The analysis of very small samples of repeated measurements II: a modified Box correction

There is a need for appropriate methods for the analysis of very small samples of continuous repeated measurements. A key feature of such analyses is the role played by the covariance matrix of the repeated observations. When subjects are few it can be difficult to assess the fit of parsimonious structures for this matrix, while the use of an unstructured form may lead to a serious lack of power. The Kenward-Roger adjustment is now widely adopted as a means of providing an appropriate inferences in small samples, but does not perform adequately in very small samples. Adjusted tests based on the empirical sandwich estimator can be constructed that have good nominal properties, but are seriously underpowered. Further, when such data are incomplete, or unbalanced, or non-saturated mean models are used, exact distributional results do not exist that justify analyses with any sample size. In this paper, a modification of Box's correction applied to a linear model-based F-statistic is developed for such small sample settings and is shown to have both the required nominal properties and acceptable power across a range of settings for repeated measurements.