Precision of bioassays for apparent and true metabolizable energy adjusted to zero nitrogen balance

Formulae are presented for calculating the variance of estimates of AMEn and TMEn obtained from several commonly used bioassay protocols. Formulae are also developed for calculating the variance of the difference between bioavailable energy (BE) estimates of two materials tested in the same bioassay. Methods are described for determining the allocation of experimental units among dietary treatments that minimizes the variance of AMEn or TMEn estimates in bioassays based upon a completely randomized allocation of the dietary treatments to the experimental units. In many situations, the precision of the assay can be considerably improved by assigning more experimental units to the control diet than to the test diets. For completely randomized designs, the precision of AMEn estimates from the basal diet substitution assay is always greater than that from the reference material substitution assay. For randomized block designs, the relationship depends upon the level of substitution and the ratio of the among to within-block variance components. However, the precision of the difference between the estimates of AMEn for two materials is the same in the basal diet and reference material substitution assays for both completely randomized and randomized block designs.