A refinement of a sample space is obtained by replacing one or more of its projectors with other projectors which add up to it; conversely a coarsening or coarse graining is obtain by adding together two or more projectors in the projective decomposition and using the sum as one of the elements in a new decomposition. Given the connection between sample spaces and event algebras as defined above, one sees that the event algebra of a refined sample space is larger than the original event algebra: i.e., it contains all the original projectors and others in addition; conversely, a coarsening leads to a new event algebra which is a subset of the old event algebra.