A statistical test for ranking data from partially balanced incomplete block designs

The analysis of partially balanced incomplete block (PBIB) ranked data is discussed. Two examples are given to illustrate two alternative approaches. Analysis of PBIB ranking data is not covered in any of the standard sensory evaluation texts and this expository note is meant to help fill this gap. For some data sets, the calculations for the first approach are simple enough to do by hand. The second approach that we consider assumes that computer software for general analysis of variance is available. Such analysis of variance software should cope with missing values via a regression method. A suggested multiple comparisons algorithm is also illustrated. R code is given to allow easy application of our first approach.