Cautionary note on conveniently dismissing χ

This cautionary note provides a critical analysis of a statistical practice that is used pervasively by researchers in strategic management and related fields in conducting covariance structure analyses: The argument that a “large” sample size renders the χ2 goodness-of-fit test uninformative and a statistically significant result should not be an indication that the model does not fit the data well. Our analysis includes a discussion of the origin of this practice, what the attributed sources really say about it, how much merit this practice really has, and whether we should continue using it or abandon it altogether. We conclude that it is not correct to issue a blanket statement that, when samples are large, using the χ2 test to evaluate the fit of a model is uninformative and should be simply ignored. Instead, our analysis leads to the conclusion that the χ2 test is informative and should be reported regardless of sample size. In many cases, researchers ignore a statistically significant χ2 inappropriately to avoid facing the inconvenient fact that (albeit small) differences between the observed and hypothesized (i.e., implied) covariance matrices exist.