4.51. Extended incomplete block designs. Occasionally, the block size obeys the relationship a + k + 2a. An extended incomplete block design consists of a single replicate of each treatment in each block along with an incomplete block design with k* $ k !

a. In the balanced case, the incomplete block design will have parameters k* $ k !

a, r* $ r !

b, and 0*. Write out the statistical analysis. (Hint: In the extended incomplete block design, we have 0 $ 2r ! b % 0*.)