I have 5 conditions in my experiment: A,B,C,D,E and my sample size is 200 subjects. I want to have 40 subjects per condition, so I assign a condition to a person randomly without replacement. E.g. Person 1 gets condition B, so I still need 40 people for conditions A,C,D,E and 39 for condition B. Now person 2 has a slightly smaller chance to get condition B again. I don't have a prespecified list of say EABCDDEBAC... etc., where I cycle through the five options It's a random allocation for every person until the 40 people per condition fill up. So I am confused whether this is a block design or completely randomized design?
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2 Answers
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If I understand your description, this is a completely randomized design. Of course, if you're sampling without replacement, the number of options on each draw dwindles as you proceed. Finally, the one remaining subject automatically gets the last slot. But that last subject had an equal chance of being chosen first--or at any other step along the way.
One way to randomize is to put 200 slips of paper in a hat, each with a subject's name. Mix them up. Mix them up again. Then draw slips out of the hat (without peeking) and put them into five stacks for conditions A, B, C, D, and E.
Another way is to use a computer program (R here) randomly to scramble the 200 numbers. You have a numbered list of the 200 subjects from 1 though 200. The subjects with numbers in the first two rows below are assigned to A, the next two rows to B, and so on. Record the seed (or print the output on paper) and save the numbered list, so you can prove (if necessary) that you assigned subjects to conditions at random.
set.seed(2020)
x = sample(1:200)
x
[1] 130 79 123 94 27 14 26 76 1 119 146 141 156 80 77 100 177 120 185 49
[21] 36 195 190 167 188 30 62 200 78 96 164 13 161 159 192 61 2 153 85 180
[41] 158 168 137 139 98 89 73 108 122 194 87 43 134 186 121 166 64 33 172 69
[61] 175 142 32 59 118 83 148 147 86 22 187 115 50 60 67 37 184 8 135 150
[81] 99 12 125 47 45 20 196 41 179 25 66 162 39 132 54 129 157 17 71 44
[101] 149 114 72 91 111 16 65 74 51 133 128 3 38 81 198 35 24 163 160 42
[121] 104 105 117 197 5 68 93 90 127 101 46 124 56 171 28 15 109 138 189 170
[141] 48 144 75 106 155 82 21 136 10 4 169 29 165 178 11 52 23 53 151 110
[161] 140 193 19 18 174 63 199 97 152 88 40 182 145 6 102 176 84 58 95 131
[181] 126 103 113 143 70 107 154 173 55 31 112 9 183 116 191 181 34 57 7 92
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In your case, the "treatment" is the condition that you assign to the subjects at random. As Bruce explained, this is simply a randomized assignment of the treatment but not a blocking factor.
A blocking factor is a part of an experimental design where you control a specific part of the experiment, so that it doesn't confound the results. It is specifically meant to avoid having "nuisance" factors add noise or variability in your results.
Say, originally the conditions are not randomly applied on weekdays, but that they follow a specific order so that
- condition all group A on Monday
- condition all group B on Tuesday
- condition all group C on Wednesday
- condition all group D on Thursday
- condition all group E on Friday
Then, day of the week would be an example of a "nuisance" variable. In this case, the day of the week might add noise/interfere with the results (i.e., maybe people are happier Friday vs. Mondays potentially confounding with the Tx effect).
However, if you don't want to study but you don't want it to affect your results, you have to control against it, so you "block" it and now you have to control against. Say by saying
- assign 8 folks in each of groups A,B,C,D,E Monday
- assign 8 folks in each of groups A,B,C,D,E Tuesday
- assign 8 folks in each of groups A,B,C,D,E Wednesday
- assign 8 folks in each of groups A,B,C,D,E Thursday
- assign 8 folks in each of groups A,B,C,D,E Friday
And now, each condition's results are not confounded by day of the week, since they've been assigned across the week days.
The wiki page: https://en.wikipedia.org/wiki/Blocking_(statistics) offers more info. Hope this helps!
