6.2 - Completely Randomized Design

 Text Section 15.3

After identifying the experimental unit and the number of replications that will be used, we now have to evaluate how treatment levels or treatment combinations are assigned to experimental units.

In a completely randomized design, treatment levels or combinations are assigned to experimental units at random. This is typically done by listing the treatment levels or treatment combinations and assigning a random number to each. By sorting on the random number, we produce a random order for application of the treatments to experimental units.

In Minitab, this can be done by listing the treatment levels (any order), listing the units, and then obtaining a random sample of size N from the N units (sampling without replacement). This produces the same thing: a randomized order to physically install the treatments.

For the greenhouse experiment we considered first, with a single factor (fertilizer) with 4 levels, we had six replications and a total of 24 experimental units (a potted plant), (Lesson1 Data). We can make a study diagram:

Greenhouse Floor plan and bench to be used for the experiment (as viewed from above).

Wall Open Walkway

We need to be able to randomly assign each of the treatment levels to 6 locations (containing a potted plant). To do this, assign physical position numbers on the bench for placing the pots.

Wall Open Walkway 4 3 2 1 5 6 7 8 9 1 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
 

In Minitab, I list the treatment levels and replications to use (order not important), along with a position number 1 to \(N_{\text{total}}\).

minitab worksheet

Then create a column heading for the assigned treatment levels (I used ‘Fert_trt’ for a heading for column 3).Choose Calc > Random Data > Sample from Columns:

minitab software path

Which brings up this dialog box:

minitab dialog box

Be sure that you do NOT have the Sample With Replacement box checked. This gives us the treatment levels to apply to each position on the greenhouse bench:

minitab worksheet

(etc..)

We then can proceed to apply the treatment levels (physically) to pots on the greenhouse bench using the randomization for the treatments as given to us by Minitab.

Fertilizer 1 (Blue) Fertilizer 2 (Red) Fertilizer 3 (Black) No Fertilizer (White) Wall Open Walkway 4 3 2 1 5 6 7 8 9 1 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24