Statistical quality control of variety trial data

I propose detection criteria for identifying an abnormal or erroneous data vector provided by a single variety trial in a longer series of variety trials. The test criteria are based on the linear effects estimated separately for each studied trial using global variance components estimated from the whole series of variety trials. The criteria comprise three mutually independent test statistics. The first one is a quadratic form in the estimated fixed effects, the second one is a quadratic form in the estimated realized linear random effects not including the residual effects, and the third one is a quadratic form in the estimated realized residual effects. Under the null hypothesis defining a valid data vector, the three quadratics have independent chi2 distributions. Under natural alternative hypotheses, they have noncentral chi2 distributions. Decomposing the total variation of the data vector studied into quadratic forms due to different types of the realized linear effects intuitively justifies the resulting test criteria. The decomposition may also be used to show that the resulting tests are likelihood ratio tests. I further present computational procedures that allow us to dispense with the need for prior estimation of the linear effects.