STUDENT'S T
The general problem relevant to WDS EPMA of having some level of confidence that a measure is equivalent to another, or larger/smaller than another, is that the sample size is small and the population variance is unknown. This type problem was first treated in 1905 by W.S. Gossett, who published his analysis under the pseudonym "Student". His employer, the Guinness Breweries of Ireland, had a policy of keeping all their research as proprietary secrets. The importance of his work argued for its being published, but it was felt that anonymity would protect the company.
In statistical evaluation of x-ray count data, an exacting criterion is that of calculating a precise range (in wt.%) and level (in %) of homogeneity. These calculations utilize the standard deviation of measured values and the degree of statistical confidence in the determination of the average.
The degree of confidence means that we wish to avoid a risk (alpha) of rejecting a good result a large per cent of the time (95 or 99%) of the time. Student's t distribution gives various confidence levels for evaluation of data, i.e. whether a particular value could be said to be within the expected range of a population -- or more likely, whether two similar compositions could be confidently said to be the same. The degree of confidence is given as 1- a, usually .95 or .99. This means we can define a range of homogeneity, in wt.%, where on the average only 5% or 1% of repeated random points would be outside this range.