50-50 multivariate analysis of variance for collinear responses

Summary. Classical multivariate analysis-of-variance tests perform poorly in cases with several highly correlated responses and the tests collapse when the number of responses exceeds the number of observations. This paper presents a new method which handles this problem. The dimensionality of the data is reduced by using principal component decompositions and the final tests are still based on the classical test statistics and their distributions. The methodology is illustrated with an example from the production of sausages with responses from near infra-red reflectance spectroscopy. A closely related method for testing relationships in uniresponse regression with collinear explanatory variables is also presented. The new test, which is called the 50–50 F-test, uses the first k components to calculate SS MODEL. The next d components are not involved in SS ERROR and they are called buffer components.