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It is well established that the χ² test is influenced by sample size and will lead to over rejection of models tested using large sample sizes. In this paper it is shown that the population parameter values of a model can also influence the χ² and lead to erroneous decisions about model acceptance/rejection. It is concluded, based on the examination of hypothetical population factor analytic models, that incremental fit indices offer a useful source of information for the analyst to assist in the interpretation of the χ² test.