Supplementary Exercises 3.18 and 3.19 of IPS7e ---------------------------------------------- A field trial on attracting creal leaf beetles to boards of different colours (similar to Exercise 2.7). Four colours (blue, green, white and yellow) and a total of 16 poles on which the boards will be mounted will be used. 3.18 ---- In a completely randomized design with 16 locations in a single field, the locations should be allocated randomly to the four colours, and it is most natural to use four replicates of each colour. The sketch below represents the field with its 16 locations. 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 The numbers 1-16 are drawn randomly from Table A/B starting at line 115. The first numbers are assigned to blue, the next four to green, the next four again to white, and the remaining numbers/locations are assigned to yellow. The following numbers are obtained from lines 115-122: 04 09 14 03 10 06 11 16 (06) (03) (04) 02 07 (16) (04) (07) (10) 13 15 ... Therefore, locations 4,9,14,3 will get blue boards; locations 10,6,11,16 will get green boards; locations 2,7,13,15 will get white boards; finally, locations 1,5,8,12 will get yellow boards. 3.19 ---- If the experiment is carried out in two oat fields, then these two fields will serve as blocks (because beetle counts within the same field are presumably more similar than counts in different fields). In a completely randomized block design, the treatments are allocated at random within each block. The locations in the two fields can be represented simply by the numbers 1-8 in each field: Field A: 1 2 3 4 5 6 7 8 Field B: 1 2 3 4 5 6 7 8 The numbers 1-8 are drawn randomly from Table A/B starting at line 105, first for Field A and afterwards for Field B. Here we only need to draw single digits from the table. 5 (5) 2 4 7 6 (7) 1, giving for Field A: blue (5,2); green (4,7); white (6,1); yellow (3,8) and continuing in row 105 from where we stopped... 1 4 8 (1) 6 7 (7) 5, giving for Field B: blue (1,4); green (8,6); white (7,5); yellow (2,3)