#### Abstract

A discussion on data structure relative to the main effects model is motivated by a severely unbalanced meta-analysis data set. This data set is used to highlight the difficulty of assessing data structure when multiple factor data sets are severely unbalanced. Both theoretical results and numerical examples are used to establish that simple approaches to examining data structure using two-way tables provide easily assimilated information about the effect of data unbalance on main effect contrast variances. In addition, notions of balance, proportionality, unbalance, and missing cells with respect to the main effects model are defined in terms of the two-way tables and are related to main effect contrast estimate variances as assessed using the D-optimality criterion.

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DATA STRUCTURE WITH RESPECT TO THE MAIN EFFECTS MODEL: A DISCUSSION MOTIVATED BY A META-ANALYSIS DATA SET

A discussion on data structure relative to the main effects model is motivated by a severely unbalanced meta-analysis data set. This data set is used to highlight the difficulty of assessing data structure when multiple factor data sets are severely unbalanced. Both theoretical results and numerical examples are used to establish that simple approaches to examining data structure using two-way tables provide easily assimilated information about the effect of data unbalance on main effect contrast variances. In addition, notions of balance, proportionality, unbalance, and missing cells with respect to the main effects model are defined in terms of the two-way tables and are related to main effect contrast estimate variances as assessed using the D-optimality criterion.