7.7 The data on the yield of F3 families of wheat presented in Exercise 3.3 in Chapter 3 are a subset from a larger investigation, in which two crosses were studied, and the F3 families were grown with and without competition from ryegrass. The experiment had a split-split plot design, with the following relationship between the block and treatment structures:

• ‘cross’ was the treatment factor that varied only among main plots

• ‘family’ was the treatment factor that varied among sub-plots within each main plot, but not among sub-sub-plots within the same sub-plot

• presence or absence of ryegrass was the treatment factor that varied among sub-sub-plots within the same sub-plot.

The mean grain yield per plant was determined in each sub-sub-plot. (When the subset of the data is considered in isolation, it has a randomized block design, as described in the earlier exercise.) The first and last few rows of the spreadsheet holding the data are presented in Table 7.15: the full data set is held in the file ‘wheat with ryegrass.xlsx’on this book’s website (see Preface). (Data reproduced by kind permission of Soheila Mokhtari.)