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In the [[design of experiments]], '''completely randomized designs''' are for studying the effects of one primary factor without the need to take other [[nuisance variable]]s into account. This article describes completely randomized designs that have one primary factor. The experiment compares the values of a [[response variable]] based on the different levels of that primary factor. For completely randomized designs, the levels of the primary factor are [[random assignment|randomly assigned]] to the [[experimental unit]]s.
==Randomization==
By [[randomization]], that is to say the run sequence of the experimental units is determined randomly. For example, if there are 3 levels of the primary factor with each level to be run 2 times, then there are 6! (where ! denotes [[factorial]]) possible run sequences (or ways to order the experimental trials). Because of the [[replication (statistics)|replication]], the number of unique orderings is 90 (since 90 = 6!/(2!*2!*2!)). An example of an unrandomized design would be to always run 2 replications for the first level, then 2 for the second level, and finally 2 for the third level. To randomize the runs, one way would be to put 6 slips of paper in a box with 2 having level 1, 2 having level 2, and 2 having level 3. Before each run, one of the slips would be drawn blindly from the box and the level selected would be used for the next run of the experiment.
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