Choosing the Best by Ranking and Selection

Selecting the best treatment(s) is a common problem in agricultural research. The usual procedure is to rank all treatment means and to claim the best treatment(s) are the highest (or lowest) subset found not to differ significantly according to a traditional multiple comparison (TMC). A least significant difference (LSD) procedure is applied most frequently. Our objective is to introduce a somewhat new methodology called simply ranking and selection (R&S) by way of agronomic examples and to illustrate why R&S may be preferred over TMC for selecting the best. Steps similar to those when using TMC to select the best are applied by R&S but it uses tabled values distinctive to several criteria for specifying “bestness.” We concentrate upon both identifying the one best treatment and selecting the subset containing that one best, but unspecified treatment. The R&S method assumes outright that the true unknown treatment means (population means) are unequal . Probabilities are derived from available information about that inequality and pertain specifically to the likeliness of making a correct selection. Conversely, LSD was developed upon the framework of testing the explicit hypothesis of equality for two specific population means and the most evident probability pertains precisely to incorrectly rejecting that equality. Probabilities associated with correctly identifying means, which are not equal, are considered only indirectly by LSD. Two examples from agronomic literature are used to demonstrate R&S methodology. We are recommending that agricultural researchers continue to use TMC for the broad general purpose for which it was designed, but furthermore, we are suggesting they become familiar with R&S and apply it for the specific purpose for which it was designed.