In this example, three plants are nested within four pots, which are nested within three houses. The FACTORS
statement requests a random permutation of the numbers 1, 2, and 3 to choose `Houses`

randomly. The second step requests a random permutation of the numbers 1, 2, 3, and 4 for each of those first three numbers
to randomly assign `Pots`

to `Houses`

. Finally, the FACTORS
statement requests a random permutation of 1, 2, and 3 for each of the 12 integers in the second set of permutations. This
last step randomly assigns `Plants`

to `Pots`

. The following statements produce Output 86.2.1:

title 'Hierarchical Design'; proc plan seed=17431; factors Houses=3 Pots=4 Plants=3 / noprint; output out=nested; run; proc print data=nested; run;

Output 86.2.1: A Hierarchical Design

Hierarchical Design |

Obs | Houses | Pots | Plants |
---|---|---|---|

1 | 1 | 3 | 2 |

2 | 1 | 3 | 3 |

3 | 1 | 3 | 1 |

4 | 1 | 1 | 3 |

5 | 1 | 1 | 1 |

6 | 1 | 1 | 2 |

7 | 1 | 2 | 2 |

8 | 1 | 2 | 3 |

9 | 1 | 2 | 1 |

10 | 1 | 4 | 3 |

11 | 1 | 4 | 2 |

12 | 1 | 4 | 1 |

13 | 2 | 4 | 1 |

14 | 2 | 4 | 3 |

15 | 2 | 4 | 2 |

16 | 2 | 2 | 2 |

17 | 2 | 2 | 1 |

18 | 2 | 2 | 3 |

19 | 2 | 3 | 2 |

20 | 2 | 3 | 3 |

21 | 2 | 3 | 1 |

22 | 2 | 1 | 2 |

23 | 2 | 1 | 3 |

24 | 2 | 1 | 1 |

25 | 3 | 4 | 1 |

26 | 3 | 4 | 3 |

27 | 3 | 4 | 2 |

28 | 3 | 1 | 3 |

29 | 3 | 1 | 2 |

30 | 3 | 1 | 1 |

31 | 3 | 2 | 1 |

32 | 3 | 2 | 2 |

33 | 3 | 2 | 3 |

34 | 3 | 3 | 3 |

35 | 3 | 3 | 2 |

36 | 3 | 3 | 1 |