Completely randomized design: Difference between revisions

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==Randomization==

ByTo [[randomization|randomize]], that is to saydetermine 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.

In practice, the randomization is typically performed by a computer program. However, the randomization can also be generated from [[random number table]]s or by some [[random number generation#Physical methods|physical mechanism]] (e.g., drawing the slips of paper).

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* {{cite book

|author1=Caliński, Tadeusz
|author2=Kageyama, Sanpei

|title=Block designs: A Randomization approach, Volume '''I''': Analysis

|series=Lecture Notes in Statistics

|volume=150

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|year=2000

|isbn=0-387-98578-6

|url-access=registration

|url=https://archive.org/details/blockdesignsrand0002cali

}}

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*{{cite book

|author=[[Oscar Kempthorne|Kempthorne, Oscar]]

|author-link=Oscar Kempthorne

|year=1979

|title=The Design and Analysis of Experiments