Transformation of the response of a linear model is a popular method in practice when attempting to satisfy the assumptions of the model. Environmental research routinely uses log-transformations due to the nature of the observed data. The choice of the transformation is often made based upon previous experience or on the comparison of models with different transformed responses. Often a transformation parameter is estimated when fitting a model to a set of data. However, in practice interpretability becomes an issue, as it is only desired to know if a particular transformation is appropriate. Thus, inference tools for a hypothesized value of the transformation, such as the log-transformation in environmental exposure models, have their merit. An examination of hypothesis tests of the transformation parameter in the general linear mixed model will be beneficial due to its practical applications, particularly for areas of environmental research. The effect of outliers on inference about the transformation parameter is also studied. © 2006 Elsevier B.V. All rights reserved.