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==Model==
Upon observing variation among all <math>n</math> data points, for instance via a [[histogram]], "[[Probability theory|probability]] may be used to describe such variation".<ref>{{cite journal |last=Kass |first=Robert E |date=1 February 2011 |title=Statistical inference: The big picture |url=http://projecteuclid.org/euclid.ss/1307626554 |journal=[[Statistical Science]] |publisher=[[Institute of Mathematical Statistics]] |volume=26 |issue=1 |pages=1–9 |doi=10.1214/10-sts337|arxiv=1106.2895 }}</ref> Let us hence denote by <math>Y_{ijk}</math> the [[random variable]] which observed value <math>y_{ijk}</math> is the <math>k</math>-th measure for treatment <math>(i,j)</math>. The '''two-way ANOVA''' models all these variables as varying [[Independence (probability theory)|independently]] and [[Normal distribution|normally]] around a mean, <math>\mu_{ij}</math>, with a constant variance, <math>\sigma^2</math> ([[homoscedasticity]]):
<math>Y_{ijk} \, | \, \mu_{ij}, \sigma^2 \; \overset{i.i.d.}{\sim} \; \mathcal{N}(\mu_{ij}, \sigma^2)</math>.
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