SIMPLE AND COMPLEX RANDOM ASSIGNMENT IN EXPERIMENTAL DESIGNS |
Valentim
Rodrigues Alferes, |
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RECOMMENDATIONS FOR DETERMINING THE NUMBER OF
EXPERIMENTAL |
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1 |
Determine the minimum number of units based on power analysis. |
2 |
Loop this number to the next integer that allows a complete
counterbalancing of treatments [CC programs], or,
if not practical, a carryover design [CO programs]. |
3 |
If you cant get the number of units required for a complete
counterbalancing or a carryover design, try a partial counterbalancing (Latin
squares) [LS programs]. |
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4 |
If a partial counterbalancing is not feasible, choose truncated counterbalancing [CC, CO, or LS design with
the additional N of cases ? line]. |
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Note. You can
download ChooseRMD.sps,
an SPSS syntax file for choosing a suitable Repeated Measures Design on the
basis of the present recommendations. |
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Minimum number of experimental units (N) in
repeated measures designs. |
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Number of Treatments [T] |
Complete Counterbalancing |
Carryover Designs |
Partial Counterbalancing |
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Single |
Double |
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N = PT = T! |
N = T |
N = 2T |
N = T |
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2 |
2 |
2 |
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2 |
3 |
6 |
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6 |
3 |
4 |
24 |
4 |
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4 |
5 |
120 |
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10 |
5 |
6 |
720 |
6 |
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6 |
7 |
5040 |
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14 |
7 |
8 |
40320 |
8 |
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8 |
9 |
362880 |
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18 |
9 |
10 |
3628800 |
10 |
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10 |
11 |
39916800 |
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22 |
11 |
12 |
479001600 |
12 |
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12 |
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Suitable repeated measures designs for CC, CO, and LS programs. |
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Number |
Number of Treatments |
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2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
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2 |
CC2 |
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3 |
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LS3 |
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4 |
CC2 |
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CO4 |
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5 |
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LS5 |
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6 |
CC2 |
CC3 |
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CO6 |
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7 |
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LS7 |
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8 |
CC2 |
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CO4 |
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CO8 |
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9 |
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LS3 |
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LS9 |
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10 |
CC2 |
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CO5 |
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CO10 |
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11 |
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LS11 |
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12 |
CC2 |
CC3 |
CO4 |
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CO6 |
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CO12 |
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13 |
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14 |
CC2 |
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CO7 |
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15 |
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LS3 |
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LS5 |
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16 |
CC2 |
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CO4 |
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CO8 |
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17 |
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18 |
CC2 |
CC3 |
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CO6 |
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CO9 |
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19 |
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20 |
CC2 |
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CO4 |
CO5 |
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CO10 |
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21 |
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LS3 |
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LS7 |
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22 |
CC2 |
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CO11 |
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23 |
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24 |
CC2 |
CC3 |
CC4 |
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CO6 |
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CO8 |
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CO12 |
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25 |
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LS5 |
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26 |
CC2 |
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27 |
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LS3 |
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LS9 |
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28 |
CC2 |
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CO4 |
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CO7 |
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29 |
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30 |
CC2 |
CC3 |
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CO5 |
CO6 |
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CO10 |
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31 |
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32 |
CC2 |
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CO4 |
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CO8 |
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33 |
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LS3 |
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LS11 |
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34 |
CC2 |
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35 |
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LS5 |
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LS7 |
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36 |
CC2 |
CC3 |
CO4 |
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CO6 |
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CO9 |
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CO12 |
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37 |
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38 |
CC2 |
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39 |
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LS3 |
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40 |
CC2 |
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CO4 |
CO5 |
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CO8 |
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CO10 |
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41 |
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42 |
CC2 |
CC3 |
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CO6 |
CO7 |
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43 |
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44 |
CC2 |
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CO4 |
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CO11 |
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45 |
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LS3 |
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LS5 |
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LS9 |
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46 |
CC2 |
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47 |
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48 |
CC2 |
CC3 |
CC4 |
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CO6 |
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CO8 |
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CO12 |
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49 |
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LS7 |
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50 |
CC2 |
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CO5 |
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CO10 |
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51 |
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LS3 |
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52 |
CC2 |
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CO4 |
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53 |
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54 |
CC2 |
CC3 |
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CO6 |
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CO9 |
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55 |
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LS5 |
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LS11 |
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56 |
CC2 |
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CO4 |
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CO7 |
CO8 |
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57 |
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LS3 |
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58 |
CC2 |
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59 |
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60 |
CC2 |
CC3 |
CO4 |
CO5 |
CO6 |
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CO10 |
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CO12 |
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61 |
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62 |
CC2 |
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63 |
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LS3 |
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LS7 |
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LS9 |
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64 |
CC2 |
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CO4 |
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CO8 |
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65 |
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LS5 |
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66 |
CC2 |
CC3 |
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CO6 |
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CO11 |
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67 |
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68 |
CC2 |
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CO4 |
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69 |
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LS3 |
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70 |
CC2 |
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CO5 |
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CO7 |
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CO10 |
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71 |
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72 |
CC2 |
CC3 |
CC4 |
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CO6 |
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CO8 |
CO9 |
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CO12 |
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73 |
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74 |
CC2 |
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75 |
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LS3 |
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LS5 |
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76 |
CC2 |
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CO4 |
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77 |
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LS7 |
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LS11 |
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78 |
CC2 |
CC3 |
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CO6 |
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79 |
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80 |
CC2 |
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CO4 |
CO5 |
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CO8 |
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CO10 |
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81 |
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LS3 |
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LS9 |
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82 |
CC2 |
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83 |
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84 |
CC2 |
CC3 |
CO4 |
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CO6 |
CO7 |
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CO12 |
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85 |
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LS5 |
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86 |
CC2 |
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87 |
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LS3 |
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88 |
CC2 |
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CO4 |
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CO8 |
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CO11 |
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89 |
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90 |
CC2 |
CC3 |
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CO5 |
CO6 |
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CO9 |
CO10 |
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91 |
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LS7 |
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92 |
CC2 |
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CO4 |
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93 |
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LS3 |
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94 |
CC2 |
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95 |
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LS5 |
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96 |
CC2 |
CC3 |
CC4 |
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CO6 |
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CO8 |
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CO12 |
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97 |
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98 |
CC2 |
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CO7 |
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99 |
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LS3 |
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LS9 |
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LS11 |
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100 |
CC2 |
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CO4 |
CO5 |
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CO10 |
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101 |
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102 |
CC2 |
CC3 |
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CO6 |
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103 |
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104 |
CC2 |
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CO4 |
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CO8 |
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105 |
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LS3 |
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LS5 |
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LS7 |
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106 |
CC2 |
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107 |
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108 |
CC2 |
CC3 |
CO4 |
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CO6 |
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CO9 |
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CO12 |
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109 |
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110 |
CC2 |
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CO5 |
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CO10 |
CO11 |
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111 |
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LS3 |
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112 |
CC2 |
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CO4 |
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CO7 |
CO8 |
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113 |
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114 |
CC2 |
CC3 |
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CO6 |
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115 |
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LS5 |
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116 |
CC2 |
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CO4 |
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117 |
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LS3 |
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LS9 |
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118 |
CC2 |
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119 |
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LS7 |
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120 |
CC2 |
CC3 |
CC4 |
CC5 |
CO6 |
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CO8 |
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CO10 |
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CO12 |
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