For the analysis of variance it is useful to describe the observations using a statistical model.

Hypotheses test: $H_1: \tau_i \neq 0$ for at least one i

In the effects model Each observation $y_{ij}$ can be represented by an overall mean, $\mu$, plus the effect of the ith treatment, $\tau_i$, plus a random error, $\epsilon_{ij}$. The effects model is not the only model to be used to represent the data. However, it has some intuitive appeal in that the average $\mu$ is a constant, and the treatment effects $\tau_i$ represent the deviation from this constant when the specific treatments are applied. This model is called single factor analysis of variance or one-way ANOVA. As the treatment effects can be considered as a deviation from the overall mean, The hypothesis test for the one way analysis of variance can be expressed in terms of the treatment effect $\tau_i$. In the null hypothesis $\tau_i$ is equal zero for every i. That is the effect of the factor is zero, there is no deviation from the overall mean. In the alternative hypothesis H₁ $\tau_i$ is different from zero for at least one i, meaning the cotton content affects the tensile strength, at least at one level of cotton content.