7.2 - Completely Randomized Design

7.2 - Completely Randomized Design

After identifying the experimental unit and the number of replications that will be used, the next step is to assign the treatments (i.e. factor levels or factor level combinations) to experimental units.

In a completely randomized design, treatments are assigned to experimental units at random. This is typically done by listing the treatments and assigning a random number to each.

In the greenhouse experiment discussed in lesson 1, there was a single factor (fertilizer) with 4 levels (i.e. 4 treatments), six replications, and a total of 24 experimental units (a potted plant). Suppose the image below is the Greenhouse Floor plan and bench that was used for the experiment (as viewed from above).

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We need to be able to randomly assign each of the treatment levels to 6 potted plants. To do this, assign physical position numbers on the bench for placing the pots.

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In Minitab, this assignment can be done by creating two columns - one with each treatment level repeated 6 times (order not important) and the other with a position number 1 to N, where N is the total number of experimental units to be used (i.e. N = 24 in this example).

minitab worksheet

Then the following Minitab command sequence ( screenshot shown below) will result in a  completely random assignment as displayed in the last screenshot.

Choose Calc > Random Data > Sample from Columns:

minitab software path

 

minitab dialog box
Note! Be sure to have the Sample With Replacement box unchecked so that all treatment levels will be assigned to the same number of pots giving rise to a proper completely randomized design for a specified number of replicates.
minitab worksheet

 

This assignment can then be used to apply the treatment levels appropriately to pots on the greenhouse bench.

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