Randomization, Blocking and Replication

Why it matters

While an experiment is run through a day, the material, the environment, the warming up of the machine or the state of the measuring instrument may change. If the first condition is always tried in the morning and another condition always at the end of the day, the source of the observed difference becomes unclear. Random order reduces this risk by spreading the conditions over time in an order chosen independently of the results. When each condition will be run must be determined before the trial. Randomness does not mean that no record is kept or that the runs are made haphazardly. On the contrary, the chosen order is kept and the actual run order is recorded separately. If an unexpected interruption occurs, its place stays visible; shuffling the table afterwards does not change the past run.

Blocking manages a known source of variability inside the comparison. If differences between days are expected, each day can be a block. The aim is not to assume that the days are the same; it is to be able to compare the conditions within the same day. For this, the conditions to be compared are represented in every block. If A low is run only on the first day and A high only on the second, the change of A is tied to the day. Collecting more specimens does not break this tie. Having a column called block is not a solution by itself either. The experiment design must really allow a comparison on a common scope. The structure of the plan comes before the calculation done afterwards. Blocking is also not forming classes according to the production result. The days are defined before the results are seen, and the place of each condition within that day is planned in advance. Gathering high responses in one block and low responses in another does not explain the source of variability. Such a separation, which has no link to the actual condition record, cannot be interpreted as if it had changed the structure of the experiment.

Replication is the independent re-running of the same condition. Replicates made with new specimens and a defined run give information on whether the result can be obtained again. Rereading the same specimen is a measurement repeat; it answers another question. If the repeated runs come from very similar sources, independence is assessed separately. Each unit may carry the effect of a common lot. For this reason the specimen identity, the material group and the run record are important. Running the same condition on different days increases the information between days, but by itself does not show the spread within each day. Which variability was observed must be stated clearly in the report.

Random order, blocking and replication are not solutions that replace one another. Random order reduces systematic matching with time; blocking keeps a particular source of difference separate in the comparison; replication provides observations about fluctuation. When the three are planned well together, more meaningful information can be obtained from a small experiment. Still, randomness does not remove all imbalances with certainty, and blocking does not prove that the effect of each day is equal in all conditions. If the condition differences vary by day, this too should be examined. Subtracting a simple day mean and saying that you have corrected every problem is not enough. The actual execution of the experiment is evaluated together with the calculated means.

Formula