will be able to complete normal statistical analysis on data sets, but with a small data set, the results are not solidified (But the data set should be considered "normal" or a "bell-shaped" distribution at least for using the Student's t distribution). There are various sorts of Student's t distributions, which change based on their Degrees of Freedom-or frankly, "the number of independent observations in a [specific] set of data" (Stat Trek). This degree of freedom is crucial when completing a Student's t distribution. The degree of freedom is equal to the sample size minus 1. Here is the equation:

 t = [ x - μ ] / [ s / sqrt( n ) ]

       x = sample mean, μ = population mean, s = standard deviation of the sample, and
       n = the sample size

The "DF" on the key for the chart distribution stands for the degree of freedom.


http://www.umass.edu/wsp/statistics/tales/gosset.html
 http://stattrek.com/probability-distributions/t-distribution.aspx