The most important person, related to the method of ‘Analysis of Variance’ in…

Analysis of Variance (ANOVA) is a statistical technique for testing whether the means of three or more groups differ significantly, by comparing the variance between group means to the variance within groups. It works by partitioning the total variability in a data set into components attributable to different sources.

R. A. Fisher developed this framework and its variance-ratio test in the 1920s while working at the Rothamsted Experimental Station; the test statistic's distribution was later named the F-distribution in his honor. This is why R. A. Fisher is the person most closely associated with the method named in the question.

By contrast, Gauss is remembered for the method of least squares and the normal (Gaussian) distribution, Laplace for probability theory and celestial mechanics, and Newton for calculus and classical mechanics. None of them originated the variance-partitioning technique the question asks about, which rules them out.